She wondrously brought out intricate details, inner voices and harmonic colorings.
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"They're a very unique stone with amazing patternations and colorings," she says.
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Mr. Boulez brought French-style colorings and vivid textural clarity to the scores.
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But the gossamer colorings and improvisatory fervor of Ms. Kibbey's account hooked me.
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His virile singing had rich colorings in softer passages and ringing top notes.
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And the painted designs, though staid, had Old World elegance and lovely soft colorings.
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The gravelly colorings of the bass John Relyea's stentorian voice were ideal for Hunding.
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The genes also showed a variety of colorings — cream, black, spotted, bay and chestnut.
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Last month, McDonald's announced it would part ways with all artificial colorings and preservatives.
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With each new group of foals, the distinct colorings have become stronger and more defined.
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Ms. Goerke sang splendidly, with silvery top notes and earthy colorings lower in her range.
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The conductor Kazem Abdullah drew lucid textures, rhythmic bite and abundant colorings from the orchestra.
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I've never heard John Adams's gurgling "China Gates" played with such delicacy and subtle colorings.
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Here their parts were sung with voluptuous colorings by the sisters Anu and Piia Komsi.
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But he also wanted to enrich Slavic opera, with its folkloric elements and rustic colorings.
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Mr. Kaufmann sings German lieder elegantly, while still bringing burnished, heroic colorings to his sound.
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Included are bisphenols such as BPA, phthalates, perfluoroalkyl chemicals, or PFCs, nitrates, and artificial food colorings.
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Right through this Beethoven performance she wondrously brought out intricate details, inner voices and harmonic colorings.
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At this stage of her career, Ms. Netrebko's voice abounds in richness, depth and dusky colorings.
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For some people it could be food additives, or things like preservatives, artificial sweeteners and food colorings.
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Still, the melting warmth and subtle colorings that have long characterized her singing were there to savor.
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He highlighted intriguing details, brought out myriad colorings, kept the pacing sure and never covered the singers.
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I want it to be kids' sodas and dangerous colorings and stuff you shouldn't drink when you're pregnant.
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Still, he sounded like a tenor, not a baritone with the particular colorings and weight that Verdi imagined.
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Other Rolex collectors like John Field, a physician from Texas, are drawn to vintage Rolexes with unusual colorings.
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Many of Kaija Saariaho's orchestral pieces unfold with minute and seemingly constant shifts of subtle sounds and colorings.
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Berg folds remnants of tonality, plush colorings, sweeping lyrical lines and sheer orchestral din into his atonal language.
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The mix of earthy colorings and vulnerability in the singing of soprano Evgenia Muraveva are ideal for Liza.
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Recently, Goff launched a series of photographs of hair colorings influenced by Monet, Vermeer, Munch, Warhol, Botticelli, and Klimt.
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The conductor Marco Armiliato gave a magisterial reading of this sophisticated music with its modernist colorings and rhythmic verve.
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Brodeur's latest is Ocean Series, which keeps with xenological colorings, objects that move from candy formations into futuristic astronomical forms.
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And the way he links crisp enunciation of the words to vocal sounds and colorings remains a model for singers.
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In the first book of "Images," Mr. Hough again balanced atmospheric colorings with pinpoint highlighting of Debussy's daring harmonic language.
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There was certainly much slashing intensity and incisive attack, but also gentleness and hazy colorings in the "Child Juliet" section.
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But it has niacin and other colorings added to it on purpose so your urine is a normal color after diluting.
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The words clearly inspired Mr. Abrahamsen to write music that ingeniously combines modernist astringencies, harmonic richness and strangely beautiful atmospheric colorings.
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Mr. Polenzani, ardent and impetuous as Rodolfo, summoned Italianate colorings and ringing top notes, while singing with subtlety and rhythmic punch.
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The rich sound he drew from his violin had lovely bloom during sustained passages and lean, silvery colorings during fleet ones.
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Until now, adversarial images fell apart when they were printed out and reproduced, because the textures and pixel colorings shifted slightly.
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The conductor, Nicola Luisotti, led a performance of bold contrasts and rich colorings, though marred by untidy execution and ensemble glitches.
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Ms. Chase had plenty to do, however, in Turina's sonata, rich with evocations of Spanish dance and swaths of French colorings.
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And as with "Butterfly," I found the jazz-infused arrangement very insightful into the colorings and seductive allure of Bizet's score.
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Today's parents, alarmed about the chemicals in artificial candy colorings, would have had more to worry about back then: outright poisons.
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Roughly 2000,22010 environmental chemicals on the market end up in our foods, including food additives, colorings, flavorings, pesticides, and food-packaging chemicals.
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Even during stretches of hazy colorings and harmonies, Mr. Nezét-Séguin brought out pungent dissonances and wayward inner voices with startling freshness.
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Mr. Gerhaher is a valued, thoughtful lieder singer, deploying no end of colorings and reverting at times to an unpressured natural voice.
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As the music shifted into passages of velvety richness and tremulous sonorities, Mr. Nézet-Séguin drew out Impressionist colorings and harmonic pungencies.
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The watery colorings of Debussy's "Reflets dans l'eau" and Stravinsky's Cubist-like deconstruction in "Piano-Rag-Music" offered different kinds of radicalism.
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Even during the reflective phrases of this Rachmaninoff song, she sounded resplendent, her voice rich and vibrant, with a touch of earthy colorings.
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The excellent clarinetist Derek Bermel brought warm colorings and moody reflectiveness to the solo part, while subtly drawing out all the jazzy touches.
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But, beyond its convoluted plot, the score, for all its harmonic lushness and myriad colorings, has been deemed frustratingly episodic and stylistically eclectic.
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This score, using the same instrumental and choral elements, also has atmospheric colorings and haziness, but much rhythmic spark and episodes of dancing.
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Instead, he showed a keen ear for colorings, details, intricate textures and brassy blasts of delirium, while giving attentive support to the singers.
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She sang with unforced power and rich colorings throughout the wide range of her voice, from chesty low tones to gleaming top notes.
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He brought rich colorings and tenderness to the dreamy "Paysage" étude and conveyed the hellbent fervor of "Mazeppa," with its staggering bursts of octaves.
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The particles, it turned out, were of ultramarine pigment, the finest and most expensive of blue colorings, made of lapis lazuli stone from Afghanistan.
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Both the subtle colorings and pummeling intensity came through in the compelling performance the conductor Michael Christie drew from the St. Louis Symphony Orchestra.
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Still, as Fiesco, a Genoese nobleman and Simon's unwitting adversary over 25 years, Mr. Furlanetto brought consummate style and darkly rich colorings to his performance.
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As Isolde went through swings of thwarted fury, yearning and despair, Ms. Stemme altered the colorings of her sound, from steely rawness to melting warmth.
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Here again were the Hvorostovsky hallmarks, especially the smoky colorings of his sound and his uncanny ability to shape a long phrase on a single breath.
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My. Tyson, presenting the Juilliard School's Leo B. Ruiz Memorial Recital, opened with Henri Dutilleux's Three Preludes for Piano, music of plush colorings and pointillist outbursts.
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He sang the stormy "Cortigiani" aria from Verdi's "Rigoletto," and the distinctive dark colorings of his sound and his communicative intensity came through in a valiant performance.
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Your options are as follows: The total number of colorings will be all options multiplied together, or in this case q x (q – 1) x (q – 2) = q3 –
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Although this plan didn't specifically call for eliminating sugar, it did recommend against parents feeding kids foods containing artificial flavors and colorings, suggesting that these might cause hyperactivity.
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No food colorings are used: Thai iced tea turns the grains burnt orange, gardenia fruit yields yellow, and butterfly pea flower is boiled until its petals stream blue.
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By the late 0003s, the Industrial Revolution, applied to food processing, provided a variety of new techniques and ingredients useful for committing fraud — artificial flavors, artificial colorings, chemical preservatives.
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The truth is that the pisco products the Andean neighbors are fighting over are quite different, with separate sets of rules for production, and even different colorings and tastes.
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But his distinctive sound — with its russet colorings and slightly hooded quality, combining Russian-style melancholy with velvety Italianate lyricism — was so penetrating, he could send big top notes soaring.
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Meantime, Nestle — another major candy brand — earlier committed to removing artificial flavors and at least two food colorings from all of its chocolate products, including Nestle Butterfinger, Crunch and Baby Ruth.
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In the first movement, "Prophecy," Mr. Gilbert drew out all the cinematic colorings and weighty fervor of the music, which builds to bold, brassy climaxes, without ever letting it seem overblown.
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Clariant moved what was then a unit with 2.6 billion francs in annual sales, with products including plastic colorings, additives and pigments, into a separate subsidiary, sparking speculation about the company's future.
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The soprano Erin Morley brought impressive coloratura technique and a sumptuous sound to her vibrant performance as Angelica, while the velvety colorings of Sasha Cooke's ample mezzo-soprano were ideal for Medoro.
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Then she would fire the pots over different types of wood, to achieve different colorings: A hard wood burned hotter, resulting in red; a soft wood would lend itself to darker colors.
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But accompanied by his longtime pianist, Ivari Ilja, Mr. Hvorostovsky sang with his trademark smoky colorings and affecting expressivity, including several bleakly poignant Russian songs that deal with death, grief and longing.
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She sings the arching melodic line that begins Strauss's transcendent trio with seamless phrasing and ethereal sound, her more mature voice blending poignantly with the youthful colorings of Ms. Morley and Ms. Garanca.
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Clariant, which had hired Goldman Sachs to try to rescue the merger, makes aircraft de-icer, retardant for wildfires, plastics colorings, chemicals to help oil drillers separate oil from water and ingredients for shampoos.
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Mr. Robertson drew out the music's misty colorings and hints of Finnish folk song, while emphasizing the visionary elements of this 1902 score, especially its structural daring, full of startling disruptions to the music's flow.
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Ms. Saariaho, born in Helsinki in 1952, has long been known for writing music rich with luminous sounds, astringently alluring harmonies, myriad instrumental colorings and atmospheric textures — qualities ideally suited to telling this medieval tale.
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But in the work's mysterious and murky sections, including the introductions to each of its two parts, Mr. van Zweden seemed intent on bringing out depths, inner voices, unusual colorings, tectonic harmonic shifts and other details.
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Even when I felt reservations about the music — its atmospheric palette of colorings sometimes seemed unvaried — my resistance was swept away by the spasms of intensity and eerie beauty these exceptional musicians drew from the score.
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Ordered by the maniacal Austrian governor Gesler to shoot an apple off the head of his beloved son, Tell sings the wrenching, sublimely eloquent aria "Sois immobile," which Mr. Finley performed with magnificent gravity and burnished colorings.
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She was again arresting on Tuesday, especially in the way she found different vocal colorings, sometimes dipping into the earthy depths of her voice, to convey the shifting moods of Tosca: fiery and fiercely jealous, yet vulnerable.
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Native to the tropical forests of Central and South America, these intelligent monkeys are named for their unique fur colorings, according to the New England Primate Conservancy, and mothers typically have a five- to six-month gestation period.
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The new desserts also don't contain artificial colorings or dyes, which are banned in countries like Norway, France, Austria, the UK and Finland, and which have been linked to neurological problems, brain cancer, ADD, ADHD and hyperactivity in children.
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Many companies, in fact, are in the process of generating new labels to reflect changes they are making in ingredients to respond to consumer demands for foods that don't contain things like artificial colorings and high-fructose corn syrup.
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With the strong-voiced, stalwart bass Mikhail Petrenko as Orestes, Ms. Goerke at her most vulnerable, and the orchestra playing with undulant sway and pungent colorings, the scene was a moment of affecting repose — before the murderous, harrowing finale.
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"Untitled" (2018) has a deep purple ground and flowers dominate the scene as they do in "New Mexico" (2018), where gobs of frosting-like paint suggest the petals and blood-orange colorings of a kingcup cactus, the maidens all but obscured.
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Doctors may prescribe compounded drugs to give patients an option that isn't commercially available, such as a dye-free medicine for people allergic to colorings or a liquid or suppository version of a drug that isn't normally sold that way.
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"Woke up to these colorings my daughter left for me on the kitchen table and this scripture text from my Dad," Mathews captioned a two-photo slideshow featuring Christmas-themed coloring pages and an excerpt from The Prayer of St. Francis de Sales.
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Consumers wanting to know where ingredients come from and why they are needed in a product have pushed companies like Campbell Soup, General Mills and Nestlé to rid many of their products of substances such as carrageenan, high-fructose corn syrup and artificial colorings.
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Yet in moments when Roméo feels transported by his sudden love for this winsome girl, as in the aria he performs beneath Juliette's bedroom window, Mr. Grigolo sang subdued romantic phrases with dark colorings and an emotional vulnerability that seemed to knock this impulsive Roméo off guard.
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That fits in with an idea proposed in 2014 of how domestication and the initial goal of breeding tamer animals able to live and work with people also led to a series of other traits commonly observed among domesticated animals: smaller brains, floppy ears, curly tails, varied colorings.
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My guess is that it didn't take too much work to help these young singers understand Puccini's characters, especially Jessica Sandidge, who brings a melting soprano voice and vulnerability to Mimi, the winsome seamstress stricken with tuberculosis, and Dangelo Diaz, a Peruvian tenor whose smoky colorings and ardency were well suited to Rodolfo, the poet.
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Yet, seizing on every piercing chord and astringent harmony, he also brought out boldly the contemporary elements of Poulenc's musical language, which subtly draws from diverse styles including modal French sacred music, Impressionist colorings and Neo-Classical fanfares and chorales, even sly hints of salon room insouciance during scenes in which aristocrats lament their political predicament.
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When Trinity Wall Street presented a Harrison centennial concert in April featuring a chorus and percussion ensemble from Rutgers University performing "La Koro Sutro," I was knocked out by the music's sheer inventiveness: the allure of its component parts; the instrumental colorings; the intricate choral writing that shifts from stretches of elegiac melodic lines sung in unison to intense passages where choristers alternate phrases antiphonally.
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In particular, it is never possible to move between 2-colorings of a forest (the graphs of degeneracy 1) or between -colorings of a complete graph in this way; their colorings are said to be frozen.See , remark following Proposition 2.6, p. 26. Cycle graphs of length other than four also have disconnected families of -colorings., p. 37.
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For a graph G on n vertices, let e_k denote the number of colorings using exactly k colors up to renaming colors (so colorings that can be obtained from one another by permuting colors are counted as one; colorings obtained by automorphisms of G are still counted separately). In other words, e_k counts the number of partitions of the vertex set into k (non-empty) independent sets. Then k! \cdot e_k counts the number of colorings using exactly k colors (with distinguishable colors).
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The 3-colorings of a path graph, which has degeneracy one. The diameter of this space of colorings is four: it takes four steps to get from either of the top two colorings to the bottom one. In the mathematics of graph coloring, Cereceda’s conjecture is an unsolved problem on the distance between pairs of colorings of sparse graphs. It states that, for two different colorings of a graph of degeneracy , both using at most colors, it should be possible to reconfigure one coloring into the other by changing the color of one vertex at a time, using a number of steps that is quadratic in the size of the graph.
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However, with one additional color, using colorings with colors, all pairs of colorings can be connected to each other by sequences of moves of this type. It follows from this that an appropriately designed random walk on the space of -colorings, using moves of this type, is mixing. This means that the random walk will eventually converge to the discrete uniform distribution on these colorings as its steady state, in which all colorings have equal probability of being chosen. More precisely, the random walk proceeds by repeatedly choosing a uniformly random vertex and choosing uniformly at random among all the available colors for that vertex, including the color it already had; this process is called the Glauber dynamics.
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The fact that the Glauber dynamics converges to the uniform distribution on -colorings naturally raises the question of how quickly it converges. That is, what is the mixing time? A lower bound on the mixing time is the diameter of the space of colorings, the maximum (over pairs of colorings) of the number of steps needed to change one coloring of the pair into the other. If the diameter is exponentially large in the number of vertices in the graph, then the Glauber dynamics on colorings is certainly not rapidly mixing.
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Nanoencapuslation in foods involves the changing of textures, flavorings, colorings, and stability in shelf-life.
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Although Cereceda's conjecture itself remains open even for degeneracy , it is known that for any fixed value of the diameter of the space of -colorings is polynomial (with a different polynomial for different values of ). More precisely, the diameter is . When the number of colorings is at least , the diameter is quadratic. A related question concerns the possibility that, for numbers of colors greater than , the diameter of the space of colorings might decrease from quadratic to linear.
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These moves may have stronger mixing properties and lower diameter of the space of colorings. For instance, both the Kempe dynamics and the heat bath dynamics mix rapidly on 3-colorings of cycle graphs, whereas the Glauber dynamics is not even connected when the length of the cycle is not four.
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Although Cereceda asked this question for a range of colors and did not phrase it as a conjecture, by 2018 a form of this question became known as Cereceda's conjecture. This unproven hypothesis is the most optimistic possibility among the questions posed by Cereceda: that for graphs with degeneracy at most , and for -colorings of these graphs, the diameter of the space of colorings is . If true, this would be best possible, as the space of 3-colorings of a path graph has quadratic diameter.
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Apollonian networks also provide examples of planar graphs having as few -colorings as possible for .The fact that Apollonian networks minimize the number of colorings with more than four of colors was shown in a dual form for colorings of maps by . The Apollonian networks are also exactly the maximal planar graphs that (once an exterior face is fixed) have a unique Schnyder wood, a partition of the edges of the graph into three interleaved trees rooted at the three vertices of the exterior face.; .
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The hues exhibited by caramel colorings and beers are fairly limited in range. The Linner hue index is used to quantify the hue of such products.
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Fur color can be influenced by environmental surrounds, and it has been found that populations in soil rich areas tend to have darker colorings than grassland living populations.
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For some graphs, such as bipartite graphs and high- degree planar graphs, the number of colors is always , and for multigraphs, the number of colors may be as large as . There are polynomial time algorithms that construct optimal colorings of bipartite graphs, and colorings of non- bipartite simple graphs that use at most colors; however, the general problem of finding an optimal edge coloring is NP-hard and the fastest known algorithms for it take exponential time. Many variations of the edge coloring problem, in which an assignments of colors to edges must satisfy other conditions than non-adjacency, have been studied. Edge colorings have applications in scheduling problems and in frequency assignment for fiber optic networks.
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His colorings are characterized by a strong reddish color and a greenish or grayish shading. Johan Stålbom married about 1757 with Susanna Beata Hammardahl. Stålbom died at Grebo in Östergötland, Sweden.
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The labels on adjacent vertices must not be additive inverses if the vertices are connected by a negative edge. There can be no proper coloring of a signed graph with a positive loop. When restricting the vertex labels to the set of integers with magnitude at most a natural number k, the set of proper colorings of a signed graph is finite. The relation between the number of such proper colorings and k is a polynomial in k.
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In knot theory, the Borromean rings are a simple example of a Brunnian link: although each pair of rings is unlinked, the whole link cannot be unlinked. There are a number of ways of seeing that the Borromean rings are linked; one is to count their Fox -colorings. A trivial link would have 125 Fox 5-colorings (one for each choice of color for each of the three links), but the Borromean rings have only five.
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He was named a Distinguished Professor in 2016. As well as his work in pure mathematics, Torres has also published works on light scattering mechanisms for the colorings of birds and insects.
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Hamiltonian colorings are a variation on antipodal colorings where, instead of considering the regular distance between nodes, the detour distance is instead considered. Specifically, a Hamiltonian coloring's nodes have the property that the detour distance plus the difference in colors is greater than or equal to one less than n, the number of nodes in the graph. If the graph G is a path, then any Hamiltonian coloring is also an antipodal coloring, which is the inspiration for the definition of Hamiltonian coloring.
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Greedy coloring algorithms have been applied to scheduling and register allocation problems, the analysis of combinatorial games, and the proofs of other mathematical results including Brooks' theorem on the relation between coloring and degree. Other concepts in graph theory derived from greedy colorings include the Grundy number of a graph (the largest number of colors that can be found by a greedy coloring), and the well-colored graphs, graphs for which all greedy colorings use the same number of colors.
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A Δ-coloring, or even a Δ-list-coloring, of a degree-Δ graph may be found in linear time.. Efficient algorithms are also known for finding Brooks colorings in parallel and distributed models of computation.; ; ; .
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All proper vertex colorings of vertex graphs with 3 vertices using k colors for k=0,1,2,3. The chromatic polynomial of each graph interpolates through the number of proper colorings. For a graph G, P(G,k) counts the number of its (proper) vertex k-colorings. Other commonly used notations include P_G(k), \chi_G(k), or \pi_G(k). There is a unique polynomial P(G,x) which evaluated at any integer k ≥ 0 coincides with P(G,k); it is called the chromatic polynomial of G. For example, to color the path graph P_3 on 3 vertices with k colors, one may choose any of the k colors for the first vertex, any of the k - 1 remaining colors for the second vertex, and lastly for the third vertex, any of the k - 1 colors that are different from the second vertex's choice.
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"Ital", which is derived from the word vital, means essential to human existence. Ital cooking in its strictest form prohibits the use of salt, meat (especially pork), preservatives, colorings, flavorings and anything artificial. Most Rastafari are vegetarian.
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The tournament has one vertex for each color in the coloring. For each pair of colors, there is an edge in the colored graph with those two colors at its endpoints, which lends its orientation to the edge in the tournament between the vertices corresponding to the two colors. Incomplete colorings may also be represented by homomorphisms into tournaments but in this case the correspondence between colorings and homomorphisms is not one-to-one. Undirected graphs of bounded genus, bounded degree, or bounded acyclic chromatic number also have bounded oriented chromatic number.
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There are several different versions of the Adidas Stan Smith. Most commonly, they are white with grass-green heel. but there are also other colorings. Since the mid-1990s, some versions come with velcro straps instead of laces.
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Uniform tilings are listed by their vertex configuration, the sequence of faces that exist on each vertex. For example 4.8.8 means one square and two octagons on a vertex. These 11 uniform tilings have 32 different uniform colorings.
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Each roll of Necco Wafers contains eight flavors: lemon (yellow), lime (green), orange (orange), clove (purple), cinnamon (white), wintergreen (pink), licorice (black), and chocolate (brown). The ingredients in Necco Wafers are sugar, corn syrup, gelatin, gums, colorings and flavorings.
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The difference is, this is a different individual. A different individual of the same species. As in a snake is a snake, but different snakes are different. Their colorings are different, different parts of their characteristics, their facial structures, subtle differences.
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Other musicians include Joey Baron, Marc Ribot, Bill Frisell, Brad Mehldau, and David Byrne.Lynch, David (March 23, 2001) "Vinicius Cantuária, Azucar, Thursday, March 15". The Austin Chronicle. The JazzTimes described the music as containing "a traditional Brazilian atmosphere with contemporary colorings".
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The FD&C; is perhaps best known by the consumer because of its use in the naming of food coloring additives, such as "FD&C; Yellow No. 6." The Act made the certification of some food color additives mandatory. Some food colorings are generally recognized as safe (GRAS) by the FDA and do not require certification.US FDA/CFSAN: Color Additive Status List The FDA lists nine FD&C; (Food, Drugs & Cosmetics) certified color additives for use in foods in the United States, and numerous D&C; (Drugs & Cosmetics) colorings allowed only in drugs for external application or cosmetics.
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Therefore circle graphs capture various aspects of this routing problem. Colorings of circle graphs may also be used to find book embeddings of arbitrary graphs: if the vertices of a given graph G are arranged on a circle, with the edges of G forming chords of the circle, then the intersection graph of these chords is a circle graph and colorings of this circle graph are equivalent to book embeddings that respect the given circular layout. In this equivalence, the number of colors in the coloring corresponds to the number of pages in the book embedding.
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Two greedy colorings of the same crown graph using different vertex orders. The right example generalises to 2-colorable graphs with vertices, where the greedy algorithm expends colors. In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but they do not in general use the minimum number of colors possible.
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The Galiceno stands between high, and weigh between . They are usually bay, black, or chestnut, while pinto colorings are not allowed by the United States registry. They have a nicely proportioned head with a straight profile. The neck is short and muscular.
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The Howard Johnson was also sold by IHC, whilst the Truck station and Freight Terminal kits have appeared in other ranges over the years and are still available, but now as part of the Walther's Trainline range and with different colorings and markings.
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Ann Natalie Trenk is an American mathematician interested in graph theory and the theory of partially ordered sets, and known for her research on proper distinguishing colorings of graphs and on tolerance graphs. She is a professor of mathematics at Wellesley College.
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Some higher-priced hydrolyzed vegetable protein products with no added sugar or colorings are sold as low-sodium soy sauce alternatives called "liquid aminos" in health food stores, similar to the way salt substitutes are used. These products are, however, not necessarily low in sodium.
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See, e.g., . Such restrictions may cause the required number of colors to increase, as they prevent certain colorings from being considered acceptable. For instance, if a coloring of the plane consists of regions bounded by Jordan curves, then at least six colors are required.
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On the other hand, when the diameter is bounded by a polynomial function of , this suggests that the mixing time might also be polynomial. In his 2007 doctoral dissertation, Cereceda investigated this problem, and found that (even for connected components of the space of colors) the diameter can be exponential for -colorings of -degenerate graphs. On the other hand, he proved that the diameter of the color space is at most quadratic (or, in big O notation, ) for colorings that use at least colors. He wrote that "it remains to determine" whether the diameter is polynomial for numbers of colors between these two extremes, or whether it is "perhaps even quadratic".
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General homomorphisms can also be thought of as a kind of coloring: if the vertices of a fixed graph H are the available colors and edges of H describe which colors are compatible, then an H-coloring of G is an assignment of colors to vertices of G such that adjacent vertices get compatible colors. Many notions of graph coloring fit into this pattern and can be expressed as graph homomorphisms into different families of graphs. Circular colorings can be defined using homomorphisms into circular complete graphs, refining the usual notion of colorings. Fractional and b-fold coloring can be defined using homomorphisms into Kneser graphs.
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Food colorings, commonly gardenia (yellow), rock tripe powder (grey), mugwort powder (green), and devil's-tongue powder (pink), are then added and mixed with small amount of water. Colored and white (uncolored) rice flour are then laid on a cloth-lined siru in about thick layers and steamed.
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The FN 509 is a striker-fired handgun with a stainless steel slide with ferritic nitrocarburizing finish and a polymer frame. Black and flat dark earth (FDE) colorings are available. Barrel length is . The slide has serrations on both front and back, for easy slide manipulation.
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A bipartite graph is (a, b)-biregular if everyvertex in one part has degree a and every vertex in the other part has degree b. It has been conjectured that all such graphs have interval colorings. Hansen proved that every bipartite graph G with ∆(G) ≤ 3 is interval colorable.
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Anna is also known for her unique pen and ink drawings, wherein she used shadings and colorings on scripted text to appear to magically form images of famous presidents and portrayals of Christ on the page. These drawings can be found in a number of Christian bookstores today.
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Mikado yellow Mikado yellow is a shade of yellow. The color is displayed at right. It is one of the colors of the national flags of Colombia and Kazakhstan. It was also once used for Lincoln automobiles,1968 Lincoln colors and is the name of various dyes and colorings.
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Although tartrazine is one of various food colors said to cause food intolerance and ADHD-like behavior in children, evidence for this claim is lacking. It is possible that certain food colorings may act as a trigger in those who are genetically predisposed, but the evidence for this effect is weak.
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Music as luminous and intimate as a Monet painting has become the standard from pianist Kevin Kern, whose In the Enchanted Garden has become a cherished favorite in over 40 countries. Subtle colorings, including violins, cellos and clarinet, combine with gentle and eloquent piano songs to evoke a setting for Summer Daydreams.
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It fuels some spirit lamps. Ethanol intended for industrial use is often produced from ethylene. Ethanol has widespread use as a solvent of substances intended for human contact or consumption, including scents, flavorings, colorings, and medicines. In chemistry, it is both a solvent and a feedstock for the synthesis of other products.
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Since the 1970s and the well- publicised advocacy of Benjamin Feingold, there has been public concern that food colorings may cause ADHD-like behavior in children. These concerns have led the FDA and other food safety authorities to regularly review the scientific literature, and led the UK FSA to commission a study by researchers at Southampton University of the effect of a mixture of six food dyes (Tartrazine, Allura Red, Ponceau 4R, Quinoline Yellow WS, Sunset Yellow and Carmoisine (dubbed the "Southampton 6")) and sodium benzoate (a preservative) on children in the general population, who consumed them in beverages; the study published in 2007. The study found "a possible link between the consumption of these artificial colours and a sodium benzoate preservative and increased hyperactivity" in the children; the advisory committee to the FDA that evaluated the study also determined that "because of study limitations, the results could not be extrapolated to the general population, and further testing was recommended". The European regulatory community, with a stronger emphasis on the precautionary principle, required labelling and temporarily reduced the acceptable daily intake (ADI) for the food colorings; the UK FSA called for voluntary withdrawal of the colorings by food manufacturers.
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Following a citizen petition filed by the Center for Science in the Public Interest in 2008, requesting the FDA ban several food additives, the FDA reviewed the available evidence, and still made no changes. The European regulatory community, with an emphasis on the precautionary principle, required labelling and temporarily reduced the acceptable daily intake (ADI) for the food colorings; the UK FSA called for voluntary withdrawal of the colorings by food manufacturers. However, in 2009 the EFSA re-evaluated the data at hand and determined that "the available scientific evidence does not substantiate a link between the color additives and behavioral effects" for any of the dyes.EFSA Panel on Food Additives and Nutrient Sources added to Food (ANS) 091113 efsa.europa.
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T-colorings correspond to homomorphisms into certain infinite graphs. An oriented coloring of a directed graph is a homomorphism into any oriented graph. An L(2,1)-coloring is a homomorphism into the complement of the path graph that is locally injective, meaning it is required to be injective on the neighbourhood of every vertex.
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Its appearance remained more or less constantly the same, yet varied in the use of the brush, the colorings and in the drawing, in order to bring up new aspects of an until then still unknown transcendent spirituality. Unlike Wassily Kandinsky, he never moved into pure abstraction and always based his forms on nature.
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In May 2016, The New York Times reviewed her performance of Beethoven's Hammerklavier Sonata: > Ms. Wang's virtuosity goes well beyond uncanny facility. Right through this > Beethoven performance she wondrously brought out intricate details, inner > voices and harmonic colorings. The first movement had élan and daring. The > scherzo skipped along with mischievousness and rhythmic bite.
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Eight asymmetric graphs, each given a distinguishing coloring with only one color (red) A graph has distinguishing number one if and only if it is asymmetric.See, e.g., For instance, the Frucht graph has a distinguishing coloring with only one color. In a complete graph, the only distinguishing colorings assign a different color to each vertex.
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A glass of cola served with ice cubes and lemon A soft drink is a beverage that typically contains carbonated water, one or more flavourings and sweeteners such as sugar, HFCS, fruit juices, and/or sugar substitutes such as sucralose, acesulfame-K, aspartame and cyclamate. Soft drinks may also contain caffeine, colorings, preservatives and other ingredients.
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Sphaerodactylus klauberi is one of the larger-sized Sphaerodactylus species. It may attain a snout-to-vent length (SVL) of . Its colorings consist of a dark-brown upper body with darker-brown or black spots which become larger on the tail. The underbody is usually orange or reddish- pink with a gray throat that may have dark mottled areas.
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This is a deep chestnut-brown backed bird, with neck collar colorings of black and white flecking; the entire belly has the same black and white mottling. It has a medium to long, stout pointed bill. The species is named for the two ornithologists-bird collectors who first described the species, Count Hans von Berlepsch and C. Riker.
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The ovate body of an adult sea apple can grow up to long. A central mouth-like cavity is surrounded by feathery tentacles, which add additional length. Sea apples, like many echinoderms, have rows of tube feet which help them move over and adhere to structures. The bodies and tentacles of sea apples come in many different colorings.
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The star chromatic number \chi_s(G) of G is the fewest colors needed to star color G. One generalization of star coloring is the closely related concept of acyclic coloring, where it is required that every cycle uses at least three colors, so the two-color induced subgraphs are forests. If we denote the acyclic chromatic number of a graph G by \chi_a(G), we have that \chi_a(G) \leq \chi_s(G), and in fact every star coloring of G is an acyclic coloring. The star chromatic number has been proved to be bounded on every proper minor closed class by . This results was further generalized by to all low-tree-depth colorings (standard coloring and star coloring being low-tree-depth colorings with respective parameter 1 and 2).
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Different choices of the sequence of vertices will typically produce different colorings of the given graph, so much of the study of greedy colorings has concerned how to find a good ordering. There always exists an ordering that produces an optimal coloring, but although such orderings can be found for many special classes of graphs, they are hard to find in general. Commonly used strategies for vertex ordering involve placing higher-degree vertices earlier than lower-degree vertices, or choosing vertices with fewer available colors in preference to vertices that are less constrained. Variations of greedy coloring choose the colors in an online manner, without any knowledge of the structure of the uncolored part of the graph, or choose other colors than the first available in order to reduce the total number of colors.
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It is possible that certain food colorings may act as a trigger in those who are genetically predisposed, but the evidence is weak. Despite concerns expressed that food colorings may cause ADHD-like behavior in children,FDA. Background Document for the Food Advisory Committee: Certified Color Additives in Food and Possible Association with Attention Deficit Hyperactivity Disorder in Children: March 30-31, 2011 the collective evidence does not support this assertion. The US FDA and other food safety authorities regularly review the scientific literature, and led the UK Food Standards Agency (FSA) to commission a study by researchers at Southampton University of the effect of a mixture of six food dyes (Tartrazine, Allura Red, Ponceau 4R, Quinoline Yellow WS, Sunset Yellow and Carmoisine (dubbed the "Southampton 6")) on children in the general population.
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DDW, The Color House (D.D. Williamson) is a global, privately held corporation providing caramel color, burnt sugar & natural colorings for the food and beverage industry. In 1865, Dutch immigrant Douw Ditmars Williamson founded D.D. Williamson in New York to manufacture burnt sugars for the brewing industry. The caramel industry moved into coloring cola and many other foods following Prohibition and the Great Depression.
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Erzya and Moksha folk costumes had reached their complete artistic expressiveness by the middle of the 19th century The people, who worked on the land, could make fabrics themselves. They produced linen or stout canvas for hempen shirts, woolen cloth for warm clothes, brightly colored wool embroidery threads. They were painted using vegetable colorings. The most interesting is the women's clothing.
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It is very similar to Sholezard, an Iranian dessert. Often in Pakistan, instead of yellow food coloring, multiple food colorings are added so the rice grains are of multiple colors. Additionally, khoya, candied fruits (murabba) and nuts are an essential part of zarda made at auspicious occasions. There also is a popular use of raisins, and other dried fruits to dish.
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Lieb used a transfer-matrix method to compute this exactly. The function f(n) also counts the number of 3-colorings of grid graphs, the number of nowhere-zero 3-flows in 4-regular graphs, and the number of local flat foldings of the Miura fold. Some historical and physical background can be found in the article Ice-type model.
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By Ramsey's theorem, for any finite number k of colors, there exists a number n such that complete graphs of n or more vertices do not have triangle-free edge colorings with k colors. For k = 2, the corresponding value of n is 6. That is, the answer to the monochromatic triangle problem on the complete graph K6 is no.
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Different trees will, in general, correspond to different Shabat polynomials, as will different embeddings or colorings of the same tree. Up to normalization and linear transformations of its argument, the Shabat polynomial is uniquely determined from a coloring of an embedded tree, but it is not always straightforward to find a Shabat polynomial that has a given embedded tree as its dessin d'enfant.
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Sperner colorings have been used for effective computation of fixed points. A Sperner coloring can be constructed such that fully labeled simplices correspond to fixed points of a given function. By making a triangulation smaller and smaller, one can show that the limit of the fully labeled simplices is exactly the fixed point. Hence, the technique provides a way to approximate fixed points.
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With the degeneracy ordering, the greedy coloring will use at most colors. This is because, when colored, each vertex will have at most already-colored neighbors, so one of the first colors will be free for it to use.; . Greedy coloring with the degeneracy ordering can find optimal colorings for certain classes of graphs, including trees, pseudoforests, and crown graphs.
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The new engine produced 130HP and pushed the 1998 XP to 60 mph. Graphically, the lower hull, cowling, and handle pole cover were now black, and the hood and cowling pod were metallic gray. The 1999 XP Limited mainly featured graphic changes, as the hull colorings remained unchanged from 1998. Many driveline upgrades were incorporated due to previous failures in the couplings.
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V. Ejov, N. Pugacheva, S. Rossomakhine, P. Zograf "An effective algorithm for the enumeration of edge colorings and Hamiltonian cycles in cubic graphs" arXiv:math/0610779v1. The Horton graph has chromatic number 2, chromatic index 3, radius 10, diameter 10, girth 6, book thickness 3Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018 and queue number 2.
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Finding a radio coloring with a given (or minimum) span is NP-complete, even when restricted to planar graphs, split graphs, or the complements of bipartite graphs.. However it is solvable in polynomial time for trees and cographs.. For arbitrary graphs, it can be solved in singly-exponential time, significantly faster than a brute-force search through all possible colorings...
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H. eleuchia engages in Müllerian mimicry with H. cydno, specifically in Ecuador. For this type of mimicry, species adopt one anothers' warning signals. In this case, coloring is used to warn a predator of the unpleasant taste of their intended prey. For instance, the subspecies H. cydno alithea has two potential colorings, one of which mimics the coloring of H. eleuchia.
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Darklands was released by MicroProse with a number of bugs, ranging from minor to major. These included many instances of what would now be called crash-to-desktop errors. Additionally, the "character colors bug" results in on-screen characters colors being replaced with random (often bright) colorings. Most of the bugs in the game were correctable by subsequently released patches.
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For instance, the number of strong orientations is and the number of acyclic orientations is .. For bridgeless planar graphs, graph colorings with colors correspond to nowhere- zero flows modulo on the dual graph. For instance, the four color theorem (the existence of a 4-coloring for every planar graph) can be expressed equivalently as stating that the dual of every bridgeless planar graph has a nowhere-zero 4-flow. The number of -colorings is counted (up to an easily computed factor) by the Tutte polynomial value and dually the number of nowhere-zero -flows is counted by . An st-planar graph is a connected planar graph together with a bipolar orientation of that graph, an orientation that makes it acyclic with a single source and a single sink, both of which are required to be on the same face as each other.
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Two vertices (or edges) of a periodic graph are symmetric if they are in the same orbit of the symmetry group of the graph; in other words, two vertices (or edges) are symmetric if there is a symmetry of the net that moves one onto the other. In chemistry, there is a tendency to refer to orbits of vertices or edges as “kinds” of vertices or edges, with the recognition that from any two vertices or any two edges (similarly oriented) of the same orbit, the geometric graph “looks the same”. Finite colorings of vertices and edges (where symmetries are to preserve colorings) may be employed. The symmetry group of a crystal net will be a (group of restrictions of a) crystallographic space group, and many of the most common crystals are of very high symmetry, i.e.
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The European regulatory community, with a stronger emphasis on the precautionary principle, required labelling and temporarily reduced the acceptable daily intake (ADI) for the food colorings; the UK FSA called for voluntary withdrawal of the colorings by food manufacturers. However, in 2009, the EFSA re-evaluated the data at hand and determined that "the available scientific evidence does not substantiate a link between the color additives and behavioral effects", and in 2014, after further review of the data, the EFSA restored the prior ADI levels.EFSA Panel on Food Additives and Nutrient Sources added to food (ANS) Reconsideration of the temporary ADI and refined exposure assessment for Sunset Yellow FCF (E 110) EFSA Journal 2014;12(7):3765 . doi:10.2903/j.efsa.2014.3765 In 2015, the EFSA found that the exposure estimates did not exceed the ADI of 7 mg/kg per day in any population.
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The European regulatory community, with a stronger emphasis on the precautionary principle, required labelling and temporarily reduced the acceptable daily intake (ADI) for the food colorings; the UK FSA called for voluntary withdrawal of the colorings by food manufacturers. However, in 2009 the EFSA re-evaluated the data at hand and determined that "the available scientific evidence does not substantiate a link between the color additives and behavioral effects". On the basis of other evidence the EFSA also reduced the acceptable daily intake (ADI) from 10 to 0.5 mg/kg. The US FDA did not make changes following the publication of the Southampton study, but following a citizen petition filed by the Center for Science in the Public Interest in 2008, requesting the FDA ban several food additives, the FDA commenced a review of the available evidence, and still made no changes.
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International Energy Statistics. United States Department of Energy To prevent confusion between kerosene and the much more flammable and volatile gasoline, some jurisdictions regulate markings or colorings for containers used to store or dispense kerosene. For example, in the United States, Pennsylvania requires that portable containers used at retail service stations for kerosene be colored blue, as opposed to red (for gasoline) or yellow (for diesel fuel).
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It is made by churning milk or cream to separate the fat globules from the buttermilk. Salt and food colorings are sometimes added to butter. Rendering butter, removing the water and milk solids, produces clarified butter or ghee, which is almost entirely butterfat. Butter is a water-in-oil emulsion resulting from an inversion of the cream, where the milk proteins are the emulsifiers.
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The use of inhibitors is dependent on the type of sugar used. The amount of inhibitor in the lollipop is usually small in comparison to the amount of sugar used. On top of that, additional flavors, colorings, and inclusions (like bubble gum or a tootsie roll) can be added to the final product, but are not a part of the main structure of a simple lollipop.
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The well-colored graphs are the graphs for which all vertex colorings produce the same number of colors. This number of colors, in these graphs, equals both the chromatic number and the Grundy number. They include the cographs, which are exactly the graphs in which all induced subgraphs are well-colored. However, it is co-NP-complete to determine whether a graph is well-colored.
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If a random graph is drawn from the Erdős–Rényi model with constant probability of including each edge, then any vertex ordering that is chosen independently of the graph edges leads to a coloring whose number of colors is close to twice the optimal value, with high probability. It remains unknown whether there is any polynomial time method for finding significantly better colorings of these graphs.
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Oligodon formosanus (Formosa kukri snake or beautiful kukri snake) is a species of snake of the family Colubridae. The scale colorings range in the brown-red spectrum. The body is a tawny light brown with two darker russet stripes running down either side of the spine, where thin black lines that break into smaller dotted patterns occasionally diagonally intersect. The underbelly is off-white.
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In planar graphs, colorings with k distinct colors are dual to nowhere zero flows over the ring \Z_k of integers modulo k. In this duality, the difference between the colors of two adjacent regions is represented by a flow value across the edge separating the regions. In particular, the existence of nowhere zero 4-flows is equivalent to the four color theorem. The snark theorem generalizes this result to nonplanar graphs.
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This lineup recorded two albums for Cuneiform Records (the first featuring Adams as well). Swope left in 1993 and was replaced by guitarist Michael Bierylo. This lineup has remained stable to 2009, and has recorded several further albums for Cuneiform. The music of the current lineup has less punk sound and more modern classical and jazz colorings than the original line-up, but their music is still very eclectic.
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As the figure dries, it is also susceptible to cracking. The cracks are filled with small pieces of copal wood and a sawdust resin mixture before painting. Oaxaca woodcarvings were all originally painted with aniline paints made with natural ingredients such as bark of the copal tree, baking soda, lime juice, pomegranate seeds, zinc, indigo, huitlacoche and cochineal. These colorings were also used for dying clothing, ceremonial paints and other uses.
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As noted above, a black bull, known as Light, and a white bull, Darkness, are introduced in Burned. The bulls were not accepted into vampyre society because this was too masculine, and vampyre society is heavily matriarchal. Their counterintuitive colorings are said to signify that each possesses something that the other wants. The bulls often take a price, or a debt, from those who ask them for favors.
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A 3-edge-coloring of the Desargues graph. In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring.
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The perfect graphs include many important families of graphs and serve to unify results relating colorings and cliques in those families. For instance, in all perfect graphs, the graph coloring problem, maximum clique problem, and maximum independent set problem can all be solved in polynomial time. In addition, several important min-max theorems in combinatorics, such as Dilworth's theorem, can be expressed in terms of the perfection of certain associated graphs.
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For example, the General Mills Betty Crocker's Cookbook, first published in 1950, was a popular book in American homes.. Highly processed foods of the mid-twentieth century included novelty elements like multi-colored Jell-O using various chemical food colorings, prepared breakfast cereals marketed to children with large amounts of sugar and artificial colors (e.g. Froot Loops). Fruit flavored punches made with artificial fruit flavorings (e.g. Tang, Hi-C).
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Let L be a link, and let π be the fundamental group of its complement, and let G be a group. A homomorphism \rho of π to G is called a G-coloring of L. A G-coloring of a knot diagram is an induced assigning an element of G to the strands of L such that, at each crossing, if c is the element of G assigned to the overcrossing strand and if a and b are the elements of G assigned to the two undercrossing strands, then a = c−1 b c or b = c−1 a c, depending on the orientation of the overcrossing strand. If the group G is dihedral of order 2n, this diagrammatic representation of a G-coloring reduces to a Fox n-coloring. The torus knot T(3,5) has only constant n-colorings, but for the group G equal to the alternating group A5, T(3,5) has non-constant G-colorings.
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The fact that the number of k-colorings is a polynomial in k follows from a recurrence relation called the deletion–contraction recurrence or Fundamental Reduction Theorem. It is based on edge contraction: for a pair of vertices u and v the graph G/uv is obtained by merging the two vertices and removing any edges between them. If u and v are adjacent in G, let G-uv denote the graph obtained by removing the edge uv. Then the numbers of k-colorings of these graphs satisfy: :P(G,k)=P(G-uv, k)- P(G/uv,k) Equivalently, if u and v are not adjacent in G and G+uv is the graph with the edge uv added, then :P(G,k)= P(G+uv, k) + P(G/uv,k) This follows from the observation that every k-coloring of G either gives different colors to u and v, or the same colors.
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Background Document for the Food Advisory Committee: Certified Color Additives in Food and Possible Association with Attention Deficit Hyperactivity Disorder in Children: March 30–31, 2011 the advisory committee to the FSA that evaluated the study also determined that because of study limitations, the results could not be extrapolated to the general population, and further testing was recommended. The European regulatory community, with a stronger emphasis on the precautionary principle, required labelling and temporarily reduced the acceptable daily intake (ADI) for the food colorings; the UK FSA called for voluntary withdrawal of the colorings by food manufacturers. However, in 2009 the EFSA re-evaluated the data at hand and determined that "the available scientific evidence does not substantiate a link between the color additives and behavioral effects." Tartrazine is among six artificial colors for which the European Union requires products that contain them to be marked with the statement May have an adverse effect on activity and attention in children.
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A coloring may or may not exist for a mixed graph. In order for a mixed graph to have a k-coloring, the graph cannot contain any directed cycles. If such a k-coloring exists, then we refer to the smallest k needed in order to properly color our graph as the chromatic number, denoted \chi(G). We can count the number of proper k-colorings as a polynomial function of k.
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It was also known as Guignet green.A. F. Holleman and E. Wiberg "Inorganic Chemistry" Academic Press, 2001, New York. Fireworks typically use barium salts to create green sparks There is no natural source for green food colorings which has been approved by the US Food and Drug Administration. Chlorophyll, the E numbers E140 and E141, is the most common green chemical found in nature, and only allowed in certain medicines and cosmetic materials.
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Sugar cake is a confection made with grated coconut, sugar and food colorings, The process of cooking is done in a saucepan on low heat to avoid burning. moulded is done immediately afterwards on a baking sheet or shallow plate. It is a popular sweet among schoolchildren in Caribbean countries including Barbados, Trinidad and Tobago, and Guyana. It was also popular during Elizabethan England due to the simple recipe and great taste.
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Montagna's use of intricate and angular drapery is linked to the works of Vivarni. His works inspired by Antonello are characterized by rounded forms whereas those inspired by Bellini feature thinner and sharper figures. His transition to use of brighter and richer colorings later in life are also attributed to Bellini's influence. A drawing with a previously mistranslated note was attributed to Montagna, but has now been identified as a gift from Bellini to Montagna.
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The Indian March was designed to look very much like Napoleon's expedition to Egypt, with engineers, painters and scientists taking part. Also meticulously devised was the public relations side of the Indian expedition. For example, the instructions for trade with the local peoples included the recommendation to sell the cloths "of the colorings most liked by the Asians". The expeditionary force was to have in stock a reserve of fireworks for festive illuminations.
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As with unsigned graphs, there is a notion of signed graph coloring. Where a coloring of a graph is a mapping from the vertex set to the natural numbers, a coloring of a signed graph is a mapping from the vertex set to the integers. The constraints on proper colorings come from the edges of the signed graph. The integers assigned to two vertices must be distinct if they are connected by a positive edge.
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H. cydno engages in the predator defense mechanism of Müllerian mimicry with H. eleuchia (specifically in Ecuador) and H. sapho by adopting colors that warn a predator of their bad taste, deterring attacks. For instance, H. cydno alithea, which has two potential colorings, mimics H. eleuchia in its yellow form, and mimics H. sapho in its white form. In contrast, H. cydno close relative, H. melpomene, mimics H. erato.Kronforst M. R., Papa R. (2015).
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Phenol is so inexpensive that it attracts many small-scale uses. It is a component of industrial paint strippers used in the aviation industry for the removal of epoxy, polyurethane and other chemically resistant coatings. Phenol derivatives have been used in the preparation of cosmetics including sunscreens, hair colorings, skin lightening preparations,DeSelms, R. H.; UV-Active Phenol Ester Compounds; Enigen Science Publishing: Washington, DC, 2008. as well as in skin toners/exfoliators.
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While the yarn used remains 100% wool, much of it is pre-dyed with commercial colorings. The craft has adapted in various ways to international trade in the designs used in the works. Some are called “commercial” as they are popular in markets rather than traditional, although traditional Zapotec designs can still be readily found. While most weavings are rugs, other products created here include blankets, pillows, director's chairs, handbags and wall hangings.
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Chick-O-Stick A Chick-O-Stick split Chick-O-Stick is a candy produced by the Atkinson Candy CompanyFood Finds: America's Best Local Foods and the People Who Produce Them - Allison Engel, Margaret Engel. pp. 81-82. that has been manufactured since the 1950s. It is made primarily from peanut butter, granulated sugar, corn syrup, and toasted coconut, with colorings and preservatives added. There is also a sugar-free version of the candy.
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The 3-clique: k(k-1)(k-2). The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial by Hassler Whitney and W. T. Tutte, linking it to the Potts model of statistical physics.
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Throughout the course of the river, the waters of the Kettle have an amber tint. This tint comes from tannins (leaf colorings) from wetlands which drain into the river, rather than manmade causes. The Kettle's flow changes fairly quickly with rainfall in the area of drainage, which is about . It is not uncommon for the river to be reduced to a trickle during dry summer spells, and rise to a whitewater torrent after a few days of rain.
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Oeneis chryxus, the chryxus Arctic or brown Arctic, is a butterfly of subfamily Satyrinae found in the far northwest regions of Canada and the United States. The brown Arctic has highly variable colorings, which tend toward light yellow to orange brown wings that help camouflage it against its mountainous rocky habitat. The larvae feed on local grasses and take two years to develop. This longer development period results in flights of adult brown Arctics only once every two years.
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Then the proper colorings arise from two different graphs. To explain, if the vertices u and v have different colors, then we might as well consider a graph where u and v are adjacent. If u and v have the same colors, we might as well consider a graph where u and v are contracted. Tutte’s curiosity about which other graph properties satisfied this recurrence led him to discover a bivariate generalization of the chromatic polynomial, the Tutte polynomial.
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Two greedy colorings of the same graph using different vertex orders. The right example generalizes to 2-colorable graphs with n vertices, where the greedy algorithm expends n/2 colors. The greedy algorithm considers the vertices in a specific order v_1,…, v_n and assigns to v_i the smallest available color not used by v_i’s neighbours among v_1,…, v_{i-1}, adding a fresh color if needed. The quality of the resulting coloring depends on the chosen ordering.
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" Regarding maps, it noted that "a good number... show Israel, the West Bank and the Gaza Strip as one geographic entity (without demarcation lines or differentiated colorings). Historically Palestinian cities (e.g., Akka, Yafa, Haifa, Safad, al-Lid, Ar-Ramla, Beer As-sabe') are included in some maps that lump together the areas controlled by the PA with those inside the State of Israel. No map of the region bears the name of "Israel" in its pre-1967 borders.
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Distinguishing colorings and distinguishing numbers were introduced by , who provided the following motivating example, based on a puzzle previously formulated by Frank Rubin: "Suppose you have a ring of keys to different doors; each key only opens one door, but they all look indistinguishable to you. How few colors do you need, in order to color the handles of the keys in such a way that you can uniquely identify each key?". Solution in vol. 12, 1980.
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It is straightforward to test whether a graph may be edge colored with one or two colors, so the first nontrivial case of edge coloring is testing whether a graph has a 3-edge-coloring. As showed, it is possible to test whether a graph has a 3-edge-coloring in time , while using only polynomial space. Although this time bound is exponential, it is significantly faster than a brute force search over all possible assignments of colors to edges. Every biconnected 3-regular graph with vertices has 3-edge-colorings; all of which can be listed in time (somewhat slower than the time to find a single coloring); as Greg Kuperberg observed, the graph of a prism over an -sided polygon has colorings (lower instead of upper bound), showing that this bound is tight.. By applying exact algorithms for vertex coloring to the line graph of the input graph, it is possible to optimally edge-color any graph with edges, regardless of the number of colors needed, in time and exponential space, or in time and only polynomial space .
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Quinn went to Williams College as an undergraduate, graduating in 1985. She earned a master's degree from the University of Illinois at Chicago in 1987, and completed her doctorate at the University of Wisconsin–Madison in 1993. Her dissertation, Colorings and Cycle Packings in Graphs and Digraphs, was supervised by Richard A. Brualdi. She taught at Occidental College until 2005, when she gave up her position as full professor and department chair to move with her husband, biologist Mark Martin, to Washington.
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A useful property of Cook's reduction is that it preserves the number of accepting answers. For example, deciding whether a given graph has a 3-coloring is another problem in NP; if a graph has 17 valid 3-colorings, the SAT formula produced by the Cook–Levin reduction will have 17 satisfying assignments. NP-completeness only refers to the run- time of the worst case instances. Many of the instances that occur in practical applications can be solved much more quickly.
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Butter remains a firm solid when refrigerated, but softens to a spreadable consistency at room temperature, and melts to a thin liquid consistency at . The density of butter is 911 grams per litre (0.950 lb per US pint). It generally has a pale yellow color, but varies from deep yellow to nearly white. Its natural, unmodified color is dependent on the source animal's feed and genetics, but the commercial manufacturing process commonly manipulates the color with food colorings like annatto or carotene.
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Neocyema is known for its vivid orange color and paedomorphic life cycle. One distinguishing feature of this group are the semi-extended jaws, which separate it from Cyematidae. The eyes of the adult form are reduced during the transition from larvae to adulthood, indicating a likelihood of blindness. The larval stage displays no black colorings, in contrast to the larval stages of other saccopharygiformes, and look similar to the orders of Eupharynx and Saccopharynx, whereas the adult stage more resembles Cyema.
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Nitrous oxide is used because it dissolves easily into the cream, and does not cause the cream to oxidize while it is in the can. Cream must have a minimum fat content of 28% to produce whipped cream with a dispenser. The recipe for the cream to be whipped typically calls for heavy cream and sugar, along with any desired flavorings or colorings. In a sealed container, this cream is pressurized with nitrous oxide, which dissolves into the cream as per its lipophilicity.
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Fahey likely got the role because, as one newspaper reviewer pointed out, she "looks enough like Liz Taylor to be her sister."Chicago Tribune, Jan 16, 1961 Fahey was not flattered by the comparison, however, telling one interviewer "the fact that I'm supposed to look like Elizabeth Whats-Her-Name had nothing to do with my getting [the part], because we don't really look alike I don't think, we just happen to have the same colorings."Lakeland Ledger, Oct. 6, 1961, p.
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Smith was instrumental in the transition from the heavy sound of military marching bands so popular before World War 1 to the lighter sounding dance music of the 1920s. Most of his recorded output are instrumentals, although Victor Records would sometimes assign an in-house vocalist to some sides. He was the first to record a Cole Porter song. Although not a jazz unit as thought of in the modern sense, Smith did often use jazz colorings in his arrangements.
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In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of a partition of the order into a minimum number of antichains. It is named for and is closely related to Dilworth's theorem on the widths of partial orders, to the perfection of comparability graphs, to the Gallai–Hasse–Roy–Vitaver theorem relating longest paths and colorings in graphs, and to the Erdős–Szekeres theorem on monotonic subsequences.
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Red tide off the California coast Various cultures divide the semantic field of colors differently from the English language usage and some do not distinguish between blue and green in the same way. An example is Welsh where glas can mean blue or green, or Vietnamese where xanh likewise can mean either. Other color names assigned to bodies of water are sea green and ultramarine blue. Unusual oceanic colorings have given rise to the terms red tide and black tide.
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The study and the generalization of this problem by Tait, Heawood, Ramsey and Hadwiger led to the study of the colorings of the graphs embedded on surfaces with arbitrary genus. Tait's reformulation generated a new class of problems, the factorization problems, particularly studied by Petersen and Kőnig. The works of Ramsey on colorations and more specially the results obtained by Turán in 1941 was at the origin of another branch of graph theory, extremal graph theory. The four color problem remained unsolved for more than a century.
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As with classical colorings, the reverse implication always holds: if G (or H, symmetrically) is K-colorable, then G × H is easily K-colored by using the same values independently of H. Hedetniemi's conjecture is then equivalent to the statement that each complete graph is multiplicative. The above known cases are equivalent to saying that K1, K2, and K3 are multiplicative. The case of K4 is widely open. On the other hand, the proof of has been generalized by to show that all cycle graphs are multiplicative.
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The muskrat's name probably comes from a word of Algonquian (possibly Powhatan) origin, muscascus (literally "it is red", so called for its colorings), or from the Abenaki native word mòskwas, as seen in the archaic English name for the animal, musquash. Because of the association with the "musky" odor, which the muskrat uses to mark its territory, and its flattened tail, the name became altered to musk-beaver;Hearne, Samuel. (1745–1792). A Journey to the Northern Ocean: The Adventures of Samuel Hearne. Surrey, BC: TouchWood Editions.
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Sweeteners, flavorings and colorings are then mixed in, and the yogurt mixture is cooled at a temperature of −6 to −2°C. To create extra volume and smooth consistency, air is incorporated into the yogurt as the mixture is agitated. With sufficient amount of air in it, the yogurt gets rapidly frozen to prevent formation of large ice crystals, and then stored in a cold place to be shipped. Frozen yogurt can be made in a soft serve freezer much the same way as soft ice cream.
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However, when is odd, colors are needed: each color can only be used for edges, a fraction of the total., problem 16.5, p. 133. The fact that either or colors are needed is an instance of Vizing's theorem. Several authors have studied edge colorings of the odd graphs, -regular graphs in which the vertices represent teams of players selected from a pool of players, and in which the edges represent possible pairings of these teams (with one player left as "odd man out" to referee the game).
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Common reasons for undertaking an elimination diet include suspected food allergies and suspected food intolerances. An elimination diet might remove one or more common foods, such as eggs or milk, or it might remove one or more minor or non-nutritive substances, such as artificial food colorings. An elimination diet relies on trial and error to identify specific allergies and intolerances. Typically, if symptoms resolve after the removal of a food from the diet, then the food is reintroduced to see whether the symptoms reappear.
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The figure shows an example of how Kempe's proof can fail for this graph. In the figure, the adjacencies between regions of this map form the Errera graph, partially four-colored with the outer region uncolored. Kempe's erroneous proof follows the idea of extending partial colorings such as this one by recoloring Kempe chains, connected subgraphs that have only two colors. Any such chain can be recolored, preserving the validity of the coloring, by swapping its two colors on all vertices of the chain.
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The report estimated that over half a million children in the United States suffer adverse behavioral reactions as a result of ingesting food dyes, with an estimated cost exceeding $5 billion per year, citing data from the Centers for Disease Control and Prevention. The report urges the Food and Drug Administration to take action to ban or curtail the use of such dyes. CSPI has urged companies to replace synthetic colorings with natural ones, and Mars, General Mills, and other major food manufacturers have begun doing so.
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In general, the surrounding graph must be systematically recolored to turn the ring's coloring into a good one, as was done in the case above where there were 4 neighbors; for a general configuration with a larger ring, this requires more complex techniques. Because of the large number of distinct four-colorings of the ring, this is the primary step requiring computer assistance. Finally, it remains to identify an unavoidable set of configurations amenable to reduction by this procedure. The primary method used to discover such a set is the method of discharging.
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White or albino ferret Ferrets with a white stripe on their face or a fully white head, primarily blazes, badgers, and pandas, almost certainly carry a congenital defect which shares some similarities to Waardenburg syndrome. This causes, among other things, a cranial deformation in the womb which broadens the skull, white face markings, and also partial or total deafness. It is estimated as many as 75 percent of ferrets with these Waardenburg-like colorings are deaf. White ferrets were favored in the Middle Ages for the ease in seeing them in thick undergrowth.
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Some flavored milk products Flavored milk is a sweetened dairy drink made with milk, sugar, flavorings, and sometimes food colorings. It may be sold as a pasteurized, refrigerated product; or as an ultra-high-temperature (UHT) treated product not requiring refrigeration. It may also be made in restaurants or homes by mixing flavorings into milk. In New England, milk blended with flavored syrups such as chocolate or strawberry in a milkshake machine, is commonly called a "milkshake"; in other parts of the country, a milkshake always includes ice cream or thickeners.
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Taffy (American English) is a type of candy. Taffy is made by stretching or pulling a sticky mass of boiled sugar, butter or vegetable oil, flavorings, and colorings until it becomes aerated (meaning that tiny air bubbles are produced, resulting in a light, fluffy and chewy candy). When this process is complete, the taffy is rolled, cut into small pastel-colored pieces and wrapped in wax paper to keep it soft. It is usually fruit-flavored, but other flavors are common as well, including molasses and the "classic" (unflavored) taffy.
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In traditional Chinese architecture, the beam can be named according to the number of purlins that it supports. Here, the beam support five purlins and thus called "five purlins cross-beam" (中文：五架梁). More information about this architectural term, please see On either side of the hall stands a room and a roofed walkway connects it with other halls at its back. The traditional decorative colorings painted on the pillars are of high artistic value and they are considered masterpieces of the Suzhou style decorative paintings ().
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Defective coloring was introduced nearly simultaneously by Burr and Jacobson, Harary and Jones and Cowen, Cowen and Woodall. Surveys of this and related colorings are given by Marietjie Frick. Cowen, Cowen and Woodall focused on graphs embedded on surfaces and gave a complete characterization of all k and d such that every planar is (k, d)-colorable. Namely, there does not exist a d such that every planar graph is (1, d)- or (2, d)-colorable; there exist planar graphs which are not (3, 1)-colorable, but every planar graph is (3, 2)-colorable.
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Information on the Public Garden from Bordeaux Tourism & Conventions It was a charity event for the benefit of Belgian war refugees sponsored by the Belgian Benevolent Society of the South West and the Girondin Artists. This event was the first of a series of exhibitions in which the art of Louis Dewis would draw serious attention from some prominent art critics of the era. :Louis Dewis embodies the Flemish spirit, in love with colorings that are warm and harmonious. He treats tenderly the humble motifs reinforcing the simplicity of their soberly translated soul.
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With Lothar Michler, Hasse wrote Theorie der Kategorien [Category Theory] (Deutscher Verlag, 1966). She also wrote Grundbegriffe der Mengenlehre und Logik [Basic Concepts of Set Theory and Logic] (Harri Deutsch, 1968). In the theory of graph coloring, the Gallai–Hasse–Roy–Vitaver theorem provides a duality between colorings of the vertices of a graph and orientations of its edges. It states that the minimum number of colors needed in a coloring equals the number of vertices in a longest path, in an orientation chosen to minimize the length of this path.
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The chromatic index should not be confused with the chromatic number or , the minimum number of colors needed in a proper vertex coloring of . Unless stated otherwise all graphs are assumed to be simple, in contrast to multigraphs in which two or more edges may be connecting the same pair of endpoints and in which there may be self-loops. For many problems in edge coloring, simple graphs behave differently from multigraphs, and additional care is needed to extend theorems about edge colorings of simple graphs to the multigraph case.
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In mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which is equivalent to it. Sperner's lemma states that every Sperner coloring (described below) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors. The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms.
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After studying chemistry in Heidelberg, Frankfurt and Freiburg, in 1931, Rudolf Wild founded his first company – Zick Zack Werk Rudolf Wild. He set the goal of producing basic materials for non-alcoholic drinks using only natural raw materials. He presented the first completely natural alcohol-free drink, with no artificial flavorings, preservatives or colorings under the brand Libella at the Interbrau trade fair in 1951. Although Rudolf Wild initially received a skeptical response from customers, his philosophy eventually won recognition as a quality characteristic throughout the beverage and food industries.
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Sing Out!. Retrieved 30 June 2014 . Quote: "Malley's inventive bass and keyboard playing works quite sympathetically with Chatterjee's resourceful drumming to give each song a harmonic structure and an unparalleled, engaging vista that transcends the strict constraints of Indian classical music, leaving the listener galvanized with the work's multiple colorings, entrancing melodies, shape-shifting tonal changes and spellbinding rhythms." His album Artistry recorded live in Kansas City with Manilal Nag on sitar, Ramesh Mishra on sarangi and Chatterjee on tabla was nominated for a Grammy Award in 2002.
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The full conjecture was proven by , and is now known as the Hajnal–Szemerédi theorem. Their original proof was long and complicated; a simpler proof was given by . A polynomial time algorithm for finding equitable colorings with this many colors was described by Kierstead and Kostochka; they credit Marcelo Mydlarz and Endre Szemerédi with a prior unpublished polynomial time algorithm. Kierstead and Kostochka also announce but do not prove a strengthening of the theorem, to show that an equitable k-coloring exists whenever every two adjacent vertices have degrees adding to at most 2k + 1\.
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The intake of dietary phenols should be limited in PST deficient patients, which is usually suggested for targeting the behavioral symptoms in autistic children. Due to the impaired ability in sulfate conjunction, a reduction in the consumption of phenols would alleviate the conditions by directly preventing its over-accumulation. Some commonly consumed foods such as apples, citrus fruits, carrots, tomatoes, and onions, together with synthetic food colorings like tartrazine, are also rich in phenols and should be avoided. Foods with an inhibitory effect on the activity of PST should also be avoided.
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Many other countries use the USP-NF instead of issuing their own pharmacopeia, or to supplement their government pharmacopeia. USP's standards for food ingredients can be found in its Food Chemicals Codex (FCC). The FCC is a compendium of standards used internationally for the quality and purity of food ingredients like preservatives, flavorings, colorings and nutrients. While the FCC is recognized in law in countries like Australia, Canada and New Zealand, it currently does not have statutory recognition in the United States, although FCC standards are incorporated by reference in over 200 FDA food regulations.
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Several algorithms are based on evaluating this recurrence and the resulting computation tree is sometimes called a Zykov tree. The running time is based on a heuristic for choosing the vertices u and v. The chromatic polynomial satisfies the following recurrence relation :P(G-uv, k)= P(G/uv, k)+ P(G, k) where u and v are adjacent vertices, and G-uv is the graph with the edge removed. P(G - uv, k) represents the number of possible proper colorings of the graph, where the vertices may have the same or different colors.
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Every penny graph contains a vertex with at most three neighbors. For instance, such a vertex can be found at one of the corners of the convex hull of the circle centers, or as one of the two farthest-apart circle centers. Therefore, penny graphs have degeneracy at most three. Based on this, one can prove that their graph colorings require at most four colors, much more easily than the proof of the more general four-color theorem.. However, despite their restricted structure, there exist penny graphs that do still require four colors.
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A blended whiskey (or blended whisky) is the product of blending different types of whiskeys and sometimes also neutral grain spirits, colorings, and flavorings. It is generally the product of mixing one or more higher-quality straight or single malt whiskey with less expensive spirits and other ingredients. This typically allows for a lower priced finished product, although expensive "premium" varieties also exist. Some examples of blended whiskey include Canadian Mist, Jameson Irish Whiskey, Seagram's Seven, Kessler Whiskey, Hibiki, and the various Scotch whisky blends sold under the Johnnie Walker brand.
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Using watercolor, gouache and oil paints, Sawyer began transforming his black and white photographs into images of glowing landscapes, in many ways reminiscent of the Hudson River School of oil painters. Commercial color film was still 30 years away, and 30 years of the golden age of hand-painted photography lay ahead. Sawyer added color to his black and white photographs by hand-painting and hand-coloring each photograph, one at a time. These early colorings were primarily grey/green, but as his skill and expertise continued, myriad colors and shades were added.
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For instance, every two-coloring of a five-cycle has a reflection symmetry. In each of these cycles, assigning a unique color to each of two adjacent vertices and using the third color for all remaining vertices results in a three-color distinguishing coloring. However, cycles of six or more vertices have distinguishing colorings with only two colors. That is, Frank Rubin's keyring puzzle requires three colors for rings of three, four or five keys, but only two colors for six or more keys or for two keys.
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Forbes, Oct 25, 2013, by Mike O'Toole with no partially hydrogenated oils, preservatives, artificial colorings, gluten, corn, or soy, and reduced sugar compared to similar candies of major brands. They produced several types of chocolate peanut butter cups and candy coated chocolate gems. After a relaunch, in March 2017, UNREAL began producing snacks with unique ingredients and creative twists, including crispy toasted quinoa and almond butter. UNREAL products are sold online and in various natural stores and conventional grocers across the United States, including Whole Foods, Sprout's Farmers Markets, Kroger, Shaw's, Market Basket, Wegman's, Big Y, and Roche Bros.
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Detox diets are dietary plans that claim to have detoxifying effects. The general idea suggests that most food contains contaminants: ingredients deemed unnecessary for human life, such as flavor enhancers, food colorings, pesticides, and preservatives. Scientists, dietitians, and doctors, while generally viewing "detox diets" as harmless (unless nutritional deficiency results), often dispute the value and need of "detox diets", due to lack of supporting factual evidence or coherent rationale. In cases where a person suffers from a disease, belief in the efficacy of a detox diet can result in delay or failure to seek effective treatment.
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Worldwide broad bean production Vicia faba is a stiffly erect, annual plant tall, with two to four stems that are square in cross-section. The leaves are long, pinnate with 2–7 leaflets, and colored a distinct glaucous () grey-green color. Unlike most other vetches, the leaves do not have tendrils for climbing over other vegetation. The flowers are long with five petals; the standard petals are white, the wing petals are white with a black spot (true black, not deep purple or blue as is the case in many "black" colorings) and the keel petals are white.
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Maque plate competing at the annual state handcrafts competition, with image of the Paricutin church There are two kinds of lacquer, laca, using more modern chemicals and maque, a pre Hispanic method using a wax derived from the female insect coccus axin found in the Tierra Caliente, as well as chia, chicalote or more recently linseed oils. These are mixed with dolomite limestone or lime-enriched plaster, locally called teputzchuta. Colorings are usually mineral in origin but sometimes from animal and vegetable sources as well. Lacquering mostly developed in the state during the colonial period in Uruapan, Patzcuaro and Quiroga.
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Modern commercial eggnog manufacturers add gelatin and other thickeners, a cost-savings measure that enables manufacturers to produce a thick beverage while using less egg and cream. "Commercial eggnog tends to contain less eggs than homemade nog". In the US, FDA regulations only require that 1.0 percent of a product's final weight be made up of egg yolk solids for it to bear the eggnog name. Under current U.S. law, commercial products sold as eggnog are permitted to contain milk, sugar, modified milk ingredients, glucose-fructose, water, carrageenan, guar gum, natural and artificial flavorings, spices, monoglycerides, and colorings.
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It obtains its sugar from the Sociedad Cooperativa Trabajadores del Ingenio Puruarán in Michoacán, purchasing 100% of the annual production. They also use real fruit such as mangos from Veracruz and Guerrero, strawberries from Guanajuato and apples from Puebla along with natural colorings. The company has nineteen facilities and thirty production lines, capable of producing 120 tons of fruit pulp and 470,970 cases of finished product in three shifts with an annual capacity of fifty million cases of finished product per year. It has two main processing plants Planta San Juan del Río in Querétaro and Planta Tizayuca in Hidalgo.
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On their back, Glens have a unique double coat that is wiry with a soft undercoat. The head, sides, and legs have only the softer coat, which typically develops a degree of waviness. The color of the coat may be wheaten or blue (the latter usually with brindling), with both wheaten and blue encompassing a range of shades. Other colorings do occasionally occur in Glens (including a mixture of wheaten and blue referred to as "grizzle" and a "blue and tan" that is blue on top with wheaten furnishings) but these rare variations, while not disqualifications, are not favored by fanciers.
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At his performances at the XIIth Archeological Conference in Kharkiv, Hnat Khotkevych wrote: "...Extremely valuable in his playing and singing was his ability to sing in Ukrainian, with colorings which are not possible to notate, bending his voice with unusual fine melizmas and with his whole apparatus of performance, which was strikingly different from the professional." Professor Mykola Sumtsov who was also involved with the organization of the conference wrote that the best performers were Terentiy Parkhomenko, Pavlo Drevchenko and Ivan Kucherenko. He did not include Kravchenko in his list. Kravchenko's renditions did not leave a deep impression on him.
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As an undergraduate at Yale, Chan won the 2005 Alice T. Schafer Prize for her undergraduate research, which resulted in three published papers on distinguishing colorings of Cayley graphs. Chan was given a Sloan Research Fellowship in 2018. She is the 2020 winner of the AWM- Microsoft Research Prize in Algebra and Number Theory, "in recognition of Chan’s advances at the interface between algebraic geometry and combinatorics", including "an astounding result" on the cohomology of moduli spaces, "foundational work on the moduli of metric graphs and tropical curves", and "beautiful new results on the expected number of turns in a random Young tableau".
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In 1926, she displayed 75 works (oils, woodcarvings, drawings, water-colorings, and tapestries) in the Asociacion Amigos del Arte exhibition. In 1928, she married the writer and art critic Guillermo de Torre, a student of the Ultraist movement and an expert on Avant- Garde art and literature, whom she had met in Spain when she was 19 years old. They had two children. In the Second World War, she became a vocal supporter of la Junta de la Victoria, an association of anti-fascist feminists in Argentina directed by Cora Ratto de Sadosky and Ana Rosa Schlieper de Martínez Guerrero.
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During the Tang dynasty, "Gibbons blood red" was a term used for certain vivid red dye colorings. Several Tang poets used the term in poetic imagery, including a couple of poems by Zhang Ji of Jiangnan (See, Schafer, 208–210, 234, and note 12 page 328). The use of this imagery imparted an exotic dimension to the poetry in which it appeared, since it implied the importation of dyed textiles of rare and mysterious color from distant lands the fantastic qualities of which could only be imagined, including the dye source for the spectacular red color of unknown origin.
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The conjecture was significant, because if true, it would have implied the four color theorem: as Tait described, the four-color problem is equivalent to the problem of finding 3-edge-colorings of bridgeless cubic planar graphs. In a Hamiltonian cubic planar graph, such an edge coloring is easy to find: use two colors alternately on the cycle, and a third color for all remaining edges. Alternatively, a 4-coloring of the faces of a Hamiltonian cubic planar graph may be constructed directly, using two colors for the faces inside the cycle and two more colors for the faces outside.
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Chocolate ice cream is generally made by blending cocoa powder along with the eggs, cream, vanilla and sugar used to make vanilla ice cream. Sometimes chocolate liquor is used in addition to cocoa powder, or it is used exclusively, to create the chocolate flavor. Cocoa powder gives chocolate ice cream its brown color, and it is uncommon to add other colorings. The Codex Alimentarius, which provides an international set of standards for food, states that the flavor in chocolate ice cream must come from nonfat cocoa solids that must comprise at least 2.0-2.5% of the mix weight.
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Some white horses are born with partial pigmentation in their skin and hair, which may or may not be retained as they mature, but when a white horse lightens, both skin and hair lose pigmentation. In contrast, grays retain skin pigment and only the hair becomes white. White colorings, whether white markings, white patterns or dominant white are collectively known as depigmentation phenotypes, and are all caused by areas of skin that lack pigment cells (melanocytes). Depigmentation phenotypes have various genetic causes, and those that have been studied usually map to the EDNRB and KIT genes.
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Unique key signatures are also sometimes devised for a particular composition. During the Baroque period, emotional associations with specific keys, known as the doctrine of the affections, were an important topic in music theory, but the unique tonal colorings of keys that gave rise to that doctrine were largely erased with the adoption of equal temperament. However, many musicians continue to feel that certain keys are more appropriate to certain emotions than others. Indian classical music theory continues to strongly associate keys with emotional states, times of day, and other extra-musical concepts and notably, does not employ equal temperament.
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In case the urine looks in pink, red, or lighter brown is generally caused by beets, blackberries, certain food colorings, hemolytic anemia, renal impairment, urinary tract infection, medication, porphyria, intra-abdominal bleeding, vaginal bleeding, neoplasm located in either bladder or kidneys pathways. If urine looks dark yellow or similar to orange color, it is a sign your pregnant with twins or even triplets. carotene, phenazopyridine, rifampin, warfarin and laxative. The causation or contributing factors of the urine color change to green or blue are those artificial colors seen in foods and drugs, or bilirubin medicines such as methylene blue, and urinary tract infections.
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A k-coloring, for some integer k, is an assignment of one of k colors to each vertex of a graph G such that the endpoints of each edge get different colors. The k-colorings of G correspond exactly to homomorphisms from G to the complete graph Kk. Indeed, the vertices of Kk correspond to the k colors, and two colors are adjacent as vertices of Kk if and only if they are different. Hence a function defines a homomorphism to Kk if and only if it maps adjacent vertices of G to different colors (i.e., it is a k-coloring).
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Finally, the third branch of algebraic graph theory concerns algebraic properties of invariants of graphs, and especially the chromatic polynomial, the Tutte polynomial and knot invariants. The chromatic polynomial of a graph, for example, counts the number of its proper vertex colorings. For the Petersen graph, this polynomial is t(t-1)(t-2)(t^7-12t^6+67t^5-230t^4+529t^3-814t^2+775t-352). In particular, this means that the Petersen graph cannot be properly colored with one or two colors, but can be colored in 120 different ways with 3 colors.
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Case 1: 1 Match for r21 from r12 In the Case 1 diagram, B1 cells show canonical values, which are color-coded to show their row-wise distribution in B2 triplets. Colors reflect distribution but not location or values. For this case: the B2 top row triplet (r21) has 1 value from B1 middle triplet, the other colorings can now be deduced. E.g. the B2 bottom row triplet (r23) coloring is forced by r21: the other 2 B1 middle values must go to bottom, etc. Fill in the number of B2 options for each color, 3..1, beginning top left.
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Food Unwrapped is a 2014 book about the food industry by the British writer Daniel Tapper. It is based on a BBC Channel 4 television series of the same name, and covers food science and food technology in mass-produced foods with the objective of "dispel[ing] food myths and reveal[ing] some truths about the food we buy". Subjects covered in the book include the relative merits of sea salt versus table salt; and the harm or lack of harm in artificial food colorings and flavorings. The book's author has also been a contributor to The Guardian and Waitrose Kitchen.
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Four different versions of Dusty were released in 2002, the first one packaged with the "Night Rhino" vehicle. The latter three were different colorings of the same design, packaged with the "Sand Razor" vehicle, in a two-pack with Desert Cobra C.L.A.W.S., and in a two-pack with a new version of the Shock Viper. In 2004, he was released as part of the Toys R Us exclusive "Desert Patrol Squad" set, which also included the figures Ambush, Gung Ho, Snake Eyes, Stalker and Tunnel Rat. He was also released carded in a two-pack with Zartan, as part of the "Valor vs Venom" toyline.
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If S\, is an IP set and S = C_1 \cup C_2 \cup\cdots\cup C_n, then at least one C_i\, is an IP set. This is known as Hindman's theorem or the finite sums theorem. In different terms, Hindman's theorem states that the class of IP sets is partition regular. Since the set of natural numbers itself is an IP set and partitions can also be seen as colorings, one can reformulate a special case of Hindman's theorem in more familiar terms: Suppose the natural numbers are "colored" with n different colors; each natural number gets one and only one of the n colors.
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By producing and releasing oxygen (as a byproduct of photosynthesis), cyanobacteria are thought to have converted the early oxygen-poor, reducing atmosphere into an oxidizing one, causing the Great Oxygenation Event and the "rusting of the Earth", which dramatically changed the composition of the Earth's life forms and led to the near-extinction of anaerobic organisms. Cyanobacteria produce a range of toxins known as cyanotoxins that can pose a danger to humans and animals. The cyanobacteria Synechocystis and Cyanothece are important model organisms with potential applications in biotechnology for bioethanol production, food colorings, as a source of human and animal food, dietary supplements and raw materials.
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Bluing has other miscellaneous household uses, including as an ingredient in rock crystal "gardens" (whereby a porous item is placed in a salt solution, the solution then precipitating out as crystals), and to improve the appearance of swimming-pool water. In Australia it was used as a folk remedy to relieve the itching of mosquito and sand fly bites. Laundry bluing is made of a colloid of ferric ferrocyanide (blue iron salt, also referred to as "Prussian blue") in water. Blue colorings have been added to rinse water for centuries, first in the form of powder blue or smalt, or using small lumps of indigo and starch, called stone blue.
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This means that a female will expel her eggs into the surrounding substrate and they will be fertilized by the male secreting his sperm onto them. Then, when fertilized, eggs will float to the epipelagic zone of the continental shelf where they will mature and hatch into the larval stage of development called leptocephalus. These larvae will be translucent, a camouflaging technique for the open ocean in order to avoid predation until they are able to mature more. When almost one year of age, the juveniles will begin to form their morphological colorings and will swim to the benthic zone and build their burrows.
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The Hadwiger conjecture states that the Hadwiger number is always at least as large as the chromatic number of G. That is, every graph with Hadwiger number k should have a graph coloring with at most k colors. The case k = 4 is equivalent (by Wagner's characterization of the graphs with this Hadwiger number) to the four color theorem on colorings of planar graphs, and the conjecture has also been proven for k ≤ 5, but remains unproven for larger values of k. Because of their low degeneracy, the graphs with Hadwiger number at most k can be colored by a greedy coloring algorithm using O(k ) colors.
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More concretely, it is a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices. Homomorphisms generalize various notions of graph colorings and allow the expression of an important class of constraint satisfaction problems, such as certain scheduling or frequency assignment problems. The fact that homomorphisms can be composed leads to rich algebraic structures: a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The computational complexity of finding a homomorphism between given graphs is prohibitive in general, but a lot is known about special cases that are solvable in polynomial time.
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The NP-completeness of NAE3SAT can be proven by a reduction from 3-satisfiability. The problem remains NP-complete when all clauses are monotone (meaning that variables are never negated), by Schaefer's dichotomy theorem. Monotone NAE3SAT can also be interpreted as an instance of the set splitting problem, or as a generalization of graph bipartiteness testing to 3-uniform hypergraphs: it asks whether the vertices of a hypergraph can be colored with two colors so that no hyperedge is monochromatic. More strongly, it is NP-hard to find colorings of 3-uniform hypergraphs with any constant number of colors, even when a 2-coloring exists.
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Many articles in The Fibonacci Quarterly deal directly with topics that are very closely related to Fibonacci numbers, such as Lucas numbers, the golden ratio, Zeckendorf representations, Binet forms, Fibonacci polynomials, and Chebyshev polynomials. However, many other topics, especially as related to recurrences, are also well represented. These include primes, pseudoprimes, graph colorings, Euler numbers, continued fractions, Stirling numbers, Pythagorean triples, Ramsey theory, Lucas-Bernoulli numbers, quadratic residues, higher-order recurrence sequences, nonlinear recurrence sequences, combinatorial proofs of number-theoretic identities, Diophantine equations, special matrices and determinants, the Collatz sequence, public-key crypto functions, elliptic curves, fractal dimension, hypergeometric functions, Fibonacci polytopes, geometry, graph theory, music, and art.
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A clique cover of a graph G may be seen as a graph coloring of the complement graph of G, the graph on the same vertex set that has edges between non-adjacent vertices of G. Like clique covers, graph colorings are partitions of the set of vertices, but into subsets with no adjacencies (independent sets) rather than cliques. A subset of vertices is a clique in G if and only if it is an independent set in the complement of G, so a partition of the vertices of G is a clique cover of G if and only if it is a coloring of the complement of G.
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The Blanton's brand was launched in 1984 under the guidance of the distillery's master distiller Elmer T. Lee, as the first modern bourbon brand marketed as a single barrel bourbon. The original brand name was "Blanton's Single Barrel Bourbon". A single barrel bourbon is one for which each bottling batch is produced from the contents of only one particular aging barrel – not mixed with whiskey from any other barrels (and not blended with neutral spirits, colorings, or flavorings). The company says that producing a high quality whiskey using this production method requires constant monitoring of every barrel in the middle of the warehouse by the Master Distiller.
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Marijn Heule, Oliver Kullmann and Victor W. Marek showed that such a coloring is only possible up to the number 7824. The actual statement of the theorem proved is There are possible coloring combinations for the numbers up to 7825. These possible colorings were logically and algorithmically narrowed down to around a trillion (still highly complex) cases, and those were examined using a Boolean satisfiability solver. Creating the proof took about 4 CPU-years of computation over a period of two days on the Stampede supercomputer at the Texas Advanced Computing Center and generated a 200 terabyte propositional proof, which was compressed to 68 gigabytes.
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A glass of Japanese Calpis A glass of Fanta melon soda A glass of German fassbrause A glass of ginger ale A glass of Swedish Julmust Kickapoo Joy Juice originated in the United States Orange soda Japanese Ramune Glasses of Red Bull Cola This is a list of soft drinks in order of the brand's country of origin. A soft drink is a beverage that typically contains water (often, but not always, carbonated water), usually a sweetener and usually a flavoring agent. The sweetener may be sugar, high-fructose corn syrup, fruit juice, sugar substitutes (in the case of diet drinks) or some combination of these. Soft drinks may also contain caffeine, colorings, preservatives and other ingredients.
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" Many members of standard-setting boards come from large food corporations. As more corporate members have joined, many nonorganic substances have been added to the National List of acceptable ingredients. The United States Congress has also played a role in allowing exceptions to organic food standards. In December 2005, the 2006 agricultural appropriations bill was passed with a rider allowing 38 synthetic ingredients to be used in organic foods, including food colorings, starches, sausage and hot-dog casings, hops, fish oil, chipotle chili pepper, and gelatin; this allowed Anheuser-Busch in 2007 to have its Wild Hop Lager certified organic "even though [it] uses hops grown with chemical fertilizers and sprayed with pesticides.
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The problem of computing the number of 3-colorings of a given graph is a canonical example of a #P-complete problem, so the problem of computing the coefficients of the chromatic polynomial is #P-hard. Similarly, evaluating P(G, 3) for given G is #P-complete. On the other hand, for k=0,1,2 it is easy to compute P(G, k), so the corresponding problems are polynomial-time computable. For integers k>3 the problem is #P-hard, which is established similar to the case k=3. In fact, it is known that P(G, x) is #P-hard for all x (including negative integers and even all complex numbers) except for the three “easy points”.
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" Music critic Anthony Tommasini has commented on the opera: : "Poulenc's subtle and intricate tonal language is by turns hymnal and haunting. Though scored for a large orchestra, the instruments are often used in smaller groups selected for particular effects and colorings. The most distinctive element of the score, though, is its wonderfully natural vocal writing, which captures the rhythms and lyrical flow of the libretto in eloquent music that hardly calls attention to itself yet lingers with you." Opera historian Charles Osborne wrote: : "The inexorable dramatic movement of the work is impressive and, in the final scene in which the nuns walk in procession to the guillotine chanting the Salve regina, extremely moving.
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The equality between the chromatic index and the list chromatic index has been conjectured to hold, even more generally, for arbitrary multigraphs with no self-loops; this conjecture remains open. Many other commonly studied variations of vertex coloring have also been extended to edge colorings. For instance, complete edge coloring is the edge-coloring variant of complete coloring, a proper edge coloring in which each pair of colors must be represented by at least one pair of adjacent edges and in which the goal is to maximize the total number of colors. Strong edge coloring is the edge-coloring variant of strong coloring, an edge coloring in which every two edges with adjacent endpoints must have different colors.
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Given a random graph G of order n with the vertex V(G) = {1, ..., n}, by the greedy algorithm on the number of colors, the vertices can be colored with colors 1, 2, ... (vertex 1 is colored 1, vertex 2 is colored 1 if it is not adjacent to vertex 1, otherwise it is colored 2, etc.). The number of proper colorings of random graphs given a number of q colors, called its chromatic polynomial, remains unknown so far. The scaling of zeros of the chromatic polynomial of random graphs with parameters n and the number of edges m or the connection probability p has been studied empirically using an algorithm based on symbolic pattern matching.
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Thieves fry Kenya's power grid for fast food, Al Jazeera, 28 December 2014 Adulterant use was first investigated in 1820 by the German chemist Frederick Accum, who identified many toxic metal colorings in food and drink. His work antagonized food suppliers, and he was ultimately discredited by a scandal over his alleged mutilation of books of the Royal Institution library. The physician Arthur Hill Hassall conducted extensive studies in the early 1850s, which were published in The Lancet and led to the 1860 Food Adulteration Act and other legislation. John Postgate led a further campaign, leading to another Act of 1875, which forms the basis of the modern legislation and a system of public analysts who test for adulteration.
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Because G is triangular, the degree of each vertex in a configuration is known, and all edges internal to the configuration are known, the number of vertices in G adjacent to a given configuration is fixed, and they are joined in a cycle. These vertices form the ring of the configuration; a configuration with k vertices in its ring is a k-ring configuration, and the configuration together with its ring is called the ringed configuration. As in the simple cases above, one may enumerate all distinct four-colorings of the ring; any coloring that can be extended without modification to a coloring of the configuration is called initially good. For example, the single-vertex configuration above with 3 or less neighbors were initially good.
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Vodka with Blue Curaçao syrup Like many other color additives, the primary use of Blue No. 1 is to correct or enhance natural coloring or to give colorless compounds a vivid hue. In the United States, of the two approved blue dyes (the other being Indigo carmine, or FD&C; Blue #2), Brilliant Blue FCF is the more common of the two. As a blue color, Brilliant Blue FCF is often found in cotton candy, ice cream, canned processed peas, packet soups, bottled food colorings, icings, ice pops, blueberry flavored products, children's medications, dairy products, sweetsNestle Aero packet ingredients listing barcode: 7613031579334 soft drinks, and drinks, especially the liqueur Blue Curaçao. It is also used in soaps, shampoos, mouthwash and other hygiene and cosmetics applications.
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A stronger version of the circular embedding conjecture that has also been considered is the conjecture that every biconnected graph has a circular embedding on an orientable manifold. In terms of the cycle double cover conjecture, this is equivalent to the conjecture that there exists a cycle double cover, and an orientation for each of the cycles in the cover, such that for every edge e the two cycles that cover e are oriented in opposite directions through e. Alternatively, strengthenings of the conjecture that involve colorings of the cycles in the cover have also been considered. The strongest of these is a conjecture that every bridgeless graph has a circular embedding on an orientable manifold in which the faces can be 5-colored.
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George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem. If P(G, k) denotes the number of proper colorings of G with k colors then one could establish the four color theorem by showing P(G, 4)>0 for all planar graphs G. In this way he hoped to apply the powerful tools of analysis and algebra for studying the roots of polynomials to the combinatorial coloring problem. Hassler Whitney generalised Birkhoff’s polynomial from the planar case to general graphs in 1932. In 1968, Read asked which polynomials are the chromatic polynomials of some graph, a question that remains open, and introduced the concept of chromatically equivalent graphs.
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A parsimonious coloring, for a given graph and vertex ordering, has been defined to be a coloring produced by a greedy algorithm that colors the vertices in the given order, and only introduces a new color when all previous colors are adjacent to the given vertex, but can choose which color to use (instead of always choosing the smallest) when it is able to re-use an existing color. The ordered chromatic number is the smallest number of colors that can be obtained for the given ordering in this way, and the ochromatic number is the largest ordered chromatic number among all vertex colorings of a given graph. Despite its different definition, the ochromatic number always equals the Grundy number.; .
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Then each edge is oriented so that the black face is on its left. A plane graph and its dual do not have the same directed medial graph; their directed medial graphs are the transpose of each other. Using the directed medial graph, one can effectively generalize the result on evaluations of the Tutte polynomial at (3,3). For a plane graph G, n times the evaluation of the Tutte polynomial at the point (n+1,n+1) equals the weighted sum over all edge colorings using n colors in the directed medial graph of G so that each (possibly empty) set of monochromatic edges forms a directed Eulerian graph, where the weight of a directed Eulerian orientation is 2 to the number of monochromatic vertices.
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With white colorings on his nose and legs, Strip's appearance was chosen for Brisco's steed; Copper and the other horses were touched up with "clown white" greasepaint to match Strip's markings. Foley artist Casey Crabtree provided sounds for horse hoof movements, work that was praised by sounds effects industry expert David Yewdall. He said of Crabtree's work on Brisco, "Her horses sounded so natural and real – their hooves, the sound of their hooves on the texture of the ground, the sound of saddle movement, bridle jingles – it was as good as anything I would want for a feature film, and this was episodic television." The make-up on many of Brisco's episodes was done by veteran artist Mel Berns Jr. Two props of the Orb were made.
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Raspberry 7 Up: This flavor was available for a short time in Norway and Denmark (and possibly other European countries) during the late '80s. It was released at the same time as Orange 7 Up. It was a clear lemon-, lime-, and raspberry-flavoured soft drink. It was pulled off the European market after 2–3 years, but can still be found in several Southeast Asian countries such as Singapore. 7 Up Free: 7 Up Free is sold in Iceland, (in Icelandic) UK, Ireland, Spain, Norway, Argentina, Finland, UAE, Uruguay, Pakistan, the Netherlands, Thailand, France and Germany. It contains no caffeine, sugar, colorings, or preservatives, and is marketed as "Natural Lemon and Lime Flavour" similar to the "100% natural" American version.
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Once copulation has taken place, the female will choose a nest site that is typically a depression covered with leaves next to a tree trunk, usually between a couple of buttresses. Members of the genus that are savanna style birds such as the small-billed tinamou will instead lay their eggs in a cavity near a clump of grass. The eggs are oval or elliptical on the smaller birds and near spherical in the larger birds, such as the undulated tinamou and the Brazilian tinamou. The colorings of the eggs are varied, but in general are brightly colored with no splotches or spots; the colors fade over time and usually will change to a less overt color midway through the incubation period.
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Any 3-CNF formula may be converted into a graph by constructing a separate gadget for each of its variables and clauses and connecting them as shown.This reduction is described in . In any 3-coloring of the resulting graph, one may designate the three colors as being true, false, or ground, where false and ground are the colors given to the false and ground vertices (necessarily different, as these vertices are made adjacent by the construction) and true is the remaining color not used by either of these vertices. Within a variable gadget, only two colorings are possible: the vertex labeled with the variable must be colored either true or false, and the vertex labeled with the variable's negation must correspondingly be colored either false or true.
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One layout has a high-level circuit supported by 87mm high pillars which have been created from three of the middle-rise piers firmly stacked together. This height suffices to clear an HO Railroad on a roadbed-type track, as well as any US-1 road circuit running a loaded car transporter. There were also three Plastic Construction Kits: a Mobil Truck Station, a Howard Johnson's Truck Stop, and a P.I.E. Freight Terminal, each molded in several colors to be glued together. These were supplied by Pola, in what was then West Germany and were also sold for a time as part of the Tyco model railroad range, but in plain Tyco 'Brown Box' packaging, sometimes with slightly different colorings or markings or with lights.
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The Moerman Therapy, also called Moerman Method or Moerman Diet is a purported cancer treatment from the Dutch practitioner (1893-1988). Its effectiveness is supported by anecdote only - there is no evidence of its worth as a cancer treatment. According to Quackwatch, "The diet prohibited all meats, all fish and shellfish, alcohol, animal fats, artificial colorings, beans, peas, lentils, mushrooms, potatoes, red cabbage, , cheeses with high fat and salt content, and other hydrogenated oils, coffee, cocoa or teas, egg whites, sugar, salt, white flour, and tobacco." In 2000, Cornelis Moerman's invention of the diet earned him a place at the head of "a list of the twenty biggest quacks of the twentieth century" as decided by the Dutch Union Against Quackery.
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Many groups such as Jews, Jains, Hindus, and Muslims, as well as vegans follow dietary restrictions which disallow the use of animal byproducts and/or alcohol in certain contexts. In many Western countries, some consumers rely on a Jewish kosher pareve certification mark to indicate that natural flavorings used in a food product are free of meat and dairy (although they can still contain fish). The Vegan Society's Sunflower symbol (which is currently used by over 260 companies worldwide) can also be used to see which products do not use any animal ingredients (including flavorings and colorings). Similarly, persons with known sensitivities or allergies to food products are advised to avoid foods that contain generic "natural flavors" or to first determine the source of the flavoring before consuming the food.
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Registration is not inflexible, and Vierne noted this in his introduction to 24 pieces de fantaisie: "It [registration] is an indication for the general colorings […] that can be modified according to the possibilities offered by the instruments on which they [the pieces] are to be performed." Vierne indicates Fonds et anches for the Récit expressif manual, and Fonds et anches, et principals for the Positif, Grand, and Pédale manuals. The Westminster tune within the piece is played on the Positif and Récit coupled, so as to give the theme substantial prominence over the pedal and harmony lines. The supporting secondary theme (rapid eighth and sixteenth note groupings against the dotted-quarter note primary theme) opening the piece is given less registration and seems to bubble along, weaving in and out of its strong namesake theme.
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Still composed the Afro-American Symphony over 3 months, during which he had no steady work. Sketches for the symphony, including a layout of its four movements, are found in a journal which Still was using to collect material for an opera called Rashana, which he never finished. In his journal, Still wrote: > "I seek in the 'Afro-American Symphony' to portray not the higher type of > colored American, but the sons of the soil, who still retain so many of the > traits peculiar to their African forebears; who have not responded > completely to the transforming effect of progress." Although he had received instruction from (among others) the French modernist composer Edgard Varèse, Still used a traditional tonal idiom in the Afro- American Symphony, infused with blues-inspired melodic lines and harmonic colorings.
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The concept of consecutive edge-coloring was introduced with the terminology 'interval edge coloring' by Asratian and Kamalian in 1987 in their paper "Interval colorings of edges of a multigraph". Since interval edge coloring of graphs was introduced mathematicians have been investigating the existence of interval edge colorable graphs as not all graphs allow interval edge coloring. A simple family of graphs that allows interval edge coloring is complete graph of even order and a counter example of family of graphs includes complete graphs of odd order. The smallest graph that doesnot allow interval colorability.There are even graphs discovered with 28 vertices and maximum degree 21 that is not interval colorable by Sevast’janov though the interval colorability of graphs with maximum degree lying between four and twelve is still unknown.
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A graph that requires four colors in any coloring, and four connected subgraphs that, when contracted, form a complete graph, illustrating the case k = 4 of Hadwiger's conjecture In graph theory, the Hadwiger conjecture states that if G is loopless and has no K_t minor then its chromatic number satisfies \chi(G) < t. It is known to be true for 1 \leq t \leq 6. The conjecture is a generalization of the four-color theorem and is considered to be one of the most important and challenging open problems in the field. In more detail, if all proper colorings of an undirected graph G use k or more colors, then one can find k disjoint connected subgraphs of G such that each subgraph is connected by an edge to each other subgraph.
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Mirsky's theorem can be restated in terms of directed acyclic graphs (representing a partially ordered set by reachability of their vertices), as the statement that there exists a graph homomorphism from a given directed acyclic graph G to a k-vertex transitive tournament if and only if there does not exist a homomorphism from a (k + 1)-vertex path graph to G. For, the largest path graph that has a homomorphism to G gives the longest chain in the reachability ordering, and the sets of vertices with the same image in a homomorphism to a transitive tournament form a partition into antichains. This statement generalizes to the case that G is not acyclic, and is a form of the Gallai–Hasse–Roy–Vitaver theorem on graph colorings and orientations .
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As federal law requires statements of origin on labels to be accurate, the Tennessee law effectively gives a firm definition to Tennessee whiskey, requiring Tennessee origin, maple charcoal filtering by the Lincoln County process prior to aging, and the basic requirements of bourbon (at least 51% corn, new oak barrels, charring of the barrels, and limits on alcohol by volume concentration for distillation, aging, and bottling). In 2014, legislation was introduced in the Tennessee legislature that would modify the 2013 law to allow the reuse of oak barrels in the Tennessee whiskey aging process. Jack Daniel's Master Distiller Jeff Arnett vehemently opposed the legislation, arguing the reuse of barrels would require the use of artificial colorings and flavorings, and would render Tennessee whiskey an inferior product to scotches and bourbons.Robert Holman, "Jack Daniel Denounces Barrel Legislation", The Tullahoma News, March 18, 2014.
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Any incident pair of a vertex and an edge, or an edge and an edge, must have distinct colors, as must any two adjacent vertices. It has been conjectured (combining Vizing's theorem and Brooks' theorem) that any graph has a total coloring in which the number of colors is at most the maximum degree plus two, but this remains unproven. If a 3-regular graph on a surface is 3-edge- colored, its dual graph forms a triangulation of the surface which is also edge colored (although not, in general, properly edge colored) in such a way that every triangle has one edge of each color. Other colorings and orientations of triangulations, with other local constraints on how the colors are arranged at the vertices or faces of the triangulation, may be used to encode several types of geometric object.
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Setco, a plastic bottles producer in Culver City, California, and Stange, a specialty flavorings and colorings company of Chicago, became subsidiaries in 1981. The company acquired Paterson Jenks, a publicly held United Kingdom corporation, in 1984, and Schwartz, the largest British spice line. Other acquisitions included Armanino Farms, the world's largest grower and processor of chives, from Armanino & Son, Inc., of San Francisco in 1986; and three California companies in 1987: Gentry Foods of Gilroy, Parsley Patch of Windsor, and The Herb Farm of Encinitas. McCormick purchased an interest in the Old Bay seasoning brand in 1990, which was famous in the Chesapeake Bay region for its use in preparing and steaming the local seafood delicacy of blue crabs, and acquired Mojave Foods Corporation of Los Angeles in 1991, and the consumer products business of Golden Dipt Company in 1993.
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The degeneracy of an undirected graph is the smallest number such that every non-empty subgraph of has at least one vertex of degree at most . If one repeatedly removes a minimum-degree vertex from until no vertices are left, then the largest of the degrees of the vertices at the time of their removal will be exactly , and this method of repeated removal can be used to compute the degeneracy of any graph in linear time. Greedy coloring the vertices in the reverse of this removal ordering will automatically produce a coloring with at most colors, and for some graphs (such as complete graphs and odd-length cycle graphs) this number of colors is optimal. For colorings with colors, it may not be possible to move from one coloring to another by changing the color of one vertex at a time.
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An algorithm for listing all maximal independent sets or maximal cliques in a graph can be used as a subroutine for solving many NP- complete graph problems. Most obviously, the solutions to the maximum independent set problem, the maximum clique problem, and the minimum independent dominating problem must all be maximal independent sets or maximal cliques, and can be found by an algorithm that lists all maximal independent sets or maximal cliques and retains the ones with the largest or smallest size. Similarly, the minimum vertex cover can be found as the complement of one of the maximal independent sets. observed that listing maximal independent sets can also be used to find 3-colorings of graphs: a graph can be 3-colored if and only if the complement of one of its maximal independent sets is bipartite.
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Its color ranges from pale yellow to amber to dark brown. Caramel color is one of the oldest and most widely used food colorings for enhancing naturally occurring colors, correcting natural variations in color, and replacing color that is lost to light degradation during food processing and storage. The use of caramel color as a food additive in the brewing industry in the 19th century is the first recorded instance of it being manufactured and used on a wide scale. Today, caramel color is found in many commercially produced foods and beverages, including batters, beer, brown bread, buns, chocolate, cookies, cough drops, spirits and liquor such as brandy, rum, and whisky, chocolate-flavored confectionery and coatings, custards, decorations, fillings and toppings, potato chips, dessert mixes, doughnuts, fish and shellfish spreads, frozen desserts, fruit preserves, glucose tablets, gravy, ice cream, pickles, sauces and dressings, soft drinks (especially colas), sweets, vinegar, and more.
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The number of states of an ice type model on the internal edges of a finite simply connected union of squares of a lattice is equal to one third of the number of ways to 3-color the squares, with no two adjacent squares having the same color. This correspondence between states is due to Andrew Lenard and is given as follows. If a square has color i = 0, 1, or 2, then the arrow on the edge to an adjacent square goes left or right (according to an observer in the square) depending on whether the color in the adjacent square is i+1 or i−1 mod 3. There are 3 possible ways to color a fixed initial square, and once this initial color is chosen this gives a 1:1 correspondence between colorings and arrangements of arrows satisfying the ice-type condition.
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After an introductory chapter, the second and third chapters concern graph coloring, the history of the four color theorem for planar graphs, its equivalence to 3-edge-coloring of planar cubic graphs, the snarks (cubic graphs that have no such colorings), and the conjecture of W. T. Tutte that every snark has the Petersen graph as a graph minor. Two more chapters concern closely related topics, perfect matchings (the sets of edges that can have a single color in a 3-edge- coloring) and nowhere-zero flows (the dual concept to planar graph coloring). The Petersen graph shows up again in another conjecture of Tutte, that when a bridgeless graph does not have the Petersen graph as a minor, it must have a nowhere-zero 4-flow. Chapter six of the book concerns cages, the smallest regular graphs with no cycles shorter than a given length.
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The problem of finding equitable colorings with as few colors as possible (below the Hajnal-Szemerédi bound) has also been studied. A straightforward reduction from graph coloring to equitable coloring may be proven by adding sufficiently many isolated vertices to a graph, showing that it is NP-complete to test whether a graph has an equitable coloring with a given number of colors (greater than two). However, the problem becomes more interesting when restricted to special classes of graphs or from the point of view of parameterized complexity. showed that, given a graph G and a number c of colors, it is possible to test whether G admits an equitable c-coloring in time O(nO(t)), where t is the treewidth of G; in particular, equitable coloring may be solved optimally in polynomial time for trees (previously known due to ) and outerplanar graphs.
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Louis Fuzelier and Jean- Philippe Rameau, Les indes galantes (1735–36) Some of Telemann's later music and of Bach's sons, Johann Joachim Quantz, Johann Adolph Hasse, Giovanni Battista Sammartini, Giuseppe Tartini, Baldassare Galuppi, Johann Stamitz, Domenico Alberti, and early Mozart are exemplars of galant style. Some of the works of the Portuguese composer Carlos Seixas are firmly in the galant style. This simplified style was melody-driven, not constructed, as so much classical music was to be, on rhythmic or melodic motifs: "It is indicative that Haydn, even in his old age, is reported to have said, 'If you want to know whether a melody is really beautiful, sing it without accompaniment'" . This simplification also extended to harmonic rhythm, which is generally slower in galant music than is the case in the earlier baroque style, thus making lavish melodic ornamentation and nuances of secondary harmonic colorings more important .
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Of the primal appeal of the flute, Rampal once told the Chicago Tribune: "For me, the flute is really the sound of humanity, the sound of man flowing, completely free from his body almost without an intermediary[...] Playing the flute is not as direct as singing, but it's nearly the same." Calling Rampal "an indisputably major artist", The New York Times said "Rampal's popularity was grounded in qualities that won him consistent praise from critics and musicians in the first decades of his career: solid musicianship, technical command, uncanny breath control, and a distinctive tone that eschewed Romantic richness and warm vibrato in favor of clarity, radiance, focus and a wide palette of colorings. Younger flutists assiduously studied and tried to copy his approaches to tonguing, fingering, embouchure (the position of the lips on the mouthpiece) and breathing." Aside from his own recorded legacy, it was as much through his inspiration of other musicians that Rampal's contribution can be appreciated.
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Many optimization problems that are NP-hard for more general classes of graphs may be solved efficiently by dynamic programming on graphs of bounded clique-width, when a construction sequence for these graphs is known. In particular, every graph property that can be expressed in MSO1 monadic second-order logic (a form of logic allowing quantification over sets of vertices) has a linear-time algorithm for graphs of bounded clique-width, by a form of Courcelle's theorem. It is also possible to find optimal graph colorings or Hamiltonian cycles for graphs of bounded clique-width in polynomial time, when a construction sequence is known, but the exponent of the polynomial increases with the clique-width, and evidence from computational complexity theory shows that this dependence is likely to be necessary. The graphs of bounded clique- width are -bounded, meaning that their chromatic number is at most a function of the size of their largest clique.
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The United States Food and Drug Administration has stated that it has "no reason to believe that there is any immediate or short term danger presented by 4-MeI at levels expected in food from the use of caramel coloring". The Agency describes the NTP carcinogenicity study as having been conducted at doses that "far exceed" current estimates of human exposure from the consumption of caramel coloring in foods and soft drinks. The Agency has stated that it is reviewing current exposure levels but does not recommend consumers change their diets based on concerns about 4-MeI. In response to statements by the Center for Science in the Public Interest that levels of 4-MeI in soft drinks "needlessly expose consumers to a chemical that causes cancer", an FDA spokesperson stated "[a] person would have to drink more than a thousand cans of soda in a day to match the doses administered in studies that showed links to cancer in rodents." The European Food Safety Authority (EFSA) reviewed the safety of caramel colorings in 2011 and revised the previously established Acceptable Daily Intakes for these products for reasons unrelated to 4-MeI exposure.
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While its main focus is on sweeteners such as sugar and high-fructose corn syrup, brief attention is given to other common soft drink additives such as caffeine, artificial colorings, and artificial sweeteners. Liquid Candy also explores the marketing and labeling of soft drinks, and ends with a number of recommendations for action, including: calling for the declaration of soft drink caloric content on restaurant menus; aggressive placement of water fountains, especially in schools; stopping the sale and advertising of soft drinks in schools; requiring medical professionals to routinely ask their patients about their soft drink consumption level; and levying taxes on soft drink sales to pay for mass-media campaigns to improve diet and promote physical activity.Michael F Jacobson PhD, Liquid Candy: How Soft Drinks are Harming Americans' Health, (CSPI, Washington DC 1998; 2nd Ed. 2005), pp. 25-27. In connection with the 2005 republication of the report, the CSPI filed a petitionPetition to Require Health Messages on Soft Drinks containing High-fructose Corn Syrup and other Caloric Sweeteners, submitted to the US Department of Health and Human Services (Food and Drug Administration) on 13 July 2005.
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For example, the larger, magnetic action figures Baron Karza and Force Commander were re-colorings of the Magnemo Kotetsu Jeeg action figures with newly designed heads. In addition, as the Micronaut line grew in popularity, Mego expanded the line by creating whole new figures from scratch such as the "Aliens" line which included Antron, Repto, Membros, Lobros, Kronos and Centaurus. The Micronaut toyline sold extremely well for Mego. According to Neal Kublan, Mego’s Executive VP of Marketing/Vice President of Mego Research & Development (1972-1980), the line generated more than $32 million in sales for the $110 million company during one period. After Mego’s 1982 bankruptcy and dissolution, the original molds for many of the toys were sold to Hourtoys/M&D; Toys for their Interchangables discount toyline, other original molds were sold to PAC Toys for use in their Lords of Light toyline and even Takara produced several series 5 toys for Italian licensee/distributor Gig’s i Micronauti line. Additionally, leftover Micronaut toyline stock from Mego’s production run was eventually sold for sale/clearance in North America by Lion Rock Limited under the Micronauts name.
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