He proved skilled at placing loyalists in critical points in the bureaucracy.
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These calls for dramatic intervention on antitrust grounds overlook three critical points.
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Do they miss critical points about intellectual property, market access, and technology transfer?
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Deep emotional issues often come to the surface, and obsessions reach critical points.
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This "home ignition zone,"as it's called, holds the critical points of vulnerability.
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"They don't allow witness to observe critical points of the process," he said.
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The problem is that the record is incomplete and conflicted on critical points.
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We all reach critical points in our lives where our mental strength is tested.
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Consider that the text of the Constitution is quite clear on two critical points.
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"Critical points, especially with (Logan) Couture out of the lineup," Sharks coach Peter DeBoer said.
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When you are dealing with a governmental agency, many critical points are matters of public concern.
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"Some critical points have been cleared, like for some tunnels and the main stations," Jamaluddin said.
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But Saint Louis went on a 12-27 spurt, with Thatch and Bess supplying the critical points.
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Wintour advised Burch through critical points in her career, including launching her first fashion show and approaching investors.
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"When you are dealing with a governmental agency, many critical points are matters of public concern," he said.
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But one of the most critical points this past week came a long way from either of those locales.
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He does see new maturity in Thiem, more controlled aggression on critical points and more skill on the attack.
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It is essential that policymakers, journalists and the public understand a few critical points about this oft-misunderstood crisis.
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Some of the sightings occurred during the most critical points of flight -- and when most accidents happen -- takeoff and landing.
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"Many critical points are matters of public concern," he said, mentioning issues like tenure, merit pay, promotions and classroom size.
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But Trump's instincts — anti-science, anti-expert, isolationist and xenophobic — risk that he will eschew that advice at critical points.
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He made several key calls to lawmakers during critical points in the negotiations, said some of those who received calls.
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Cameras are set up at critical points of races to record images that can later be examined by U.S.A. Cycling officials.
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It was the only brief moment of frustration for Federer, who, as usual, found a way to win the critical points.
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But with Fognini alternating between brilliant and brutal, and Murray seemingly perplexed by it all, Murray won the most critical points.
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What materials at critical points have in common, Polyakov realized, is their symmetries: the set of geometric transformations that leave these systems unchanged.
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It supports pregnant, postpartum, and nursing women and helps young children have their nutritional needs met at critical points in a their development.
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During this conversation, the show reaches one of its darkest and most self-critical points by bringing up BoJack's relationship with Sarah Lynn.
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It is imperative that passengers comply with crew instructions during all phases of flight, especially at the critical points of takeoff and landing.
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Yet Correa clearly tried to gain a competitive edge for the Cardinals, infiltrating the Astros' system at critical points on the baseball calendar.
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Athill died last week at the age of 101, and her words, at several critical points in this reader's life, provided a lifeline.
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The Times articles miss two critical points: This is not a free-speech issue, and Yale promotes residential college living space as, well, home.
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Within three minutes, the Falcon Heavy's two side boosters separated from the central rocket in one of the most critical points of the flight.
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At three critical points in this postseason, he liked what he saw from a pitcher already in the game and let him finish it.
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However, a few critical points have been obscured by noise over the last few days, and I'm worried that the "bigger picture" is being ignored.
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Russian intelligence officers had funneled tens of thousands of emails they stole from Democratic computers to WikiLeaks, which released them at critical points during the presidential race.
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"We're right in the hunt now for a playoff position and these are some critical points coming up for us," Maple Leafs forward James van Riemsdyk told reporters.
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The sixth-seeded Williams came up big on the critical points to make quick work of Siegemund in a 6-1 6-2 victory in Arthur Ashe Stadium.
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The first-generation Honda Ridgeline had a modest sail pillar, but Honda was able to ditch the feature for the second generation by reinforcing critical points throughout the unibody.
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Biden accused the Trump administration of ignoring early warning signs about the pandemic and of downplaying the disease at critical points when the virus was primarily concentrated in China.
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Ms. Gatliff created a type of infrastructure by gluing small plastic markers of varying sizes to the skull to match the depths of tissue at critical points around the face.
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In a statement to Iranian TV, the group said 15 missiles hit 20 critical points killing 80 soldiers, wounding 200 more and destroying large quantities of military equipment, including helicopters.
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The typically reserved 63-year-old American broke Watson six times and showed rare flashes of emotion after critical points in the two-hour affair, pumping her fist and shouting.
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Dyn's service disruption was yet another demonstration of how attacks on various critical points on the Internet can impact millions of users, and how vulnerable those points may currently be.
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Third-seeded Marin Cilic of Croatia was pushed to three sets but won the critical points to beat 20-year-old Borna Coric of Croatia 6-3, 2-6, 63-3.
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To the Editor: "A Traffic Ticket of $13,000," by Emily Reina Dindial and Ronald J. Lampard (Op-Ed, May 28), makes critical points about the punitive policy of suspending driver's licenses.
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It's one of a few books I've read recently (including 'Code Girls' by Liza Mundy) that highlight the often untold role that women have played at critical points in our history.
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The museum's narrative begins at the dawn of the 21994th century and traces the rise of Palestinian nationalism, its struggles with Zionism and Israel, and Mr. Arafat's role at critical points.
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The former vice president accused the Trump administration of ignoring early warning signs about the pandemic and of downplaying the disease at critical points when the virus was primarily concentrated in China.
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Germany and Britain are America's closest intelligence-sharing partners, and both nations sit atop critical points along fiber-optic cables that are key to intercepting communications from Russia to the Middle East.
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Active management serves an essential function in markets, above all providing price discovery and liquidity, at critical points moving against the grain and all of the trading vehicles programmed to move with it.
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Just as Fudge makes severe misjudgments at various critical points such as the return of Voldemort, Cameron, a Remain campaigner, appears to have downplayed the possibility of a Brexit to save political face.
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Yet systems of belief keep cropping up that challenge established science, from concerned-yet-defiant anti-vaxxers to parents who insist on raising vegan children, even at the most critical points in their development.
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But caught in the middle is an Afghan population that is on edge about what that last part might look like, after a deal that excluded their government and left many critical points ambiguous.
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He misses two critical points: why would anyone else join such a system, to be taken advantage of, rather than focus on trading and other economic relations with partners that behave and treat others decently?
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At a two-day hearing, he denied remembering Hammack's note at critical points in the trial that might have jogged his memory, including Hammack's testimony and Jones's use of that testimony in his closing argument.
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Oklahoma City Thunder 111 - Phoenix Suns 107 Chris Paul had 20 points and 10 assists, and he scored six critical points in the final 1:03 to lift Oklahoma City to a victory at Phoenix.
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The moon's nodes—north and south—symbolize where we are heading in life and what we are leaving behind, while the eclipses are new and full moons that find us at critical points on our journey.
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Perhaps the most tantalizing tidbit from the 2,800 pages of declassified documents comes from the files of this man, James Jesus Angleton, the devious CIA counter intelligence chief who misled the Warren commission at critical points.
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Oscar da Silva's 27 points and 15 rebounds, and 10 critical points from Tyrell Terry in the second half led Stanford to a 70-113 upset of No. 11 Oregon on Saturday afternoon in Palo Alto, Calif.
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In a statement to state television the elite Revolutionary Guard said 303 missiles hit 20 critical points killing 80 soldiers, wounding 200 and destroying large quantities of military equipment, including helicopters, according to the Mehr news agency.
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Mr. Rosenstein's meetings show his mind-set at one of the most critical points in Mr. Trump's administration — the eight days between when Mr. Comey was fired and Mr. Rosenstein appointed Robert S. Mueller III as special counsel.
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Chris Paul had 23 points and 10 assists, and he scored six critical points in the final 1:03 to lift the Oklahoma City Thunder to a 111-107 road win over the Phoenix Suns on Friday night.
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Speaking from a makeshift studio at his home in Delaware, Biden accused the Trump administration of ignoring early warning signs about the pandemic and of downplaying the disease at critical points when the virus was primarily concentrated in China.
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Mr. Uribe has announced that he and his partisans are taking to the streets to seek a new referendum against critical points of the agreement, and that he will seek the presidency in 2018 under the banner of indignation.
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Were it not for people who were willing to step up at critical points and vouch for my abilities and potential as a student, scientist and teacher, my expertise and experience would not be applied as they are today.
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Though this memoir offers more than a portrait of Cunningham, reminiscence of Cunningham intuits a lot of the critical points argued about his work that may make the reader lean in to know more about the past New York art scene.
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Speaking ahead of talks with Pakistan Prime Minister Imran Khan on the sidelines of the World Economic Forum, Trump said trade and borders were both critical points for discussion, while Khan said that for him Afghanistan was the top priority.
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Newsom has said his office is hard at work trying to move them indoors, either with beds in hotels or motels, or through 450 state-owned trailers California plans to deploy to "critical points," according to the Los Angeles Times.
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She briefly worked as a Montessori school teacher only to realize it wasn't her calling, and her relationships with friends and lovers influenced some of the most critical points of the Chez Panisse identity: design, politics, film, and fresh food.
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The special counsel, Robert S. Mueller III, had also mounted a parallel criminal inquiry into Russia's theft of tens of thousands of emails from the Democratic computers and transfer of them to WikiLeaks, which released them at critical points during the campaign.
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The team boiled it down to seven critical points: In addition to these core concepts there are many secondary ones that pop up for consideration: Wobble, or the amount a key moves laterally (yes, this is deliberate), snap ratio, involving the feedback from actuation.
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As condensed matter physicists were just discovering, when materials that are completely different at the microscopic level are tuned to the critical points at which they undergo phase transitions, they suddenly exhibit the same behaviors and can be described by the exact same handful of numbers.
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He also reiterated in that case the critical points that the government may not second-guess the reasonableness of a person's faith and that a substantial burden on religious exercise occurs whenever there is government action contrary to a firmly held religious belief (or a financial penalty).
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In 2012, researchers used Rattazzi and Rychkov's trick to home in on the values of the critical exponents of the 3-D Ising model, a notoriously complex CFT that is in the same universality class as real magnets, water, liquid mixtures and many other materials at their critical points.
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"What we're talking about here is not to rebuild or re-engineer the entire grid but to really ask the question of, are there some back-to-the-future answers at critical points that might protect us from the kind of attack we know is coming," King explained.
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PANAMA CITY — In an emphatic destruction of Honduras on Friday, the United States men's soccer team seemed to glide effortlessly across the field in almost dreamlike fashion, producing six goals and 3 critical points that moved them closer to their goal of qualifying for the 13 World Cup.
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Museums are increasingly thinking about ways to curate and conserve time-based media works, as important examples from the late 20th century — by artists such as Bruce Nauman, Jenny Holzer, Jason Rhodes, and Vito Acconci — have already or are just about to approach critical points in their lifespan and legacy.
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As Congress grapples with allegations that Mr. Trump tried to pressure Ukraine to help his 2020 re-election effort, the Stone case has revived the story of how Russian operatives stole tens of thousands of Democratic emails and funneled them to WikiLeaks, which released them at critical points in the 2016 campaign.
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The revelation could shed light on Mr. Trump's thinking at two critical points under scrutiny by impeachment investigators: his decision in early September to release $391 million in security assistance to Ukraine and his denial to a key ambassador around the same time that there was a "quid pro quo" with Kyiv.
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Though she was pleased with the formula of the products and the shade range for catering to women of color, Aina also had a few more critical points to make — namely, that the price of $48 per stick seemed a little steep, and that the contour/highlight kit came a few years too late.
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Countless iconic moments, explosions of production at the most critical points of famous games, cannot seriously be set aside in favor of this video of Tony Allen, after having been abandoned by nearly every decent player on his team, stepping up for no rational reason man can divine to beat the East-leading but still fairly tragic Cleveland Cavaliers pretty much by himself.
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Williams and the other Americans who proved unwilling to put their weekend plans on hold were simply the faces of a flawed government strategy to combat coronavirus—one that was created in line with the American ethos of personal responsibility, a belief system that has dominated political discourse on both sides of the aisle over the last three decades, and is now failing us in one of the most critical points of our history.
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At times Facebook's response to political attacks certainly looks like an attempt to drown out critical points by deploying self-serving but selective data points — so, for instance, it talks at length in the letter about the work it's doing in Myanmar, where its platform has been accused by the UN of accelerating ethnic violence as a result of systematic content moderation failures, but declines to state how many fake accounts it's identified and removed in the market; nor will it disclose how much revenue it generates from the market.
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In practice, there are many instances in which access to the internet is contingent on de facto gatekeepers: in one example, the ongoing battle over net neutrality highlights the power that internet service providers have over the free flow of data; as another, the massive cyberattack against DNS provider Dyn last year, which left internet users in much of Europe and North America unable to access Twitter, Netflix, Reddit, and many other sites, shows that the centralized nature of the domain name resolution system introduces critical points of failure into what we think of as a globally distributed network.
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Bond critical points (BCP) evidence the chalcogen bond between S and Cl−.
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He introduced the method of the critical points at infinity, which is a fundamental step in the calculus of variations.
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Molecular graphs of GeH and Ge2H in the lowest lying electronic state. Bond critical points shownin orange with corresponding ellipticity values, ring critical points shown in yellow, and attractors shown in purple with AIM charges plus NBO charges shown in parentheses. In an atoms- in-molecules (AIM) analysis of GeH, 3 critical points (2 attractors and a bond critical point) were found. Computed NBO and AIM charges both showed a positive charge on germanium and a negative charge on the hydrogen, indicating a significant charge transfer to hydrogen and generating a Ge+H− polarization.
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For the (instanton) version for three- manifolds, it is the space of SU(2)-connections on a three-dimensional manifold with the Chern–Simons functional. Loosely speaking, Floer homology is the Morse homology of the function on the infinite-dimensional manifold. A Floer chain complex is formed from the abelian group spanned by the critical points of the function (or possibly certain collections of critical points). The differential of the chain complex is defined by counting the function's gradient flow lines connecting certain pairs of critical points (or collections thereof).
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The Hessian matrix plays an important role in Morse theory and catastrophe theory, because its kernel and eigenvalues allow classification of the critical points.
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Throughout the period he provided key leadership and guidance to the United States Antarctic Program at a number of critical points in its evolution.
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This forces the first player to capture, leaving the dead two shape. The critical points are circled in the "Unsettled groups with three empty points" diagram.
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This optimizes the validated protocol for routine use, including analysis of the critical points by scanning the entire procedure to identify and control the potential risks.
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Earlier critical points were revived Aram Toptchyan. "Moïse de Khorène" in Claude Mutafian (ed.), Arménie, la magie de l'écrit. Somogy, 2007, p. 143. . in the second half of the twentieth century.
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In differential topology, a mathematical discipline, and more specifically in Morse theory, a gradient-like vector field is a generalization of gradient vector field. The primary motivation is as a technical tool in the construction of Morse functions, to show that one can construct a function whose critical points are at distinct levels. One first constructs a Morse function, then uses gradient-like vector fields to move around the critical points, yielding a different Morse function.
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Twenty fractals were discovered in solvent associated surface areas of > 5000 protein segments . The existence of these fractals proves that proteins function near critical points of second-order phase transitions, realizing Schrodinger's conjecture.
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Fluctuations about stable stationary states are extremely small except near critical points (Kondepudi and Prigogine 1998, page 323).Kondepudi, D., Prigogine, I, (1998). Modern Thermodynamics. From Heat Engines to Dissipative Structures, Wiley, Chichester, 1998, .
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Another piece in the puzzle is work on computational complexity, specifically that critical points have been shown to exist in NP-complete problems, where near-optimum solutions are widely dispersed and separated by barriers in the search space causing local search algorithms to get stuck or severely hampered. It was the evolutionary self-organised criticality model by Bak and Sneppen and the observation of critical points in combinatorial optimisation problems that lead to the development of Extremal Optimization by Stefan Boettcher and Allon Percus.
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Multibrot sets are bounded sets found in the complex plane for members of the general monic univariate polynomial family of recursions : z \mapsto z^d + c.\ For an integer d, these sets are connectedness loci for the Julia sets built from the same formula. The full cubic connectedness locus has also been studied; here one considers the two-parameter recursion z \mapsto z^3 + 3kz + c , whose two critical points are the complex square roots of the parameter k. A parameter is in the cubic connectedness locus if both critical points are stable.
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In mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced by Émile Picard for complex surfaces in his book , and extended to higher dimensions by . It is a complex analog of Morse theory that studies the topology of a real manifold by looking at the critical points of a real function. extended Picard–Lefschetz theory to varieties over more general fields, and Deligne used this generalization in his proof of the Weil conjectures.
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The atmosphere of Venus is 96.5% carbon dioxide and 3.5% nitrogen. The surface pressure is 9.3 MPa (93 bar) and the surface temperature is 735 K, above the critical points of both major constituents and making the surface atmosphere a supercritical fluid. The interior atmospheres of the solar system's gas giant planets are composed mainly of hydrogen and helium at temperatures well above their critical points. The gaseous outer atmospheres of Jupiter and Saturn transition smoothly into the dense liquid interior, while the nature of the transition zones of Neptune and Uranus is unknown.
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The notion of a Morse function can be generalized to consider functions that have nondegenerate manifolds of critical points. A Morse–Bott function is a smooth function on a manifold whose critical set is a closed submanifold and whose Hessian is non-degenerate in the normal direction. (Equivalently, the kernel of the Hessian at a critical point equals the tangent space to the critical submanifold.) A Morse function is the special case where the critical manifolds are zero-dimensional (so the Hessian at critical points is non- degenerate in every direction, i.e., has no kernel).
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The KPA's communications and supply were not capable of exploiting a breakthrough and of supporting a continuing attack in the face of massive air, armor, and artillery fire that could be concentrated against its troops at critical points.
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See . The other (even complex valued) critical points of the iterative function during one entire round are those that pass through the value 0.5 in the first round. A convergent cycle must attract at least one critical point.See .
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During the rescue operations, a 12-year-old girl died. The damage was around DM 24 million (converted c. 12 million euros). After the disaster, the entire canal line was checked for weaknesses and retrofitted at critical points.
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Morse originally applied his theory to geodesics (critical points of the energy functional on paths). These techniques were used in Raoul Bott's proof of his periodicity theorem. The analogue of Morse theory for complex manifolds is Picard–Lefschetz theory.
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As another corollary from the Second Fundamental Theorem, one can obtain that : T(r,f')\leq 2 T(r,f)+S(r,f),\, which generalizes the fact that a rational function of degree d has 2d − 2 < 2d critical points.
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Catastrophe theory analyzes degenerate critical points of the potential function — points where not just the first derivative, but one or more higher derivatives of the potential function are also zero. These are called the germs of the catastrophe geometries. The degeneracy of these critical points can be unfolded by expanding the potential function as a Taylor series in small perturbations of the parameters. When the degenerate points are not merely accidental, but are structurally stable, the degenerate points exist as organising centres for particular geometric structures of lower degeneracy, with critical features in the parameter space around them.
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William Shaw (1749–1831) was a Scottish Gaelic scholar, writer, minister and Church of England cleric. He is known also as friend and biographer of Samuel Johnson. His 1781 paper on the Ossian controversy is still considered a good survey of critical points.
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These men were stationed at critical points for use in fire-fighting missions.Mikesh, p. 29 The 555th suffered one fatality and 22 injuries fighting fires. Through Firefly, the military used the United States Forest Service as a proxy agency to combat FuGo.
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RERP upgrades were completed on 25 July 2018. The Air Force received the last modified aircraft on 1 August 2018. , Lockheed is investigating drag reduction by plasma-heating of turbulent transonic airflow in critical points, saving overall weight by reducing fuel consumption.
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The study of liquid–liquid critical points is an active research area with hundreds of articles having been published, though only a few of these investigations have been experimental since most modern probing techniques are not fast and/or sensitive enough to study them.
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By Fermat's theorem, all local maxima and minima of a differentiable function occur at critical points. Therefore, to find the local maxima and minima, it suffices, theoretically, to compute the zeros of the gradient and the eigenvalues of the Hessian matrix at these zeros.
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This is where the game lacks realism, and it is also one of the many critical points of the developers. Hostile animals share the same properties. For example, all bears, except the polar bear, look, sound, and usually weigh the same amount. The only difference is their colour.
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Note that the foregoing proof of analyticity derived an expression for a system of n different function elements fi(x), provided that x is not a critical point of p(x, y). A critical point is a point where the number of distinct zeros is smaller than the degree of p, and this occurs only where the highest degree term of p vanishes, and where the discriminant vanishes. Hence there are only finitely many such points c1, ..., cm. A close analysis of the properties of the function elements fi near the critical points can be used to show that the monodromy cover is ramified over the critical points (and possibly the point at infinity).
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In general it is not easy to compute this invariant, which was initially introduced by Lazar Lyusternik and Lev Schnirelmann in connection with variational problems. It has a close connection with algebraic topology, in particular cup-length. In the modern normalization, the cup-length is a lower bound for the LS-category. It was, as originally defined for the case of X a manifold, the lower bound for the number of critical points that a real-valued function on X could possess (this should be compared with the result in Morse theory that shows that the sum of the Betti numbers is a lower bound for the number of critical points of a Morse function).
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The stereographic projection from the sphere to the plane preserves critical points of geodesic curvature. Thus simple closed spherical curves have four vertices. Furthermore, on the sphere vertices of a curve correspond to points where its torsion vanishes. So for space curves a vertex is defined as a point of vanishing torsion.
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Exekias was an ancient Greek vase-painter and potter. A good portion of his vase work included scenes from Greek mythology. He was known for his ability to capture the most critical points of a story and illustrate them into one simple scene. The amphora portraying Achilles killing Penthesilea is such an example.
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Kesselring now had to convince the Army that air support should be concentrated at critical points. He strove to improve army–air cooperation with new tactics and the appointment of Oberst Martin Fiebig as a special close air support commander.Plocher, The German Air Force versus Russia, 1941, pp. 89, 93, 97–98.
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On 31 January 1965, Colonel Bounleut Saycocie also decided on a coup. While unaware of Phoumi's efforts, Bounleut led three companies from the Groupement Mobile 17 (Mobile Group 17) regiment as they occupied Vientiane's radio station and other critical points. The coup was largely bloodless. Five announcements were aired on the radio station.
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For unconstrained problems with twice- differentiable functions, some critical points can be found by finding the points where the gradient of the objective function is zero (that is, the stationary points). More generally, a zero subgradient certifies that a local minimum has been found for minimization problems with convex functions and other locally Lipschitz functions. Further, critical points can be classified using the definiteness of the Hessian matrix: If the Hessian is positive definite at a critical point, then the point is a local minimum; if the Hessian matrix is negative definite, then the point is a local maximum; finally, if indefinite, then the point is some kind of saddle point. Constrained problems can often be transformed into unconstrained problems with the help of Lagrange multipliers.
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After a week behind bars, the case against Muste for allegedly disturbing the peace was dismissed. More than 100 strikers were jailed but the strike continued.Hentoff, Peace Agitator, pg. 50. While the police anticipated more violence and even placed machine guns at critical points along Lawrence's principal streets, Muste and the strike committee chose nonviolence.
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By definition, a symmetric obstruction theory is a perfect obstruction theory together with nondegenerate symmetric bilinear form. Example: Let f be a regular function on a smooth variety (or stack). Then the set of critical points of f carries a symmetric obstruction theory in a canonical way. Example: Let M be a complex symplectic manifold.
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The audit is taken in steps. An initial assessment involves the collecting of information about the building and its ventilation and air conditioning (HVAC); its critical points; and its possible sources of contamination. This is done through visual inspection. Then, there is the standardised measurement and analysis of factors such as certain chemicals and microbes.
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Porteous has suggestions for readers wanting to know more about singularity theory. The underlying theme is the study of critical points of appropriate distance-squared functions. A second edition was published in 2001, where the author was able to report on related work by Vladimir Arnold on spherical curves. In fact, Porteous had translated Arnold's paper from the Russian.
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The Picard–Lefschetz formula describes the monodromy at a critical point. Suppose that f is a holomorphic map from an (k+1)-dimensional projective complex manifold to the projective line P1. Also suppose that all critical points are non-degenerate and lie in different fibers, and have images x1,...,xn in P1. Pick any other point x in P1.
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At this stage it becomes important for one to look back on one's life with satisfaction before they die. In 1963, Dr. Robert Butler published a paper on the critical points surrounding the importance of life review and reminiscence. Butler is credited with starting the movement of reminiscence therapy.Woods, B., Spector, A.E., Jones, C.A., Orell, M., Davies, S.P.2009.
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Morse homology can be carried out in the Morse–Bott setting, i.e. when instead of isolated nondegenerate critical points, a function has critical manifolds whose tangent space at a point coincides with the kernel of the Hessian at the point. This situation will always occur, if the function considered is invariant w.r.t a non-discrete Lie group.
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Self organisation is one of the defining properties of complex systems. The basic idea is that open systems will reorganise at critical points of instability. Holling’s adaptive renewal cycle is an illustration of reorganisation that takes place within the cycles of growth and renewal.Gunderson, L. H., and Holling C. S. (2002) Panarchy: understanding transformations in human and natural systems.
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The existence of these fractals proves that proteins function near critical points of second-order phase transitions. In groups of organisms in stress (when approaching critical transitions), correlations tend to increase, while at the same time, fluctuations also increase. This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants.
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In thermodynamics, a critical line is the higher-dimensional equivalent of a critical point.B. Widom, Theory of Phase Equilibrium, J. Phys. Chem 1996, 13190-13199 It is the locus of contiguous critical points in a phase diagram. These lines cannot occur for a single substance due to the phase rule, but they can be observed in systems with more variables, such as mixtures.
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In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function. The usefulness of derivatives to find extrema is proved mathematically by Fermat's theorem of stationary points.
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In mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient computational tool for reducing a function to canonical form near critical points. It was introduced by Vladimir Arnold in 1975.Vladimir Arnold "Spectral sequence for reduction of functions to normal form", Funct. Anal. Appl. 9 (1975) no.
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Zhukov, tome 2, p. 37. Even with these new reserves, Soviet forces committed to the operation numbered only 1,100,000 men, only slightly outnumbering the Wehrmacht. Nevertheless, with careful troop deployment, a ratio of two-to-one was reached at some critical points. On 5 December 1941, the counteroffensive for "removing the immediate threat to Moscow" started on the Kalinin Front.
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Portable intercoms are commonly used by special event production crews and professional sports teams. Performing arts venues such as theaters and concert halls often have a combination of permanently mounted and portable intercom elements. Motorsports race tracks often have both portable and permanent intercom stations mounted at critical points around the racecourse for use by race officials and emergency medical technicians.
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They freed logs that had jammed at critical points such as sluices, bends, bridges and ox-bows. Later a smaller workforce was employed. Under good conditions it took 10 days for log rafts to reach Celle, otherwise it might take up to 3 weeks. There were 10 assembly points on the Ise where the logs were tied together into rafts.
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This is a three-manifold invariant connected to Donaldson theory introduced by Floer himself. It is obtained using the Chern–Simons functional on the space of connections on a principal SU(2)-bundle over the three-manifold. Its critical points are flat connections and its flow lines are instantons, i.e. anti-self- dual connections on the three-manifold crossed with the real line.
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He was always at the critical points and took away battlegroups or even single battalions from less threatened sectors. With these units holes were plugged at other locations or short counterattacks were executed and so opportunities were created for bigger solutions. Thus, a closed front was guaranteed while the mixing and tearing apart of units was viewed as the smaller evil.
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The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point.
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As is well known, one of Keynes's critical points to classical economics is the determined to clear the labor market. On the contrary in Keynes, the real wage rate is determined in commodity markets. Many Marxian economists consider real wage rate is affected by labor market. However labor market can affect the nominal wage rate for the present and the commodity market can affect nominal prices.
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She traveled to Russia, and wrote a monograph on chi-squared tests with Mikhail Nikulin. In 1990 she and Igor Evstigneev wrote a second monograph, on random fields. Her research in this period also concerned metric entropy and asymptotic efficiency. She began her work in biostatistics, involving studies of different mammalian populations, and led a major study on statistical estimation near critical points of a parameter.
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The Lesbian Group of CWLU took on this newspaper's title and was also known as Blazing Star. Secret Storm was another newspaper published by a CWLU group of the same name. Formerly known as Outreach, Secret Storm reflected their ideas and thoughts via their newspaper. They raised controversial yet critical points and discussed current, significant issues with women that they met through neighborhood projects.
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Trials started in 2013 with the VTS also supervising the access to Bergen from the south. In particular Vatlestraumen and Hjelteskjæret were critical points where multiple sea lanes meet. Due to surplus working capacity amongst the two people on duty, this could be carried out without additional cost. The boathouse underwent a major upgrade in 2014, receiving a dormitory section and a new workshop.
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Wearing stocking masks and armed with a .303 rifle, the two men cut through the fencing and held the watchman, John Morritt, up at gunpoint. Haabjoern set the charges at three critical points of the machinery and informed the watchman of their plans whilst also checking whether any personnel would be passing through the site. They then left the facility in Morritt's car, taking him with them.
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It is the gradient flow of the Calabi functional; extremal Kähler metrics are the critical points of the Calabi functional. A convergence theorem for the Calabi flow was found by Piotr Chruściel in the case that has complex dimension equal to one. Xiuxiong Chen and others have made a number of further studies of the flow, although as of 2020 the flow is still not well understood.
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In mathematics, circle-valued Morse theory studies the topology of a smooth manifold by analyzing the critical points of smooth maps from the manifold to the circle, in the framework of Morse homology.. It is an important special case of Sergei Novikov's Morse theory of closed one-forms.. Michael Hutchings and Yi-Jen Lee have connected it to Reidemeister torsion and Seiberg–Witten theory..
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The student ends up with full and accurate notes for use as a study guide. Research suggests that guided notes improve student recording of critical points in lecture, as well as quiz scores on related content. In addition, an investigation carried out on students with learning problems showed that the use of the guided notes is an effective strategy to improve the performance of these students.
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Global Handwashing Day (GHD) is an international handwashing promotion campaign to motivate and mobilize people around the world to improve their handwashing habits. Washing hands at critical points during the day and washing with soap are both important. Global Handwashing Day occurs on 15 October of each year. The global campaign is dedicated to raising awareness of handwashing with soap as a key factor in disease prevention.
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The following theorem answers that question. :Theorem. Suppose f is a smooth real-valued function on M and p is a non-degenerate critical point of f of index γ, and that f(p) = q. Suppose f−1[q − ε, q + ε] is compact and contains no critical points besides p. Then Mq+ε is homotopy equivalent to Mq−ε with a γ-cell attached.
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Due to the Gauss equation, the δ-invariants of a Riemannian submanifold can be controlled by the length of the mean curvature vector and the size of the sectional curvature of the ambient manifold. Submanifolds of space forms which satisfy the equality case of this inequality are known as ideal immersions; such submanifolds are critical points of a certain restriction of the Willmore energy.
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Though based at Sasebo, Japan, Nye County spent much time between April 1966 and March 1967, offloading supplies at critical points along the central coast of South Vietnam. Ordered to Pusan, Korea, she decommissioned 27 March 1967, and was turned over to the Military Sea Transportation Service. Manned largely by a Korean crew, she continued to sail in Far Eastern waters in 1970, as USNS Nye County (T-LST-1067).
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These were used to attack en masse at critical points, ideally in cooperation with tanks but rarely with foot infantry.Dunn, p. 233. In defense, cavalry was useful in checking enemy advances at an early stage, attacking German flanks and quickly evading enemy reaction. Cavalry actions of 1941 were poorly led and executed, with high casualties; the tactics improved when cavalry divisions were reinforced with mechanized infantry units and anti-aircraft artillery.
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Uniformity - The zinc coating surrounding the wire is tightly bonded to the steel and uniformly distributed; weak spots on the wire will not be found. Ductility - Bethanizing steel with 99.9 percent zinc, bonds them together tightly without any room for layers of zinc iron alloy. Zinc iron alloy is a brittle substance that induces cracking, leaving steel at critical points exposed. The zinc coating is more ductile and less brittle.
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A smooth real-valued function on a manifold M is a Morse function if it has no degenerate critical points. A basic result of Morse theory says that almost all functions are Morse functions. Technically, the Morse functions form an open, dense subset of all smooth functions M → R in the C2 topology. This is sometimes expressed as "a typical function is Morse" or "a generic function is Morse".
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Morse theory can be used to prove some strong results on the homology of manifolds. The number of critical points of index γ of f : M → R is equal to the number of γ cells in the CW structure on M obtained from "climbing" f. Using the fact that the alternating sum of the ranks of the homology groups of a topological space is equal to the alternating sum of the ranks of the chain groups from which the homology is computed, then by using the cellular chain groups (see cellular homology) it is clear that the Euler characteristic \chi(M) is equal to the sum :\sum(-1)^\gamma C^\gamma\,=\chi(M) where Cγ is the number of critical points of index γ. Also by cellular homology, the rank of the nth homology group of a CW complex M is less than or equal to the number of n-cells in M. Therefore, the rank of the γth homology group,i.e.
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He had great disguise on both his first and second serves, and his second serve was nearly as powerful as his first. He was known for producing aces on critical points, even with his second serves. Sampras was able to hit winners from both his forehand and backhand from all over the court. He was able to catch attacks wide to his forehand using his speed and hitting a forehand shot on the run.
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Turkey against Austria on 29 March 2016. Turkey were drawn in Group D in qualification for the 2014 World Cup, together with Andorra, Estonia, Hungary, the Netherlands and Romania, finishing fourth. Turkey began to lose critical points during qualification and Abdullah Avcı was sacked soon after. Fatih Terim was put in charge for the third time to lead the national team, but a 2–0 defeat against the Netherlands ended hopes of qualification.
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Henderson's total of 201 wins was a Baylor men's basketball record until current coach Scott Drew passed him in 2014. His 233 losses remains a school record. Henderson has been noted for barring his players from smoking, drinking, and swearing, and for what author Allan Zullo called his "nervous habit of tying and untying his shoes at critical points in a game so he wouldn't have to watch a play unfold."Zullo, pp. 103–104.
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The stern was strengthened at critical points, new bulwark fairings were added, and an H-bitt was installed through which cabling is threaded to keep it centered during towing operations. Also installed was a hydraulic towing winch, referred to as a double-drum waterfall winch, holding or more of wire rope on each drum. One drum supports booster retrievals while the other is devoted to external tank towing. Liberty Star carrying the DeepWorker 2000 submersible.
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All available men from Headquarters Company and special units were formed into squads and put into the fight at the most critical points. At one time, the regimental reserve was down to six men. When the attack finally ceased shortly after 12:00 the 23rd Regiment had an estimated combat efficiency of only 38 percent. This heavy night and day battle cost the KPA 2nd Division most of its remaining offensive strength.
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The main lift struts had a wide chord airfoil section and themselves contributed to lift. The main undercarriage legs were fitted to these struts at the crank- point, each axle supported by a pair of V-struts to the lower fuselage. There was a castoring tailwheel under the tailplane. The fuselage was mostly constructed from square-section duralumin tube with some steel at critical points and alloy formers and stringers to shape it.
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He is known for using practical demonstrations in his lectures to illustrate critical points; for example illuminating the nature of quantum operators through their likeness to sausage machines. He believes that the fruits of scientific research should be made accessible to all, and he regularly gives media interviews and public demonstration lectures at schools and science fairs at home and abroad. In 1997 he won the Imperial College Excellence in Teaching Award.
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At about the same time as Hironaka's work, the catastrophe theory of René Thom was receiving a great deal of attention. This is another branch of singularity theory, based on earlier work of Hassler Whitney on critical points. Roughly speaking, a critical point of a smooth function is where the level set develops a singular point in the geometric sense. This theory deals with differentiable functions in general, rather than just polynomials.
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To compensate, only the stable phenomena are considered. One can argue that in nature, anything destroyed by tiny changes is not going to be observed; the visible is the stable. Whitney had shown that in low numbers of variables the stable structure of critical points is very restricted, in local terms. Thom built on this, and his own earlier work, to create a catastrophe theory supposed to account for discontinuous change in nature.
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These frequently mentioned critical points correspond with the artist's feeling for the present, which Novalis shares with many other contemporaries of his time. Thus a triadic structure can be found in most of his works. This means that there are three corresponding structural elements which are written differently concerning the content and the form. Hardenberg's intensive study of the works of Jakob Böhme, from 1800, had a clear influence on his own writing.
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Glider troops and a French civilian. The man on the left, Private Musty, is armed with a German MP 40\. The Germans knew the invasion was imminent if not the exact location; Major Schmidt, in command of the bridges, had been told that they were one of the most critical points in Normandy. The defenders however were not on full alert and only two sentries were on duty when the gliders landed.
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Quantum critical points arise when a susceptibility diverges at zero temperature. There are a number of materials (such as CeNi2Ge2) where this occurs serendipitously. More frequently a material has to be tuned to a quantum critical point. Most commonly this is done by taking a system with a second-order phase transition which occurs at nonzero temperature and tuning it—for example by applying pressure or magnetic field or changing its chemical composition.
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A Van Hove singularity is a singularity (non-smooth point) in the density of states (DOS) of a crystalline solid. The wavevectors at which Van Hove singularities occur are often referred to as critical points of the Brillouin zone. For three-dimensional crystals, they take the form of kinks (where the density of states is not differentiable). The most common application of the Van Hove singularity concept comes in the analysis of optical absorption spectra.
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In mathematics, specifically differential geometry, a geometric flow is the gradient flow associated to a functional on a manifold which has a geometric interpretation, usually associated with some extrinsic or intrinsic curvature. They can be interpreted as flows on a moduli space (for intrinsic flows) or a parameter space (for extrinsic flows). These are of fundamental interest in the calculus of variations, and include several famous problems and theories. Particularly interesting are their critical points.
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In telecommunication, diurnal phase shift is the phase shift of electromagnetic signals associated with daily changes in the ionosphere. The major changes usually occur during the period of time when sunrise or sunset is present at critical points along the path. Significant phase shifts may occur on paths wherein a reflection area of the path is subject to a large tidal range. In cable systems, significant phase shifts can be occasioned by diurnal temperature variance.
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Giant planets are also sometimes called jovian planets, after Jupiter ("Jove" being another name for the Roman god "Jupiter"). They are also sometimes known as gas giants. However, many astronomers now apply the latter term only to Jupiter and Saturn, classifying Uranus and Neptune, which have different compositions, as ice giants. Both names are potentially misleading: all of the giant planets consist primarily of fluids above their critical points, where distinct gas and liquid phases do not exist.
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An anomalous property of the air transport networks is that nodes with relatively low degrees may have very high betweenness centrality. It is an important observation related to the robustness of complex networks. According to this finding the critical points of the system are not necessarily the hubs, but some other cities which uniquely provides routes to certain regions. For example, Alaska can be easily isolated from the other parts of the worldwide air transport network.
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Schematic picture of a 2-bridge knot. In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given by the z-coordinate has only two maxima and two minima as critical points. Equivalently, these are the knots with bridge number 2, the smallest possible bridge number for a nontrivial knot. Other names for 2-bridge knots are rational knots', 4-plats, and ''''' ().
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In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking. Critical phenomena take place in second order phase transitions, although not exclusively.
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In the left half of Figure 6 (x < 0), the black, red, and green fixed points are semistable, unstable, and stable, respectively. This is mirrored by the magenta, black, and blue points on the right half (x > 0). Each of these halves thus behaves like a saddle-node bifurcation; in other words, the imperfect transcritical bifurcation can be approximated by two saddle-node bifurcations when close to the critical points, as evident in the red curves of Figure 4.
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The player character starts her journey stranded on a frozen island, with only the clothes on her back. She must scavenge for resources (weapons, food, etc.) to survive the frozen landscape, dynamically generated weather and other hostilities. After some exploration, players must track down behemoths known as "Gods", finding ways to scale their massive bodies and strike the chimes located at critical points. Each one is unique and must be studied to understand how to defeat it.
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By contrast, Union gunners created massed batteries at critical points along the line. These were able both to support siege operations with concentrated fires and keep the Confederate guns silent by smothering the embrasures of the small Confederate battery positions. As the siege progressed, Confederate artillery fire dwindled to ineffective levels, whereas the Union artillery blasted away at will. As much as any other factor, Union fire superiority sealed the fate of the Confederate army besieged in Vicksburg.
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In 2009 and 2010, the catering establishments have been upgraded with a new infrastructure, and the terrace on the Flamingo pond. As of 2009, the zoo had 303 specimens of 51 species. The zoo got much more green and colorful by a greening concept that was implemented at 16 critical points and continued by 2010 in a second stage, and the entrance area was renewed. Dining facilities were further extended, and the wheelchair area in the Otarium.
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Only drastic administrative intervention saved the county from utter destruction. The counts and large monasteries took the lead in these efforts, building the first heavy emergency dikes to bolster critical points. Later special autonomous administrative bodies were formed, the waterschappen ("water control boards"), which had the legal power to enforce their regulations and decisions on water management. They eventually constructed an extensive dike system that covered the coastline and the polders, thus protecting the land from further incursions by the sea.
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In our analogy, the above theorem says that the two hikers will depart in directions perpendicular to each other. A consequence of this theorem (and its proof) is that if is differentiable, a level set is a hypersurface and a manifold outside the critical points of . At a critical point, a level set may be reduced to a point (for example at a local extremum of ) or may have a singularity such as a self-intersection point or a cusp.
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Communications infrastructure The Port of Rotterdam and the coastal towns of Beverwijk and Katwijk are seen as part of many critical points in a logistic chain. In Beverwijk, the Atlantic Crossing cable number 1 (AC-1), a cable that transports speech and data traffic between the U.S., the U.K., the Netherlands and Germany, meets shore, while in Katwijk the TransAtlantic Telephone cable number 14 (TAT-14), meets shore. The latter is mostly vital for data and internet traffic.Staff writer (undated).
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The plan for Paddington Reservoir began with the creation of the Botany Swamps water scheme in 1859. This water scheme, developed by Edward Bell and Will Wadsworth proposed a number of reservoirs at critical points around the city. Construction of the Paddington Reservoir was completed by 1866 and connected to the Botany Swamps pumping station. This offered a new source of water to elevated suburbs of Sydney which had up until then had only been serviced by wells and a water- cart service.
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The Ising model is mathematically based and can analyse the critical points of phase transitions in ferromagnetic order due to spins of electrons having magnitudes of ±. The spins interact with their neighbouring dipole electrons in the structure and here the Ising model can predict their behaviour with each other. This model is important for solving and understanding the concepts of phase transitions and hence solving the Curie temperature. As a result, many different dependencies that affect the Curie temperature can be analysed.
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Define an action of the Lorentz group on the set of all Riemann P-functions by first setting where are the entries in for a Lorentz transformation. Define where is a Riemann P-function. The resulting function is again a Riemann P-function. The effect of the Möbius transformation of the argument is that of shifting the poles to new locations, hence changing the critical points, but there is no change in the exponents of the differential equation the new function satisfies.
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Wing is curious as to whether it is statistically possible to prevent weight gain and subsequent obesity. It has been found that there are three critical points in a person's life which have the most effective weight loss. These are childhood, the time surrounding pregnancy, and the menopausal transition. Leonard Epstein worked alongside Wing to assist in complete multiple trials on the behavior treatments of obese children around the ages of 8–12 years old and their overweight parent(s).
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It has been proposed that some biological systems might lie near critical points. Examples include neural networks in the salamander retina, bird flocks gene expression networks in Drosophila, and protein folding. However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality. It has also been suggested that biological organisms share two key properties of phase transitions: the change of macroscopic behavior and the coherence of a system at a critical point.
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If we have a function which describes the system's potential energy, we can determine the system's equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable, we apply the second derivative test: Diagram of a ball placed in an unstable equilibrium.
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Angelo Battelli (28 March 1862 – 11 December 1916) was an Italian scientist, notable for having measured temperatures and heats of fusion of non-metallic substances, metallic conductivities and thermoelectric effects in magnetic metals, and the Thomson effect. He investigated osmotic pressures, surface tensions, and physical properties of carbon disulfide (CS2), water (H2O), and alcohols, especially their vapor pressures, critical points, and densities. He studied X-rays and cathode rays. He investigated the resistance of solenoids to high-frequency alternating currents.
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In these cases, the properties of the metal are radically transformed by the critical fluctuations, departing qualitatively from the standard Fermi liquid behavior, to form a metallic state sometimes called a non-Fermi liquid or a "strange metal". There is particular interest in these unusual metallic states, which are believed to exhibit a marked preponderance towards the development of superconductivity. Quantum critical fluctuations have also been shown to drive the formation of exotic magnetic phases in the vicinity of quantum critical points.
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From 1964 to 1966 Varchenko studied at the Moscow Kolmogorov boarding school No. 18 for gifted high school students, where Andrey Kolmogorov and Ya. A. Smorodinsky were lecturing mathematics and physics. Varchenko graduated from Moscow State University in 1971. He was a student of Vladimir Arnold. Varchenko defended his Ph.D. thesis Theorems on Topological Equisingularity of Families of Algebraic Sets and Maps in 1974 and Doctor of Science thesis Asymptotics of Integrals and Algebro-Geometric Invariants of Critical Points of Functions in 1982.
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The acquired image is verified by using the SHA-1 or MD5 hash functions. At critical points throughout the analysis, the media is verified again to ensure that the evidence is still in its original state. The process of verifying the image with a hash function is called "hashing." Given the problems associated with imaging large drives, multiple networked computers, file servers that cannot be shut down and cloud resources new techniques have been developed that combine digital forensic acquisition and ediscovery processes.
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His presence near the line of scrimmage kept the Green Bay Packers' running game in check. His sack and forced fumble resulted in three critical points in the second quarter when the Broncos offense had stalled without star running back Terrell Davis. Near the end of the fourth quarter, the game was tied at 24 and Green Bay had the ball on 3rd down & 8\. Atwater knocked down a critical pass on a blitz where the receiver was left wide open, forcing the Packers to punt.
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They argue that development is a dynamic interactive process, which is different for every individual, because every individual has their own experiences. Inventing a stage that only describes (not explains) a time period in the life of a few individuals (mostly white, middle-class young people living in Western societies within this decade), and has nothing to say about people living in different conditions or different points in history is not a scientific approach. Arnett has taken up some of these critical points in public discussion.
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"Black Coffee" has continued to receive praise in retrospective reviews. According to the Daily Mirrors Ian Sturgess, the track "boasts one of the most infectious pop choruses of all time." Clem Bastow of The Sydney Morning Herald said the song in particular won All Saints "major critical points" over the Spice Girls and complemented their "impeccable back catalogue". In the Daily Record, Julie MacCaskill wrote that "Black Coffee" along with "Pure Shores", "Under the Bridge" and "Never Ever" are a testament to the group's "pop power".
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After World War II, the road was built further north into Vinje in Telemark county. There were two critical points in the construction of this road that were very difficult to build. The first was at Fånekleivi on the east shore of the Byglandsfjorden, about south of the village of Bygland and the second one was at Byklestigen, just south of the village of Bykle. Both of these areas were difficult to pass using a horse and they could be dangerous in the winters.
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It also case brings up many important issues that are still being addressed to this day. One of the critical points that the Quinlan case brings up is the patient's right to deny or withdraw treatment. Cases in which the patient rejected or withdrew treatment were then unheard of and went against medical ethics in preserving one's life. Debates on allowing patients the right to self-determination were controversial, and they would be evaluated for the next couple of decades from state to state.
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Secondly the many shop-fronts which had been renewed post-unification were all sealed in terms of water-tightness: the floodwaters rose outside whilst the units inside stayed dry, but at certain critical points the weight of the water suddenly destroyed the shopfronts. Ironically the older "leaky" shopfronts did not suffer this fate as the water built up equally on each side. Whilst international media mainly concentrated on the impact upon Dresden the impact upon Pirna was proportionately much worse. Schöna and Bad Schandau were also hit.
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In Morse theory, a mathematical discipline, Jacobi sets provide a method of studying the relationship between two or more Morse functions. For two Morse functions, the Jacobi set is defined as the set of critical points of the restriction of one function to the level sets of the other function. The Jacobi set can also be defined as the set of points where the gradients of the two functions are parallel. If both the functions are generic, the Jacobi set is a smoothly embedded 1-manifold.
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The Palais–Smale compactness condition, named after Richard Palais and Stephen Smale, is a hypothesis for some theorems of the calculus of variations. It is useful for guaranteeing the existence of certain kinds of critical points, in particular saddle points. The Palais-Smale condition is a condition on the functional that one is trying to extremize. In finite-dimensional spaces, the Palais–Smale condition for a continuously differentiable real-valued function is satisfied automatically for proper maps: functions which do not take unbounded sets into bounded sets.
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On February 3, Olviopol (now Pervomaisk) and Ochakov (now Ochakiv) were captured. On February 6, the Red Army approached Odessa. Early in the morning of February 7, they broke into the city, and on February 8, Odessa was completely captured by the Red Army. Great help to the Red Army in taking the city was provided by the Odessa workers, who, on the orders of the Revolutionary Committee, had taken up arms and seized critical points in Odessa just before the approach of the regular units.
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Retrieved: 22 November 2015. This detrimental effect was countered with an anti-corrosion coating applied after fabrication. No armour protection was provided for the pilot, engine or other critical points of the aircraft, and self-sealing fuel tanks, which were becoming common at the time, were not used. This made the Zero lighter, more maneuverable, and the longest-ranged single-engine fighter of World War II, which made it capable of searching out an enemy hundreds of kilometres away, bringing it to battle, then returning to its base or aircraft carrier.
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The Tylliria/Dillirga region, where Kokkina is situated, had been a place of intense confrontation between the Greek Cypriot and Turkish Cypriot communities during the inter-communal struggle of 1963–1964. On 4 April 1964, armed groups originating from both communities had fought over a strategic location overlooking the region's only highway. There had also been several sporadic incidents of gunfire between villages of the region. On 8 April 1964, the United Nations Peacekeeping Force in Cyprus (UNFICYP) managed to arrange a ceasefire which was enforced by stationing UNFICYP troops at several critical points.
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94 On October 5, Henry ordered the second assault. Henry led the assault force, leaving the rest of the troops under Ferdinand the Holy, Ferdinand of Arraiolos and Bishop Álvaro of Evora, to defend their flanks and keep the Moroccan relief army at bay, but the second assault failed as badly as the first. The city's defenders rushed to the critical points, and poured on rapid and heavy missile fire. The Portuguese assaulters were prevented from reaching the walls (only one ladder managed to be set up – and was promptly destroyed).
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During the 2005 World Series on Fox, a new white banner was introduced. This would resemble a chrome finish, and the team abbreviations became white letters in the team's main color; the next few years, the new banner was adopted for all games. This banner, unlike the 2001–2004 version, would not be removed for the final out of the World Series but was dropped at other critical points (like whenever Alex Rodriguez came to bat, tied with an April record 14 home runs, and when Barry Bonds had 753).
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The stern was strengthened at critical points, new bulwark fairings were added, and an H-bitt was installed through which cabling is threaded to keep it centered during towing operations. Also installed was a hydraulic towing winch, referred to as a double-drum waterfall winch, holding or more of wire rope on each drum. One drum supports booster retrievals while the other is devoted to external tank towing. Freedom Star had been used to support scientific research operations including research for the National Oceanic and Atmospheric Administration and several universities.
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Ordinary cusps appear when the tangent to the curve is parallel to the direction of projection (that is when the tangent projects on a single point). More complicated singularities occur when several phenomena occurs simultaneously. For example, rhamphoid cusps occur for inflection points (and for undulation points) for which the tangent is parallel to the direction of projection. In many cases, and typically in computer vision and computer graphics, the curve that is projected is the curve of the critical points of the restriction to a (smooth) spatial object of the projection.
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Map of the Mittelland region of Switzerland The new type of underground freight infrastructure will be complementary to the Swiss road and rail network, and relieve it at critical points. The first scheduled section of about in the central Swiss Plateau (Mittelland) will connect Härkingen/Niederbipp and the city of Zürich from the early 2030s. Later, a comprehensive network is planned between the Bodensee in eastern Switzerland and Lake Geneva in western Switzerland, with offshoots to Basel and Luzern. The tunnels will be built at a depth of up to and have a diameter of .
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Borcea's scientific work ranged from vertex operator theory to zero distribution of polynomials and entire functions, via correlation inequalities and statistical mechanics. His thesis consists of two seemingly independent parts: one in vertex operator theory and the other devoted to the geometry of zeros of complex polynomials in one variable. In vertex operator theory, Julius generalized results of Mirko Primc and Arne Meurman and gave a classification of annihilated fields. As concerns complex polynomials, he tackled Sendov’s conjecture on zeros and critical points of complex polynomials in one variable.
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In a more negative review, Jim Wirth of NME compared the song to Madonna's album Ray of Light, commenting it "sounds so close to Madonna that it's almost indistinguishable". Retrospective reviews for "Pure Shores" have been also positive. According to the Daily Mirrors Ian Sturgess, the track "boasts one of the most infectious pop choruses of all time." Clem Bastow of The Sydney Morning Herald said the song along with "Black Coffee" won All Saints "major critical points" over the Spice Girls and complemented their "impeccable back catalogue".
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This approach to Morse theory was known in some form to René Thom and Stephen Smale. It is also implicit in John Milnor's book on the h-cobordism theorem. From the fact that the Morse homology is isomorphic to the singular homology, the Morse inequalities follow by considering the number of generators -- that is, critical points -- necessary to generate the homology groups of the appropriate ranks (and by considering truncations of the Morse complex, to get the stronger inequalities). The existence of Morse homology "explains", in the sense of categorification, the Morse inequalities.
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The 1st Provisional Marine Brigade suffered 185 killed and around 500 wounded during the Battle of Pusan Perimeter, most of which probably occurred at Yongsan. Once again the fatal weakness of the KPA had cost it victory after an impressive initial success-its communications and supply were not capable of exploiting a breakthrough and of supporting a continuing attack in the face of massive air, armor, and artillery fire that could be concentrated against its troops at critical points. By September 8, the KPA attacks in the area had been repulsed.
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The hard shoulder is usually demarcated by road markings in the form of a single dashed yellow line with the addition of yellow cat's eyes. On motorways, and at critical points on other routes (e.g. between junctions or interchanges, or beneath overpasses) a solid yellow line is used, denoting additional restrictions on usage of the hard shoulder. At junctions and on-ramps and off-ramps, the yellow line peels away into the turn, with a dashed white line (with green cats' eyes) denoting a lane division following the main route (i.e.
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The main mathematical tools to study critical points are renormalization group, which takes advantage of the Russian dolls picture or the self-similarity to explain universality and predict numerically the critical exponents, and variational perturbation theory, which converts divergent perturbation expansions into convergent strong-coupling expansions relevant to critical phenomena. In two- dimensional systems, conformal field theory is a powerful tool which has discovered many new properties of 2D critical systems, employing the fact that scale invariance, along with a few other requisites, leads to an infinite symmetry group.
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GEMA often features in discussions about copyright, private copying, webradio and file sharing. For example, the private copying levy on blank recordable media and recording devices was brought into question, especially as it not clear what rights the buyer acquires by paying this sum. In an online petition initiated by Monika Bestle on May 19, 2003, artists and event-organizers demanded a revision of GEMA's regulations with respect to better transparency, adjusted payment methods and other critical points. The petition was signed by 106,575 citizens and remains under parliamentary review since July 17, 2009.
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The USAF then concentrated strong air support over the regimental perimeter to aid the ground troops. Casualties came to the aid stations from the infantry companies in an almost steady stream during the morning. All available men from Headquarters Company and special units were formed into squads and put into the fight at the most critical points. At one time, the regimental reserve was down to six men. When the attack finally ceased shortly after 12:00 the 23rd Regiment had an estimated combat efficiency of only 38 percent.
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The sterns were strengthened at critical points, new bulwark fairings were added, and an H-bitt was installed through which cabling is threaded to keep it centered during towing operations. A hydraulic towing winch was also installed, referred to as a double-drum waterfall winch, holding 2,000 feet or more of wire rope on each drum. One drum supports booster retrievals while the other is devoted to external tank towing. The ships have also occasionally been used to support scientific research operations including research for the National Oceanic and Atmospheric Administration and several universities.
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However, cylindrical contact homology is not always defined due to the presence of holomorphic discs and a lack of regularity and transversality results. In situations where cylindrical contact homology makes sense, it may be seen as the (slightly modified) Morse homology of the action functional on the free loop space, which sends a loop to the integral of the contact form alpha over the loop. Reeb orbits are the critical points of this functional. SFT also associates a relative invariant of a Legendrian submanifold of a contact manifold known as relative contact homology.
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Modern systems are based on handheld data loggers and RFID sensors. The system provides a means to record the time when the employee reaches certain points on their tour. Checkpoints or watchstations are commonly placed at the extreme ends of the tour route and at critical points such as vaults, specimen refrigerators, vital equipment, and access points. Some systems are set so that the interval between stations is timed so if the employee fails to reach each point within a set time, other staff are dispatched to ensure the employee's well-being.
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These results generalize and formalize the 'rule' stated in the previous section. Using the two previous results and the fact that there exists a Morse function on any differentiable manifold, one can prove that any differentiable manifold is a CW complex with an n-cell for each critical point of index n. To do this, one needs the technical fact that one can arrange to have a single critical point on each critical level, which is usually proven by using gradient-like vector fields to rearrange the critical points.
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In order to analyse the length and strength of various interactions within the molecule, Richard Bader's "Atoms in molecules" theorem may be applied. Due to the complex description of the electron field provided by this aspherical model, it becomes possible to establish realistic bond paths between interacting atoms as well as to find and characterise their critical points. Deeper insight into this data yields useful information about bond strength, type, polarity or ellipticity, and when compared with other molecules brings greater understanding about the actual electron structure of the examined compound.
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Djokovic played his first official match since Wimbledon at the Australian Open. After defeating Donald Young in straight sets, he defeated Gaël Monfils in the second round after dropping the first set, with Monfils succumbing to extreme heat in the latter stages of the match. With a victory over Albert Ramos Viñolas in third round, Djokovic set up a meeting with Korean Chung Hyeon. In a match of constant breaks of serve, Djokovic eventually lost in straight sets due to relentless backcourt defense from Chung and copious unforced errors on critical points.
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On 3 December, all existing anti-tank battalions were reassigned to General Headquarters and converted to tank destroyer battalions. The new tank destroyer doctrine was formally stated in Field Manual 18–5, Tactical Employment, tank destroyer Unit, in June 1942. It laid down a focused doctrine—"There is but one objective of tank destroyer units… the destruction of hostile tanks"—and repeatedly emphasized an offensive, vigorous spirit. Tank destroyer units were expected to be employed as complete battalions, held in reserve and committed at critical points, rather than parceled out as small defensive strongpoints.
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Depiction of the 7th India Armada (Almeida, 1505), from the Memória das Armadas, c. 1568 The Seventh India Armada was assembled in 1505 on the order of King Manuel I of Portugal and placed under the command of D. Francisco de Almeida, the first Portuguese Viceroy of the Indies. The 7th Armada set out to secure the dominance of the Portuguese navy over the Indian Ocean by establishing a series of coastal fortresses at critical points – Sofala, Kilwa, Anjediva, Cannanore – and reducing cities perceived to be local threats (Kilwa, Mombasa, Onor).
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A phase diagram displaying spinodal curves, within the binodal coexistence curves and two critical points: an upper and lower critical solution temperature. In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero. The locus of these points (the inflection point within a G-x or G-c curve, Gibbs free energy as a function of composition) is known as the spinodal curve.G. Astarita: Thermodynamics: An Advanced Textbook for Chemical Engineers (Springer 1990), chaps 4, 8, 9, 12.
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Dom Luís de Ataíde decided to distribute his forces in 19 critical points along the eastern river banks, where artillery batteries were established, garrisoned with 20 to 80 men and a contingent of lascarins, to keep the colossal army of Bijapur from crossing. Every battery was to have visual contact with the next and their garrisons were not to leave their posts unless ordered to.Pereira (1617), 1986 edition, pg. 348 The deeper waters of the Mandovi and Zuari rivers, to the north and south respectively, were patrolled by four galleys, a half-galley, and twenty small galleys called foists.
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This file and the fact that the software is completely open-source makes it easy to reproduce the work, that can help supporting the open science paradigm, and allows fast reuse on different patients data. In image-guided surgery, registration time and accuracy are critical points, considering that, during the registration, the patient is on the operating table, and the images to be registered have lower resolution compared to the target ones. In this field, the possibility to exploit elastix with high-level languages, such as OpenCL, opens to research in the usage of GPUs and other hardware accelerators.
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Scapa Flow Scapa Flow made a near-ideal anchorage. Situated at the centre of the Orkney Islands off the north coast of Scotland, the natural harbour, large enough to contain the entire Grand Fleet, was surrounded by a ring of islands separated by shallow channels subject to fast-racing tides. That U-boats still posed a threat had long been realised, and a series of countermeasures were installed during the early years of the First World War. Blockships were sunk at critical points; and floating booms deployed to block the three widest channels, operated by tugboats to allow the passage of friendly shipping.
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Since mid-2004, hill size became the official measurement for the size of hills, replacing construction points (also known as K-points, K-spots and critical points), which however remain the basis for issuing points. The distance is measured as a straight line from the takeoff to the knoll, and then follows the landing surface until reaching the hill size point. The world's largest hills are Vikersundbakken in Vikersund, Norway and Letalnica Bratov Gorišek in Planica, Slovenia with hill size of 240 meters. The hills normally mark the hill size physically with a horizontal line across the hill.
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A dessin that is not clean can be transformed into a clean dessin in the same surface, by recoloring all of its points as black and adding new white points on each of its edges. The corresponding transformation of Belyi pairs is to replace a Belyi function β by the pure Belyi function . One may calculate the critical points of γ directly from this formula: , , and . Thus, γ−1(1) is the preimage under β of the midpoint of the line segment [0,1], and the edges of the dessin formed from γ subdivide the edges of the dessin formed from β.
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In 1979-1980 she visited Harvard University where she learned gauge field theory from Clifford Taubes. This lead results about point singularities in the Yang- Mills equation and the Yang–Mills–Higgs equations. Her interest in singularities soon brought her deeper into geometry, leading to a classification of singular connections and to a condition for removing two- dimensional singularities in work with Robert Sibner. Realizing that instantons could under certain circumstances be viewed as monopoles, the Sibners and Uhlenbeck constructed non-minimal unstable critical points of the Yang-Mills functional over the four-sphere in 1989.
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In general the pattern of frequent but irregular services is largely dictated by the LDHS timetable (itself not on a standard pattern), the timing of cross-country services which are constrained by critical points off the ECML, and the needs of freight services. South of Newcastle a critical physical section is the 2-track line between Northallerton and Newcastle. Timetable developments should endeavour to even out the gaps especially through Durham. Various stakeholders, with potential access to funds, have aspirations for improved services and facilities, including new stations at East Linton (west of Dunbar) and Reston (north-west of Berwick).
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The first major general statement of the principle involved is that the asymptotic behaviour of I(k) depends only on the critical points of f. If by choice of g the integral is localised to a region of space where f has no critical point, the resulting integral tends to 0 as the frequency of oscillations is taken to infinity. See for example Riemann-Lebesgue lemma. The second statement is that when f is a Morse function, so that the singular points of f are non-degenerate and isolated, then the question can be reduced to the case n = 1.
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The critical points to end the rebellion were the water war, engaged by Egyptian forces upon the Druze population and the effective defeat of the main insurgent force in Wadi al-Taym. It persuaded Druze leaders to negotiate peace with Ibrahim Pasha. Sheikh Hasan al-Bitar of Rashaya and the Christian Jiris Abu ad-Dibs mediated the agreement, whereby Ibrahim Pasha agreed to give amnesty to insurgents and to put the Druze into forced labor in lieu of exemption from conscription, in return for the surrender of Druze arms and those seized from Egyptians. The agreement was signed on July 23, 1838.
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If the volume of two gases that are kept at constant temperature and pressure below critical conditions is gradually reduced, condensation will start. When a certain volume is reached, the amount of condensation will gradually increase upon further reduction in volume until the gases are liquefied. If the composition of the gases lies between their true and pseudo critical points the condensate formed will disappear on continued reduction of volume.On retrogade condensation and the critical phenomena of mixtures of two substancesOn the abnormal phenomena near the critical point This disappearance of condensation is called retrograde condensation.
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The most important points on a PES are the stationary points where the surface is flat, i.e. parallel to a horizontal line corresponding to one geometric parameter, a plane corresponding to two such parameters or even a hyper-plane corresponding to more than two geometric parameters. The energy values corresponding to the transition states and the ground state of the reactants and products can be found using the potential energy function by calculating the function's critical points or the stationary points. Stationary points occur when 1st partial derivative of the energy with respect to each geometric parameter is equal to zero.
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They proposed a test called Asymptotic Decider to correctly track the interpolant on the faces of the cube. In fact, as observed by Natarajan in 1994, this ambiguity problem also occurs inside the cube. In his work, the author proposed a disambiguation test based on the interpolant critical points, and added four new cases to the Marching Cubes triangulation table (subcases of the cases 3, 4, 6 and 7). At this point, even with all the improvements proposed to the algorithm and its triangulation table, the meshes generated by the Marching Cubes still had topological incoherencies.
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Let (M, g) be a connected Riemannian manifold. Then the following statements are equivalent: # The closed and bounded subsets of M are compact; # M is a complete metric space; # M is geodesically complete; that is, for every p in M, the exponential map expp is defined on the entire tangent space TpM. Furthermore, any one of the above implies that given any two points p and q in M, there exists a length minimizing geodesic connecting these two points (geodesics are in general critical points for the length functional, and may or may not be minima).
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An intuitive guess of the effect of a quantum critical point being affected by noise would be that the external noise defines an effective temperature. This effective temperature would introduce a well defined energy scale in the problem and break the scale invariance of the quantum critical point. On the contrary, it was recently found that certain types of noise can induce a non-equilibrium quantum critical state. This state is out-of-equilibrium because of the continuous energy flow introduced by the noise, but it still retains the scale invariant behavior typical of critical points.
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Egyptian warships shelled Houthi positions as they advanced on critical points in Aden, and coalition warplanes repeatedly struck the attackers, as well as installations they seized. Saudi Arabia reportedly inserted special forces troops into Aden, which a Saudi official told CNN were "coordinating and guiding" resistance to the Houthis and their allies. The Saudi government declined to officially comment on whether it had commandos on the ground in Aden. On 3 May, a small force of no more than 50 fighters from at least three Arab countries reportedly landed near Aden International Airport and took up arms against troops loyal to Saleh.
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Supardjo cites a number of reasons for the failure of the movement. Primarily, he notes that the movement had neither an overall leader nor a clear chain of command. There was a loose structure in the cooperation between the PKI and the military, and the two groups were constantly arguing over courses of strategic action, which led to moments of indecisiveness during critical points in the movement. However, Supardjo later reveals in the document that the PKI was the true body behind the movement, and for that reason, he believes Kamaruzaman Sjam played the leading role.
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Non-directional and hybrid personal line markers are used to indicate the identity of a diver who has passed along the line and has not yet returned to that point. They are attached to the line in the same way as cave arrows, and are deployed on the way into the cave, usually at critical points such as forks or jumps, and are used to indicate to other divers that someone is further in along the line. They are marked to identify the diver, and are recovered by the diver on the way out. Cookies (round markers), rectangular referencing exit markers and clothes pegs are used for this purpose.
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The museum contains only one hall, which introduces only one painting that is usually of great cultural significance. Before visitors can familiarize themselves with the painting, they watch a 45-minute film, describing the peculiarities of the exhibit, its history and the biography of the painter. Such a presentation, starred by famous Russian actors such as Mikhail Ulyanov, Vyacheslav Tikhonov, Rostislav Plyatt, Oleg Yefremov, Oleg Tabakov, Ya. Smolenskiy, provide visitors with the opportunity to plunge into the atmosphere of the times, when the painting was created, to become utterly absorbed by the critical points of the painter's life and to get acquainted with the major milestones of his work.
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There is very little published literary criticism of creative nonfiction works, despite the fact that the genre is often published in respected publications such as The New Yorker, Vanity Fair, Harper's, and Esquire. A handful of the most widely recognized writers in the genre such as Robert Caro, Gay Talese, Joseph Mitchell, Tom Wolfe, John McPhee, Joan Didion, John Perkins, Ryszard Kapuściński, Helen Garner and Norman Mailer have seen some criticism on their more prominent works. "Critics to date, however, have tended to focus on only one or two of each writer's works, to illustrate particular critical points."Lounsberry, page xvi These analyses of a few key pieces are .
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There are rules for the interaction of these forces, which may force some or all of the moving ships to stop, being pinned by the reacting enemy. After movement, the non-moving player can also move a few limited reserves of ships to battles so as to shore up the defense of critical points. After combat, the moving player retrogrades or moves ships that were in combat back to source of supply or repair, and finally moves a limited number of ships vast distances to prepare for the coming enemy turn. Combat itself is resolved in a number of combat rounds after the two players each deploy their battleforces.
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This is a result of having temperatures and the pressures well above those of the critical points for hydrogen and helium, meaning that there is no sharp boundary between gas and liquid phases. Hydrogen becomes a supercritical fluid at a pressure of around 12 bar.Guillot (1999) Since the lower boundary of the atmosphere is ill-defined, the pressure level of 10 bars, at an altitude of about 90 km below 1 bar with a temperature of around 340 K, is commonly treated as the base of the troposphere. In scientific literature, the 1 bar pressure level is usually chosen as a zero point for altitudes—a "surface" of Jupiter.
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Edward Witten came up with a related construction in the early 1980s sometimes known as Morse–Witten theory. Morse homology can be extended to finite-dimensional non-compact or infinite-dimensional manifolds where the index remains finite, the metric is complete and the function satisfies the Palais–Smale compactness condition, such as the energy functional for geodesics on a Riemannian manifold. The generalization to situations in which both index and coindex are infinite, but the relative index of any pair of critical points is finite, is known as Floer homology. Sergei Novikov generalized this construction to a homology theory associated to a closed one-form on a manifold.
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The Kingston Trio's influence on the development of American popular music has been considerable. According to music critic Bruce Eder writing for Allmusic.com: > In the history of popular music, there are a relative handful of performers > who have redefined the content of the music at critical points in > history—people whose music left the landscape, and definition of popular > music, altered completely. The Kingston Trio were one such group, > transforming folk music into a hot commodity and creating a demand—where > none had existed before—for young men (sometimes with women) strumming > acoustic guitars and banjos and singing folk songs and folk-like novelty > songs in harmony.
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Langton made numerous contributions to the field of artificial life, both in terms of simulation and computational models of given problems and to philosophical issues. He early identified the problems of information, computation and reproduction as intrinsically connected with complexity and its basic laws. Inspired by ideas coming from physics, particularly phase transitions, he developed several key concepts and quantitative measures for cellular automata and suggested that critical points separating order from disorder could play a very important role in shaping complex systems, particularly in biology. These ideas were also explored simultaneously, albeit with different approximations, by James P. Crutchfield and Per Bak among others.
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Degenerate points between potential energy surfaces lie in what is called the intersection or seam space with a dimensionality of 3N-8 (where N is the number of atoms). Any critical points in this space of degeneracy are characterised as minima, transition states or higher-order saddle points and can be connected to each other through the analogue of an intrinsic reaction coordinate in the seam. In benzene, for example, there is a recurrent connectivity pattern where permutationally isomeric seam segments are connected by intersections of a higher symmetry point group. The remaining two dimensions that lift the energetic degeneracy of the system are known as the branching space.
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Temporary urbanism can involve risks. Indeed, temporary and self-organized projects could also be used to keep unused lands attractive while the economy is in crisis and therefore facilitating the state withdrawal from its responsibilities. As Margit Mayer pointed out, “principles such as self-management, self-realization and all kinds of unconventional or insurgent creativity (…) have lost the radical edge they used to entail in the context of the overbearing Keynesian welfare state - in today’s neoliberal urbanism they have been usurped as essential ingredients of sub-local regeneration programs”. The concept itself of austerity urbanism is the subject of different critical points of views.
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Wöhler started his axle investigations by research into the theory of elasticity and was led, in 1855, to a method for predicting the deflection of lattice beams that anticipated the work of Émile Clapeyron. He also introduced the practice of supporting one end of a bridge on roller bearings to allow for thermal expansion. 5. S-N Curve of aluminium alloy His work on fatigue marks the first systematic investigation of S-N Curves, also known as Wöhler curves, to characterise the fatigue behaviour of materials. Such curves can be used to minimise the problem of fatigue by lowering the stress at critical points in a component.
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The principal configuration mechanism is Varnish Configuration Language (VCL), a domain- specific language (DSL) used to write hooks that are called at critical points in the handling of each request. Most policy decisions are left to VCL code, making Varnish more configurable and adaptable than most other HTTP accelerators. When a VCL script is loaded, it is translated to C, compiled to a shared object by the system compiler, and loaded directly into the accelerator which can thus be reconfigured without a restart. A number of run- time parameters control things such as the maximum and the minimum number of worker threads, various timeouts, etc.
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In his book The Goal, the protagonist is a manager in charge of a troubled manufacturing operation. At any point in time, one particular constraint (such as inadequate capacity at a machine tool) limits total system throughput, and when the constraint is resolved, another constraint becomes the critical one. The plot of Goldratt's stories revolve around identifying the current limiting constraint and raising it, which is followed by finding out which is the next limiting constraint. Another common theme is that the system being analyzed has excess capacity at a number of non-critical points, which, contrary to conventional wisdom, is absolutely essential to ensure constant operation of the constrained resource.
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One of Fermat's theorems states that optima of unconstrained problems are found at stationary points, where the first derivative or the gradient of the objective function is zero (see first derivative test). More generally, they may be found at critical points, where the first derivative or gradient of the objective function is zero or is undefined, or on the boundary of the choice set. An equation (or set of equations) stating that the first derivative(s) equal(s) zero at an interior optimum is called a 'first-order condition' or a set of first-order conditions. Optima of equality-constrained problems can be found by the Lagrange multiplier method.
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Even in games with a linear story, players interact with the game world by performing a variety of actions along the way. More recently, some games have begun offering multiple endings to increase the dramatic effect of moral choices within the game, although early examples also exist. Still, some games have gone beyond small choices or special endings, offering a branching storyline, known as an interactive narrative, that players may control at critical points in the game. Sometimes the player is given a choice of which branch of the plot to follow, while sometimes the path will be based on the player's success or failure at a specific challenge.
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For a continuously differentiable function of several real variables, a point P (that is, a set of values for the input variables, which is viewed as a point in Rn) is critical if all of the partial derivatives of the function are zero at P, or, equivalently, if its gradient is zero. The critical values are the values of the function at the critical points. If the function is smooth, or, at least twice continuously differentiable, a critical point may be either a local maximum, a local minimum or a saddle point. The different cases may be distinguished by considering the eigenvalues of the Hessian matrix of second derivatives.
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One generalization of the study of harmonic functions is the study of harmonic forms on Riemannian manifolds, and it is related to the study of cohomology. Also, it is possible to define harmonic vector-valued functions, or harmonic maps of two Riemannian manifolds, which are critical points of a generalized Dirichlet energy functional (this includes harmonic functions as a special case, a result known as Dirichlet principle). This kind of harmonic map appears in the theory of minimal surfaces. For example, a curve, that is, a map from an interval in R to a Riemannian manifold, is a harmonic map if and only if it is a geodesic.
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Expeditionary maneuver warfare (EMW) is the current concept that guides how the United States Marine Corps organizes, deploys and employs its forces. Utilizing maneuver warfare and the Marine Corps' expeditionary heritage, EMW emphasizes strategically agile and tactically flexible Marine Air Ground Task Forces with the capability to project power against critical points in the littorals and beyond. EMW was designed to fit the United States Navy's "Sea Basing" concept as outlined in the Sea Power 21 plan. This concept has influenced Marine Corps equipment procurement in recent years, leading to the purchase of the MV-22 Osprey, Expeditionary Fighting Vehicle, F-35 Lightning II and the M777 Lightweight Howitzer.
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If the "New German School" was to be imagined as a group of artists with similar aims, joining Liszt with Wagner was already problematic; but there was still a further problem, regarding Berlioz. Berlioz very decidedly declared in spring 1860, following the concerts given by Wagner at the Parisian Théâtre Italien, that he himself had nothing to do with Wagner's style and ideology. All those who had claimed that he was representative of a joint school together with Wagner were calumniators. In contrast to Brahms and Joachim in their "Manifesto", Berlioz gave a detailed list of critical points as well as a list of principles he supported.
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The membrane is tested immediately after installation and prior to being covered up by any following construction processes. The area below the membrane is temporarily pressurized with a mixture of clean air and a non-toxic and inert tracer gas that is sensitive to detection. Special equipment is then used to trace all leaks within the installation, with particular attention being paid to critical points and junctions formed between the membrane material and other structural elements prior to conducting a sweep of the complete area. Any leaks are identified and sealed, and the membrane is re-tested before it passes and the certificate is issued.
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These forts, built in masonry and shaped stone, were designed to shelter their garrison against bombardment. One organizing feature of the new system involved the construction of two defensive curtains: an outer line of forts, backed by an inner ring or line at critical points of terrain or junctions (see, for example, Séré de Rivières system in France). Traditional fortification however continued to be applied by European armies engaged in warfare in colonies established in Africa against lightly armed attackers from amongst the indigenous population. A relatively small number of defenders in a fort impervious to primitive weaponry could hold out against high odds, the only constraint being the supply of ammunition.
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Jupiter also has metallic hydrogen near its center, but much of its volume is hydrogen, helium, and traces of other gases above their critical points. The observable atmospheres of all these planets (at less than unit optical depth) are quite thin compared to their radii, only extending perhaps one percent of the way to the center. Thus the observable portions are gaseous (in contrast to Mars and Earth, which have gaseous atmospheres through which the crust can be seen). The rather misleading term has caught on because planetary scientists typically use rock, gas, and ice as shorthands for classes of elements and compounds commonly found as planetary constituents, irrespective of the matter's phase.
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An exception was the city of La Paz, where two separate regiments of carabineers were kept under the direct control of the director general and the president. Other exceptions to the integral brigade organization were made in sections of the country where dependence on the regular departmental brigade forces was not deemed advisable or feasible. Two such areasSan Ignacio de Velasco in Santa Cruz Department and Tupiza in Potosí Departmenthad independent carabineer detachments in addition to the department brigades. Certain departmental brigade personnel of the rural command were assigned to a series of frontier posts scattered at twenty-seven critical points along the borders and at river and lake ports of entry.
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Because the Blackwater River drains a large area of southern Virginia east of the Fall Line, when heavy rainfall occurs throughout the area, severe flooding occasionally occurs at several points as the large volume of water flows downstream. Critical points of such flooding have been near Zuni along U.S. Route 460, and in the independent city of Franklin, which borders Southampton County and Isle of Wight County. Unlike the marshy areas upstream, at these points the river's channel is limited, and flood stages can be reached very quickly. This occurred during Hurricane Floyd in 1999, and again in October 2006, after an unnamed Nor'-Easter storm dumped 10 inches (25 cm) of rain on the region.
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It was the battle in which the KPA made the most substantial gains, splitting the US 2nd Infantry Division in half and briefly capturing Yongsan, where they were very close to breaching through to the US forces' supply lines and threatening other divisions' rear areas. However, once again the fatal weakness of the KPA had cost it victory after an impressive initial success—its communications and supply were not capable of exploiting a breakthrough and of supporting a continuing attack in the face of massive air, armor and artillery fire that could be concentrated against its troops at critical points. By September 8, the KPA attacks in the area had been repulsed.
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Ground officers contended there was rarely sufficient artillery available, and the flexibility of aircraft would be ideal for massing firepower at critical points, while producing a greater psychological effect on friendly and hostile forces alike. Moreover, unlike massive, indiscriminate artillery strikes, small aerial bombs would not render ground untrafficable, slowing attacking friendly forces. Although the prevailing view in official circles was largely indifferent to CAS during the interwar period, its importance was expounded upon by military theorists, such as J. F. C. Fuller and Basil Liddell Hart. Hart, who was an advocate of what later came to be known as 'Blitzkrieg' tactics, thought that the speed of armoured tanks would render conventional artillery incapable of providing support fire.
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The books starts with a general introduction to Complex Dynamics, Chaos and fractals. In particular the Feigenbaum scenario and the relation to Julia sets and the Mandelbrot set is discussed. The following special sections provide in depth detail for the shown images: Verhulst Dynamics, Julia Sets and Their Computergraphical Generation, Sullivan's Classification of Critical Points, The Mandelbrot Set, External Angles and Hubbard Trees, Newton's Method for Complex Polynomials: Cayley's Problem, Newtons's Method for Real Equations, A Discrete Volterra-Lotka System, Yang-Lee Zeros, Renormalization (Magnetism and Complex Boundaries). The book also includes invited Contributions by Benoît Mandelbrot, Adrien Douady, Gert Eilenberger and Herbert W. Franke, which provide additional formality and some historically interesting detail.
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In Peel's view, Bradfield, Eton and Fettes all saw Chenevix-Trench become headmaster at "critical points in their history", and he was "a headmaster whose personality met many of their priorities, breathing fresh life into creaking limbs". The book argues that, despite Chenevix-Trench's shortcomings being "too readily obvious", "overshadowing the flaws stands his passionate concern for the individual, a vital quality for any leader to possess". The book ends with a quotation from Chenevix-Trench about the importance of education: > What is a boy? He is a person who is going to carry on what you have > started, to sit where you are sitting and, when you are gone, attend to > those things you think are so important.
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PFF crews found themselves given ever increasingly sophisticated and complex jobs that were constantly modified and developed tactically during the bombing campaign from 1943 until the end of the war. Some of the more usual tasks were as: "Finders"; these were 8 Group aircraft tasked with dropping sticks of illuminating flares, firstly at critical points along the bombing route to aid navigation and keep the bomber stream compact and then across the approximate target area. If conditions were cloudy then these were dropped "blind" using H2S navigational radar. "Illuminators"; were PFF aircraft flying in front of the main force who would drop markers or target indicators (TIs) onto the designated 'aiming point' already illuminated by the "Finders".
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Her research group further identified uridylation-meditated pre-miRNA degradation pathway by LIN28 and TUT4, contributing to a better understanding of how microRNA-mediated gene expression regulation is involved in embryonic stem cell maintenance and cancer cell development. She also discovered the molecular basis for pri-miRNA recognition and cleavage by the Drosha-DGCR8 complexes, and pre-miRNA processing by Dicer. These findings suggested several critical points to be considered for designing more efficient short hairpin RNA (shRNA) vectors and also contributed to the improvement of RNA interference technologies. The research team led by Narry Kim and Chang Hyeshik confirmed the predicted subgenomic RNAs of SARS-CoV-2 along with new RNA and dozens of unknown subgenomic RNAs.
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The Oscar-winning Disney short Lend a Paw also featured Pluto being influenced by a shoulder angel and devil. In Mickey Mouse Clubhouse, a Disney animated series aimed at preschoolers, Pete has similar manifestations—though simply colored white and red rather than depicted with wings and a halo/horns and a pitchfork, respectively. The film Cloud Atlas is an example of utilizing a shoulder angel plot device in feature film, in which the character played by Hugo Weaving whispers bad and good advice to the character played by Tom Hanks. Old Georgie (Hugo Weaving) appears only in critical points of the story, where Zachry's mind (Tom Hanks) is split between right and wrong choices.
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The M2 Bradley Infantry Fighting Vehicle (IFV) consists of five variants: the M2, M2A1, M2A2, M2A2 ODS (Operation Desert Storm improvements), and M2A3. Their main mission is to provide protected transport of an infantry squad (up to six passengers) to critical points. Aside from carrying mechanized infantry into close contact with the enemy, the M2 can also provide overwatching fire to dismounting infantrymen. It is adequately armored to provide protection against small arms fire and artillery, and able to combat any vehicle on the battlefield using its TOW or Stinger missiles. The M2 IFV also has six external firing ports for the squad M231 Firing Port Weapon on the M2 and M2A1 versions only.
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Parsons had several conversations with Daniel Bell on a "post-industrial society", some of which were conducted over lunch at William James Hall. After reading an early version of Bell's magnum opus, "The Coming of the Post-Industrial Society", Parsons wrote a letter to Bell, dated November 30, 1971, to offer his criticism. Among his many critical points, Parsons stressed especially that Bell's discussion of technology tended to "separate off culture" and treat the two categories "as what I would call culture minus the cognitive component." Parsons' interest in the role of ethnicity and religion in the genesis of social solidarity within the local community heavily influenced another of his early 1960s graduate students, Edward Laumann.
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The index is most naturally thought of as a pair :(i_-, i_+), where i_- is the dimension of the unstable manifold at a given point of the critical manifold, and i_+ is equal to i_- plus the dimension of the critical manifold. If the Morse–Bott function is perturbed by a small function on the critical locus, the index of all critical points of the perturbed function on a critical manifold of the unperturbed function will lie between i_- and i_+. Morse–Bott functions are useful because generic Morse functions are difficult to work with; the functions one can visualize, and with which one can easily calculate, typically have symmetries. They often lead to positive-dimensional critical manifolds.
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At critical points throughout the game, the main character is given the option of marrying one of two women he has encountered during his travels. This choice determines the new main character of the next generation—the child (or children) of the previous lead. The choice also affects the gameplay, as the main character may be Orakian or a mix of Layan and Orakian, which differ in their ability to use techniques and their level of proficiency with them. Two paths in the second generation in turn lead to four paths in the third and final generation, and depending on which of the four main characters is played, the ending will vary.
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Due to abnormal weather patterns and warming temperatures in the Arctic and Northern Bering Sea region, sea ice has receded making larger areas of navigable waters available to shipping vessels. The heavy reliance of the indigenous people on the marine environment is now vulnerable with the lack of sea ice during critical points in the seasons. The sea ice loss not only affects the surrounding marine ecosystem but also the local coastal communities making the shoreline vulnerable to storm surges and increased erosion. This has created a double hazard for the marine species populations in the region, with their environment slowly disappearing and also increased ship traffic increasing marine casualties from ship strikes.
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The inefficiency of North Korean logistics remained a fatal weakness of the North Korean Army, costing it crucial defeats after an initial success with combat forces. The North Koreans' communications and supply were not capable of exploiting a breakthrough and of supporting a continuing attack in the face of massive air, armor, and artillery fire that could be concentrated against its troops at critical points. Several units lost crucially needed supply lines in the middle of their offensives, particularly when crossing the Naktong River which had few stable bridges remaining. The NK 3rd Division stopped receiving food and ammunition supply as it pushed on Taegu in mid- August, forcing one of its regiments to withdraw from the captured Triangulation Hill.
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Moscow women dig anti-tank trenches around their city in 1941 By 13 October 1941, the Wehrmacht had reached the Mozhaisk defense line, a hastily constructed set of four lines of fortifications protecting Moscow's western approaches which extended from Kalinin towards Volokolamsk and Kaluga. Despite recent reinforcements, only around 90,000 Soviet soldiers manned this line—far too few to stem the German advance.Zhukov, tome 2, p. 17. Given the limited resources available, Zhukov decided to concentrate his forces at four critical points: the 16th Army under Lieutenant General Rokossovsky guarded Volokolamsk, Mozhaisk was defended by 5th Army under Major General Govorov, the 43rd Army of Major General Golubev defended Maloyaroslavets, and the 49th Army under Lieutenant General Zakharkin protected Kaluga.
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Reclassified again, 2 March 1959, she emerged from conversion as an amphibious assault carrier, LPH-5. Capable of transporting a battalion landing team and carrying helicopters in place of planes, Princetons mission became that of vertical envelopment—the landing of Marines behind enemy beach fortifications and providing logistics and medical support as they attack from the rear to seize critical points, cut enemy supplies, sever communications, and link up with assault forces landed on the beaches. Since this was a Marine Corps mission, Marines made up a major portion of the ship's company in the Air, Operations, and Supply Departments. From May 1959 – January 1960, Princeton trained with Marine units from Camp Pendleton, then deployed to WestPac to train in Okinawan waters.
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In complex analysis, the theorem states that the finite zeros of the derivative r'(z) of a nonconstant rational function r(z) that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of r(z) and particles of negative mass at the poles of r(z) , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance. Furthermore, if C1 and C2 are two disjoint circular regions which contain respectively all the zeros and all the poles of r(z) , then C1 and C2 also contain all the critical points of r(z) .
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In 2001, ASA became one of four guarantors to enter into a Voluntary Flexible Agreement (VFA) with the US federal government, changing its focus from back-end default collections to an emphasis on delinquency and default prevention. The Voluntary Flexible Agreement enabled Federal Family Education Loan Program guarantors to develop programs and techniques to help borrowers avoid student- loan default and all of its negative consequences. ASA’s Wellness program was designed to deliver debt management information to borrowers at critical points along the life of their loan in order to prevent repayment problems before they start. Results of these Wellness activities proved that the proactive approach to giving student loan borrowers the right information at exactly the right time were effective in preventing repayment problems.
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For a real-valued smooth function f : M → R on a differentiable manifold M, the points where the differential of f vanishes are called critical points of f and their images under f are called critical values. If at a critical point b, the matrix of second partial derivatives (the Hessian matrix) is non-singular, then b is called a non-degenerate critical point; if the Hessian is singular then b is a degenerate critical point. For the functions :f(x)=a + b x+ c x^2+d x^3+\cdots from R to R, f has a critical point at the origin if b = 0, which is non-degenerate if c ≠ 0 (i.e. f is of the form a + cx2 + ...) and degenerate if c = 0 (i.e.
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The idea first came to him to grow his own chair during a weekend wood-hunting excursion with his son. He started box elder seeds in 1903, selecting and planting either 28 or 32 of the saplings in a carefully designed pattern in the spring of 1907. In the spring of 1908, the trees had grown to six feet tall and he began training them along a trellis, grafting the branches at critical points to form the parts of his chair. In 1913, he cut all the trees except those forming the legs, which he left to grow and increase in diameter for another year, before harvesting and drying the chair in 1914; eleven years after he started the box elder seeds.
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With a population of about a million, Luoyang became the second largest city in the empire, and with its close proximity to the Luo River it benefited from southern agricultural fertility and trade traffic of the Grand Canal. However, the Tang court eventually demoted its capital status and did not visit Luoyang after the year 743, when Chang'an's problem of acquiring adequate supplies and stores for the year was solved. As early as 736, granaries were built at critical points along the route from Yangzhou to Chang'an, which eliminated shipment delays, spoilage, and pilfering. An artificial lake used as a transshipment pool was dredged east of Chang'an in 743, where curious northerners could finally see the array of boats found in southern China, delivering tax and tribute items to the imperial court.
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One of the first examples of an exotic sphere found by was the following: Take two copies of B4×S3, each with boundary S3×S3, and glue them together by identifying (a,b) in the boundary with (a, a2ba−1), (where we identify each S3 with the group of unit quaternions). The resulting manifold has a natural smooth structure and is homeomorphic to S7, but is not diffeomorphic to S7. Milnor showed that it is not the boundary of any smooth 8-manifold with vanishing 4th Betti number, and has no orientation-reversing diffeomorphism to itself; either of these properties implies that it is not a standard 7-sphere. Milnor showed that this manifold has a Morse function with just two critical points, both non-degenerate, which implies that it is topologically a sphere.
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In differential topology, given a family of Morse-Smale functions on a smooth manifold X parameterized by a closed interval I, one can construct a Morse- Smale vector field on X × I whose critical points occur only on the boundary. The Morse differential defines a chain map from the Morse complexes at the boundaries of the family, the continuation map. This can be shown to descend to an isomorphism on Morse homology, proving its invariance of Morse homology of a smooth manifold. Continuation maps were defined by Andreas Floer to prove the invariance of Floer homology in infinite dimensional analogues of the situation described above; in the case of finite-dimensional Morse theory, invariance may be proved by proving that Morse homology is isomorphic to singular homology, which is known to be invariant.
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Typically, supercritical fluids are completely miscible with each other, so that a binary mixture forms a single gaseous phase if the critical point of the mixture is exceeded. However, exceptions are known in systems where one component is much more volatile than the other, which in some cases form two immiscible gas phases at high pressure and temperatures above the component critical points. This behavior has been found for example in the systems N2-NH3, NH3-CH4, SO2-N2 and n-butane-H2O. The critical point of a binary mixture can be estimated as the arithmetic mean of the critical temperatures and pressures of the two components, For greater accuracy, the critical point can be calculated using equations of state, such as the Peng-Robinson, or group-contribution methods.
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The women of the Furude clan have all acted as Infection Queens, and Rika is the sole remaining representative of her clan after the death of her parents. Miyo kills Rika in each reality to unleash the disease and vindicate the work of her adoptive grandfather, who was mocked and shamed by the scientific community for his thesis about the disease. After several hundred loops, Keiichi becomes aware of them in a handful of flashbacks and subconsciously remembers several of his past loops, which allows him to avoid several critical points where various characters would be murdered or driven insane, and the group of friends nearly manages to outwit Miyo. In the final loop, the group asks Hanyu to join them, and the spirit manages to manifest a physical body.
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Study of saddle-node, transcritical, pitch-fork, period doubling, Hopf, secondary Hopf (Neimark) bifurcations of stable solutions allows for a theoretical discussion of the circumstances and occurrences which arise at the critical points. Parameter continuation also gives a more dependable system to analyze a dynamical system as it is more stable than more interactive, time-stepped numerical solutions. Especially in cases where the dynamical system is prone to blow-up at certain parameter values (or combination of values for multiple parameters). It is extremely insightful as to the presence of stable solutions (attracting or repelling) in the study of Nonlinear Partial Differential Equations where times stepping in the form of the Crank Nicolson algorithm is extremely time consuming as well as unstable in cases of nonlinear growth of the dependent variables in the system.
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Teams eliminated from playoffs can affect other teams in the league as they play, often having a spoiler effect on teams still in contention for playoff spots. For example, a baseball team that is ten games out of contention for a playoff berth could defeat a team that has a playoff berth several times. This could cause the would-be playoff team to be passed by in the rankings by the team directly behind it before the final positions at the end of the season are determined. In individual participant sports, such as automobile racing, a racer with no hope of obtaining a championship title could prevent a racer with a chance at the title by defeating them, preventing the contending racer from earning critical points toward winning the title.
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In 2011–2013, as a Marie Curie Incoming International Fellowship recipient (ACOLA project), he was working at the Department of Chemical Physics in Weitzmann Institute in Israel. His work was concentrated on the analysis of quantum control landscapes and, jointly with D.J. Tannor drawing a distinction between kinematic and dynamic critical points he demonstrated the existence of trapping behaviour for quantum control systems. His present affiliations are with the Steklov Institute of Mathematics (in the period from 2016 to 2019 he headed the Laboratory of Mathematical Methods for Quantum Technologies there, which in 2019 grew up in the Department of Mathematical Methods for Quantum Technologies under his leadership)Department at the Steklov Institute headed by A. Pechen (website) and National University of Science and Technology MISiS, both located in Moscow. In 2013–2016, he served as Academic Secretary of the Steklov Institute.
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During the 2005 World Series, a new white banner was introduced. This would resemble a chrome finish, and the team abbreviations became white letters in the team's main color; the next few years, the new banner was adopted for all games. This banner, unlike the 2001–2004 version, would not be removed for the final out of the World Series but was dropped at other critical points (like whenever Alex Rodriguez came to bat, tied with an April record 14 home runs, and when Barry Bonds had 753). Beginning with the 2006 NFL season, Fox's other properties, the NFL, NASCAR, the Bowl Championship Series, and Formula One, again upgraded their graphics packages (Formula One used a different graphics package than the other three properties), but baseball broadcasts continued to use this on-screen design in 2007.
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The base of the manifold had an additional bifurcated duct that ran aft through either side of the fuselage, providing additional thrust to supplement the fishtails in the wing; these two jet nozzles could be furnished with pilot-controlled spoilers. A further duct from the manifold supplies the pitch and yaw control nozzles present in the tail unit, as well as another duct for a pitch-trim nozzle. The extensive ducting necessitated careful insulation and heat-shielding to safely contain the hot gasses; despite this, traditional lightweight alloys were used extensively across the main structure, save for a few critical points. View of the nose and forward fuselage The fuselage is of conventional stressed-skin construction, the structuring being a mix of longitudinal members and vertical frames, reinforced at key areas such as the wings, undercarriage and engine mounting.
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Misiurewicz points are named after the Polish-American mathematician Michał Misiurewicz.Michał Misiurewicz home page, Indiana University-Purdue University Indianapolis Note that the term "Misiurewicz point" is used ambiguously: Misiurewicz originally investigated maps in which all critical points were non-recurrent (that is, there is a neighborhood of every critical point that is not visited by the orbit of this critical point), and this meaning is firmly established in the context of dynamics of iterated interval maps.Wellington de Melo, Sebastian van Strien, "One-dimensional dynamics". Monograph, Springer Verlag (1991) The case that for a quadratic polynomial the unique critical point is strictly preperiodic is only a very special case; in this restricted sense (as described above) this term is used in complex dynamics; a more appropriate term would be Misiurewicz–Thurston points (after William Thurston, who investigated postcritically finite rational maps).
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Diagram showing cross- section of pitting corrosion Certain conditions, such as low concentrations of oxygen or high concentrations of species such as chloride which compete as anions, can interfere with a given alloy's ability to re-form a passivating film. In the worst case, almost all of the surface will remain protected, but tiny local fluctuations will degrade the oxide film in a few critical points. Corrosion at these points will be greatly amplified, and can cause corrosion pits of several types, depending upon conditions. While the corrosion pits only nucleate under fairly extreme circumstances, they can continue to grow even when conditions return to normal, since the interior of a pit is naturally deprived of oxygen and locally the pH decreases to very low values and the corrosion rate increases due to an autocatalytic process.
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J. Michael Sproule (1997) Propaganda and Democracy, page 184, > Cambridge University Press In 1942 Cantril conducted a small-sample survey of Vichy officials in Morocco, prior to Operation Torch, that revealed the intensity of the anti-British sentiment of the French forces there. This information influenced the disposition of forces during the operation, with American troops landing near Casablanca and mixed forces at Oran and Algiers.John Gray Geer (2004) Public opinion and polling around the world: a historical encyclopedia, Volume 1, ABC-CLIO According to George Gallup, "On the basis of his opinion studies, [Cantril] advised Presidents Roosevelt, Eisenhower, and Kennnedy at critical points in history. Judged by subsequent events his advice was exceptionally sound."George Gallup (1969) "Hadley Cantril 1906 — 1969", Public Opinion Quarterly 33(3): 506 In 1955 he and Lloyd Free founded the Institute for International Social Research (IISR).
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Lexington: Lexington Books by Johansen, Ledoit and Sornette.A. Johansen, D. Sornette and O. Ledoit, Predicting Financial Crashes using discrete scale invariance, Journal of Risk 1 (4), 5–32 (1999)A. Johansen, O. Ledoit and D. Sornette, Crashes as critical points, International Journal of Theoretical and Applied Finance 3 (2), 219–255 (2000) This approach is now referred to in the literature as the JLS model. Recently, Sornette has added the S to the LPPL acronym of "log-periodic power law" to make clear that the "power law" part should not be confused with power law distributions: indeed, the "power law" refers to the hyperbolic singularity of the form \ln[p(t)] = \ln[p(t_c)] - B (t_c -t)^m, where \ln[p(t)] is the logarithm of the price at time t, 00 and t_c is the critical time of the end of the bubble.
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During the so-called Fantastic War (1762-1763) between Portugal and Spain and the simultaneous Seven Years’ War that involved most European powers, three support batteries were built under the guidance of the Count of Schaumburg-Lippe on the 2 kilometer stretch of coastline covering Cresmina Beach and Guincho Beach on the west coast of Portugal, north of the River Tagus estuary. Their main objective was to provide quarters for small garrisons that could hinder the landing of Franco- Spanish forces via the beaches, where troops could be easily landed. This would allow time for the alarm to be raised to enable critical points in the defence of Lisbon, 30km away, to be reinforced. The Cresmina battery was the most southerly of the three batteries and, in addition to protecting the beaches, also crossed fire with the Fort of São Brás de Sanxete. Rebuilding was carried out in 1793.
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Gelbart's early interest in science was inspired by his time as an undergraduate researcher in the molecular spectroscopy group of William Klemperer at Harvard. As a graduate student at the University of Chicago, with his mentors Stuart A. Rice, Karl Freed, and Joshua Jortner, he developed the modern theory of non-radiative processes ("radiationless transitions") in molecular photophysics. He was a US National Science Foundation/NATO Postdoctoral Fellow at the, University of Paris in 1971, and a Miller Institute Postdoctoral Fellow at UC Berkeley in 1972, during which time he switched fields and formulated a general theory of collision-induced optical properties of simple fluids. He was appointed Assistant Professor of Chemistry, at UC Berkeley in 1972, continuing his researches on the quantum mechanical theory of molecular spectroscopy and on the statistical mechanical theory of intermolecular and multiple light scattering in liquids away from and near their critical points.
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On different occasions, the National Force was called in the state of Espírito Santo as well as in the state of Mato Grosso do Sul, primarily to help containing rebellions inside prisons. On another occasion, the federal government offered to send the National Force to assist the state of São Paulo against acts of violence organized there, in 2006, again by prisoners against the state public safety forces, but the federal government offer was refused by the state government, as the state claimed control over the prisoners. The governor of the state of Rio de Janeiro, Sérgio Cabral Filho asked for support from the National Public Security Force back in 2007 when the state suffered from a wave of attacks by several criminal factions. The Federal Government agreed to send a contingent of about 500 men and 52 vehicles to patrol 19 critical points within the state, mostly the favelas' areas.
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Two other mission assignments were to deploy the Global Low Orbiting Message Relay Satellite (GLOMR) out of a Getaway Special canister in the cargo bay, and to operate five materials processing experiments, which were mounted in the orbiter's payload bay on a separate device called the German Unique Support Structure. The experiments included investigations into fluid physics, with experiments in capillarity, Marangoni convection, diffusion phenomena, and critical points; solidification experiments; single crystal growth; composites; biological studies, including cell functions, developmental processes, and the ability of plants to perceive gravity; medical experiments, including the gravitational perceptions of humans, and their adaptation processes in space; and speed-time interaction studies of people working in space. One equipment item of unusual interest was the Vestibular Sled, an ESA contribution consisting of a seat for a test subject that could be moved backward and forward with precisely controlled accelerations and stops, along rails fixed to the floor of the Spacelab aisle.
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Although the immediate cause of an almost complete failure of the maize harvest in large parts of the Shire Highlands was a lack of rain at critical points in the growing season, the extent and intensity of the ensuing famine in the area has been attributed to a number of additional causes. Later research has cast doubt on the reality of those causes that were widely canvassed at the time, and suggested other possible reasons. Even before 1949, Nyasaland's colonial Agriculture Department held negative views about African agricultural practices, and predicted that, unless they were checked, they would cause a rapid decline in soil fertilityVaughan (1987), pp. 60-1, 64-9. This opinion has been contradicted by more recent research, which showed that in 1998, almost 50 years after the 1949 famine, most soils in Malawi were adequate for growing maize, as fertility had declined much less rapidly than the department had forecast.
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While Hall appreciates the good effects this first view of cultural identity has had in the postcolonial world, he proposes a second definition of cultural identity that he views as superior. Hall's second definition of cultural identity "recognises that, as well as the many points of similarity, there are also critical points of deep and significant difference which constitute 'what we really are'; or rather – since history has intervened – 'what we have become.'" In this view, cultural identity is not a fixed essence rooted in the past. Instead, cultural identities “undergo constant transformation” throughout history as they are "subject to the continuous 'play' of history, culture, and power". Thus Hall defines cultural identities as “the names we give to the different ways we are positioned by, and position ourselves within, the narratives of the past.” This view of cultural identity was more challenging than the previous due to its dive into deep differences, but nonetheless it showed the mixture of the African diaspora.
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Ferguson formed one of a deputation to wait on James VI in 1583 to discharge the duty of admonishing him 'to beware of innovations in court', to check reports before credit was given to them, and remind him of the affair of the escaped Jesuit, William Holt. He jocularly told the king that Fergus was the first king of Scotland, and that he was Fergus-son; but recognising that King James had the possession and was an honest man he would give him his right. In the discussion warmth was displayed by some of the deputies, but Ferguson succeeded in giving a new turn to the topics at critical points, the result being that as they took their leave 'the king laid his hands upon every one of them.' In August of the same year Ferguson and six other ministers were cited by the king to attend a convention at St Andrews to answer for certain proceedings of the assembly.
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At a nonzero temperature phase transition, the fluctuations that develop at a critical point are governed by classical physics, because the characteristic energy of quantum fluctuations is always smaller than the characteristic Boltzmann thermal energy k_B T. At a quantum critical point, the critical fluctuations are quantum mechanical in nature, exhibiting scale invariance in both space and in time. Unlike classical critical points, where the critical fluctuations are limited to a narrow region around the phase transition, the influence of a quantum critical point is felt over a wide range of temperatures above the quantum critical point, so the effect of quantum criticality is felt without ever reaching absolute zero. Quantum criticality was first observed in ferroelectrics, in which the ferroelectric transition temperature is suppressed to zero. A wide variety of metallic ferromagnets and antiferromagnets have been observed to develop quantum critical behavior when their magnetic transition temperature is driven to zero through the application of pressure, chemical doping or magnetic fields.
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Let Ω be a connected open set in the complex plane C and ƒ:Ω → C a holomorphic function. If ƒ is not constant, then the set of the critical points of ƒ, that is, the zeros of the derivative ƒ'(z), has no limit point in Ω. So each critical point z0 of ƒ lies at the center of a disc B(z0,r) containing no other critical point of ƒ in its closure. Let γ be the boundary of B(z0,r), taken with its positive orientation. The winding number of ƒ(γ) with respect to the point ƒ(z0) is a positive integer called the ramification index of z0. If the ramification index is greater than 1, then z0 is called a ramification point of ƒ, and the corresponding critical value ƒ(z0) is called an (algebraic) branch point. Equivalently, z0 is a ramification point if there exists a holomorphic function φ defined in a neighborhood of z0 such that ƒ(z) = φ(z)(z − z0)k for some positive integer k > 1\.
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The rear area of Army Group South was not yet of elevated operational importance (the focus on the southern sector would increase as the focus of the Wehrmacht's operation was shifted towards the Caucasus in 1942 and 1943), but there were incidents of attacks by partisan groups against German supply lines. Although the Ukrainian people at large were initially either indifferent towards or even enthusiastic about the end of Soviet rule and the arrival of German forces, small groups of Red Army troops, communist functionaries, and NKVD-trained auxiliaries remained to deal damage against critical points that were of importance to the German war effort. Until October, overall activity by partisans was low and major singular acts of German military reprisals against local civilian populations were rare.The only major singular instance of a crime against humanity committed by German forces in the area until October 1941 was the mass execution of 63 male Jews, accused of sabotage of a local factory and of assistance to Soviet aircraft, in Chervone, carried out by units overseen by the 454th Security Division.
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Dos Caras would win the UWA World Heavyweight Championship twice more from El Canek during their feud, but the storyline never results in a Luchas de Apuestas match between El Canek and Dos Caras. While the UWA kept using the appeal of El Canek fighting against foreigners it was not until November 22, 1989 that they had another foreigner win the championship as Big Van Vader pinned El Canek. As time went on the UWA struggled to draw the crowds they were used to during their heyday of the 1980s the UWA had a harder time drawing a paying audience for El Canek fighting foreigners such as Buffalo Allen, P.N. News, Konnan, King Haku, or Kokina. On January 31, 1993 El Canek lost the championship to Canadian Vampire Casanova, a decision that was later held up as one of the critical points in the later demise of the UWA as the fans did not like Vampiro and the attendance dropped significantly while he was champion and never recovered even after El Canek regained the championship.
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1, 1998, pp. 189–194. 34\. Aboda, K., Kharrat, R. And Khorasha, F.: Modeling and simulation of EDC Production Rector of Abadan Petrochemical Plant, Proceeding of the 4th National Chemical Engineering Congress, Vol. 1, 1998, pp. 517–522. 35\. Pedram, B. and Kharrat, R.: Computer Simulation of Heat Pump Application in Distillation Towers, Proceeding of the 4th National Chemical Engineering Congress, Vol. 2, 1998, pp. 97–103. 36\. Ghanizadeh, S. and Kharrat, R.: Modification Reddlich-Kwong Equation of State for the prediction of Hydrocarbon Fluid Properties, Proceeding of the 4th National Chemical Engineering Congress, Vol. 2, 1998, pp. 323–335. 37\. Ghanizadeh, S. and Kharrat, R.: The Computation of Vapor Pressure Using EOS Near Critical Points, Proceeding of the 4th National Chemical Engineering Congress, Vol. 2, 1998, pp. 479–484. 38\. Kharrat, R. Afkhami F.: Experimental Study of the Application of Malas and the Effect of Salt on the Rheological & Physical Properties of Drilling Fluids, Proceeding of the 4th National Chemical Engineering Congress, Vol. 4, 1998, pp. 38–42. 39\. Tahmasibi, H., Jamialahmadi, M., and Kharrat, R.: The Investigation of Scaling in Porous Media, Proceeding of the 4th National Chemical Engineering Congress, Vol. 1, 1998, pp. 60–64. 40\.
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William Martin and Michael Russell suggest that the first cellular life forms may have evolved inside alkaline hydrothermal vents at seafloor spreading zones in the deep sea. These structures consist of microscale caverns that are coated by thin membraneous metal sulfide walls. Therefore, these structures would resolve several critical points germane to Wächtershäuser's suggestions at once: # the micro-caverns provide a means of concentrating newly synthesised molecules, thereby increasing the chance of forming oligomers; # the steep temperature gradients inside the hydrothermal vent allow for establishing "optimum zones" of partial reactions in different regions of the vent (e.g. monomer synthesis in the hotter, oligomerisation in the cooler parts); # the flow of hydrothermal water through the structure provides a constant source of building blocks and energy (chemical disequilibrium between hydrothermal hydrogen and marine carbon dioxide); # the model allows for a succession of different steps of cellular evolution (prebiotic chemistry, monomer and oligomer synthesis, peptide and protein synthesis, RNA world, ribonucleoprotein assembly and DNA world) in a single structure, facilitating exchange between all developmental stages; # synthesis of lipids as a means of "closing" the cells against the environment is not necessary, until basically all cellular functions are developed.
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The Schiller Institute updated its 2014 study on the impact of the Chinese 'New Silk Road' project and considers that the Alentejo port of Sines is a fundamental link for the success of this global initiative. The port is considered by the world's leading experts in the sector as a key link in the global trade liaison project launched in 2013 by the current president of the People's Republic of China, in particular for its special and privileged geostrategic position of connecting the continents of Africa and North and South America. The latest version of the study 'The New Silk Road becomes the world's terrestrial bridge: a shared future for mankind', which updates a first version of 2014 by the Schiller Institute (Germany) considers that the port of Sines is one of the two "critical points" for the development of this project, due to its more Atlantic vocation, alongside the Spanish port of Algeciras, which is more Mediterranean. "Not only Spain, but also Portugal, have eagerly welcomed Xi's proposal and, over the last year, have been actively working on specific proposals and projects to make this a reality," said the Schiller Institute study.
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