70 Sentences With "half line" | Random Sentence Generator

As a rule of thumb, we rounded redacted lines to the nearest approximate half line.

Almirón played a comfortable ball to a teammate a few feet across the half line, where Michael Bradley then pressured.

"He then stated that I probably knew what was said," the memo continues, before a half line of text in the memo is redacted.

Tolkien lays down three rules of Old English alliteration. "One full lift in each half-line must alliterate." In the second half-line, only the first lift may alliterate: the second must not. In the first half-line, both lifts can alliterate; the stronger one must do so.

The Norse poets, unlike the Old English poets, tended to make each line a complete syntactic unit, avoiding enjambment where a thought begun on one line continues through the following lines; only seldom do they begin a new sentence in the second half- line. This example is from the Waking of Angantyr: Fornyrðislag has two lifts per half line, with two or three (sometimes one) unstressed syllables. At least two lifts, usually three, alliterate, always including the main stave (the first lift of the second half-line). It had a variant form called málaháttr ("speech meter"), which adds an unstressed syllable to each half- line, making six to eight (sometimes up to ten) unstressed syllables per line.

One can also consider the sine-Gordon model on a circle, on a line segment, or on a half line. It is possible to find boundary conditions which preserve the integrability of the model. On a half line the spectrum contains boundary bound states in addition to the solitons and breathers.

One interesting behavior is seen, for a four cell neighborhood and a square grid, when the initial condition consists of a half line of excited cells (1's) going off to infinity and below this half line a half line of refractory cells (2's). The rest of the cells are resting when t=0. Like this: ................................................................... ....00000000000000000000000000000000000000000000000000000000000.... ....00000000000000000000000000000000000000000000000000000000000.... ....00000000000000000001111111111111111111111111111111111111111.... ....00000000000000000002222222222222222222222222222222222222222.... ....00000000000000000000000000000000000000000000000000000000000.... ....00000000000000000000000000000000000000000000000000000000000.... ................................................................... The spiral which is produced can be seen in. This spiral can easily be seen by following the pattern forward for a few iterations "by hand".

Press the brush on the table, spread the bristles fanwise with a knife and cut away from each side about a half-line deep.

Then form the diagram by linking a half-line to a name and then to the other half line. Now count the number of ways to form the named diagram. Each permutation of the s gives a different pattern of linking names to half-lines, and this is a factor of . Each permutation of the half-lines in a single gives a factor of 4!.

The basic Anglo-Saxon poetic line consists of two half-lines, connected by alliteration. This means that there is a word or syllable in the second half-line, which will alliterate with one or more important words or syllables in the first half-line. These alliterated words or syllables will have more stress.Frederic G Cassidy and Richard M. Ringler, eds. Bright’s Old English Grammar and Reader.

His investigation of the oral Homeric style—"stock epithets" and "reiteration" (words, phrases, stanzas)—established that these formulae were artifacts of oral tradition easily applied to a hexametric line. A two-word stock epithet (e.g. "resourceful Odysseus") reiteration may complement a character name by filling a half-line, thus, freeing the poet to compose a half-line of "original" formulaic text to complete his meaning.

The half-line at the tail end of the arrow carries momentum , while the half-line at the head-end carries momentum . If one of the two half-lines is external, this kills the integral over the internal , since it forces the internal to be equal to the external . If both are internal, the integral over remains. The diagrams that are formed by linking the half-lines in the s with the external half-lines, representing insertions, are the Feynman diagrams of this theory.

If the rotation angles of a double rotation are equal then there are infinitely many invariant planes instead of just two, and all half-lines from are displaced through the same angle. Such rotations are called isoclinic or equiangular rotations, or Clifford displacements. Beware: not all planes through are invariant under isoclinic rotations; only planes that are spanned by a half-line and the corresponding displaced half-line are invariant. Assuming that a fixed orientation has been chosen for 4-dimensional space, isoclinic 4D rotations may be put into two categories.

The Bloch spectrum consists of the half-line E0 < E from which certain closed intervals [E2j−1, E2j] (j = 1, 2, ...) are omitted. These are forbidden bands (or gaps) so the (E2j−2, E2j−1) are allowed bands.

He notes that these rules force the second half-line to have its stronger lift first, so lines tend to fall away at the end, contrasting with a "rise in intensity" at the start of the next line.

A. Golubinskii and V. V. Sychev, A similar solution of the Navier–Stokes equations, Uch. Zap. TsAGI 7 (1976) 11–17.Rajamanickam, P., & Weiss, A. D. (2020). A note on viscous flow induced by half-line sources bounded by conical surfaces.

The last line about salvation for "us all" ("") reaches high tension, in terms of both harmony and fortissimo on "all", which is released within only two beats to pianissimo, then the last half line is repeated, beginning softly and fading away.

The other two are the Laguerre polynomials, which are orthogonal over the half line [0,\infty), and the Hermite polynomials, orthogonal over the full line (-\infty,\infty), with weight functions that are the most natural analytic functions that ensure convergence of all integrals.

The Mittag-Leffler distributions are two families of probability distributions on the half-line [0,\infty). They are parametrized by a real \alpha \in (0, 1] or \alpha \in [0, 1]. Both are defined with the Mittag-Leffler function, named after Gösta Mittag-Leffler.

O be some other name, > belonging to a man! > What's in a name? That which we call a rose, > By any other word would smell as sweet. > Malone reasoned that the awkward half-line of ‘belonging to a man’ could be reconnected into verse through correction with Q1.

Historically the first point processes that were studied had the real half line R+ = [0,∞) as their state space, which in this context is usually interpreted as time. These studies were motivated by the wish to model telecommunication systems,Palm, C. (1943). Intensitätsschwankungen im Fernsprechverkehr (German). Ericsson Technics no.

By convention an NTSC video frame is considered to start with an even field followed by an odd field. The disparity of the line numbering compared to other systems is solved by defining the line numbering to start five equalizing pulses (or 2 and a half lines) earlier than on all other systems (including Systems A and E even though they had no equalizing pulses) on the first equalizing pulse following an active line or half line. This has the effect of placing a half line of video at the end of the even (first) field and the beginning of the odd (second field). Thus the line numbers correspond to the real lines of the video frame.

Afrida cosmiogramma is a species of moth in the family Nolidae (nolid moths). It was described by Harrison Gray Dyar Jr. in 1913 and is found in Cuba. The wingspan is about 10 mm. The forewings are white, with the basal space brownish, limited by a dark half-line from the costa.

The Panther's retreat and return after three nights mirrors the story of the death and resurrection of Jesus. The poem uses similar language and imagery to homiletic writings. The word stenc, used in The Panther to describe the fragrance the Panther exudes whilst singing, is used elsewhere in the Old English corpus as a symbol of holiness and is a key theme of the poem. The half-line þæt is æþele stenc ('that is a noble fragrance') is the last half-line of the poem, summarising the quotation attributed to St. Paul in the concluding passage of the poem; > Monigfealde sind geond middangeard > god ungnyðe þe us to giefe dæleð > ond to feorhnere fæder ælmihtig, > ond se anga hyht ealra gesceafta, > uppe ge niþre.

For example, the Dirichlet problem of the heat equation on the half-line, i.e., the problem u_0 and g_0 given, can be solved via the sine-transform. The analogous problem on a finite interval can be solved via an infinite series. However, the solutions obtained via integral transforms and infinite series have several disadvantages: 1\.

The 16-syllable hazaj meter is also among the three most commonly used meters in Urdu verse,. and it is one of the typical meters of the ghazal genre. The following example comes from a ghazal written by Ghalib in 1816. Like the Turkish version of the metre, it has no break in the middle of the half-line.

Given a line and any point A on it, we may consider A as decomposing this line into two parts. Each such part is called a ray and the point A is called its initial point. It is also known as half-line, a one- dimensional half-space. The point A is considered to be a member of the ray.

This was the work of Layamon, a parish priest of Ernley in Worcestershire. The opening lines give us the best information we have about him. Their metre should be noted. It is a relic of the Old English verse, each half-line (or each line, as here printed) containing two principal accents, and being more or less closely connected with its fellow.

Variations of these meters can be found. Some exist in shorter or longer forms, for example with either three or four feet in each half-line (known as trimeter and tetrameter respectively). Some meters have a catalectic variation, in which the end of the line is shortened by one syllable. A whole series of Arabic technical terms exists to describe these variations.

An external ray is a curve that runs from infinity toward a Julia or Mandelbrot set.J. Kiwi : Rational rays and critical portraits of complex polynomials. Ph. D. Thesis SUNY at Stony Brook (1997); IMS Preprint #1997/15. Although this curve is only rarely a half-line (ray) it is called a ray because it is an image of a ray.

Rotational symmetry with respect to any angle is, in two dimensions, circular symmetry. The fundamental domain is a half-line. In three dimensions we can distinguish cylindrical symmetry and spherical symmetry (no change when rotating about one axis, or for any rotation). That is, no dependence on the angle using cylindrical coordinates and no dependence on either angle using spherical coordinates.

The fundamental domain is a half-plane through the axis, and a radial half-line, respectively. Axisymmetric or axisymmetrical are adjectives which refer to an object having cylindrical symmetry, or axisymmetry (i.e. rotational symmetry with respect to a central axis) like a doughnut (torus). An example of approximate spherical symmetry is the Earth (with respect to density and other physical and chemical properties).

Despite the division, there is some consensus regarding aspects of the verse's structure. A Saturnian line can be divided into two cola or half-lines, separated by a central caesura. The second colon is shorter than or as long as the first. Furthermore, in any half-line with seven or more syllables, the last three or four are preceded by word-end.

See also Bostock, King & McLintock 1976, 304–313. Some lines contain rhymes, using a poetic form pioneered in the ninth century by Otfrid of Weissenburg (ca. 790–875).Otfrid still used the traditional long lines divided centrally at a caesura, but with rhymes or assonances at each half-line, and in general no attempt at alliteration. On Otfridian verse, see Bostock, King & McLintock, 322–326.

In this section Tolkien describes variations on the basic patterns. For example, dips (between lifts) were usually monosyllabic, but the number of syllables was not limited by Old English metre, so a series of weak syllables was permitted in a half-line. Other variations included breaking a lift into two syllables, the first short but stressed, the second weak, with for instance 'vĕssel' in place of 'boat'.

Sievers' analysis was a system of five patterns which indicated how the poetic line (or, more specifically, the poetic half-line) was to be emphasized or not, e.g. stressed-unstressed-stressed-unstressed, unstressed-stressed-unstressed-stressed, etc. This seemingly elementary analysis was significant because of the difficulty experienced by previous scholars in identifying where the poetic line began and ended. Germanic poetry, in its written form, rarely indicated the line division.

Goalies must stay on their side of the court and can't cross the half line (can't cross half court line). Goalies can touch the ball with any part of their body, meaning that they can pick up the ball off the ground without it being considered an "illegal" move. It is still illegal for goalies to travel with the ball in their hands; however, they can dribble the ball.

A Turkish poem in this meter is the following from the 16th-century poet Bâkî, which begins as follows: : : :"Oh beloved, since the origin we have been the slaves of the shah of love" :"Oh beloved, we are the famed sultan of the heart's domain"Andrews, Walter G, Ottoman Lyric Poetry: An Anthology, p. 93. Unlike in the Rumi poem quoted above, there is no break in the middle of the half-line.

The refrain must be identical with the beginning of the first line: it may be a half-line, and rhymes with the second line. It has three stanzas and its rhyme scheme is as follows: A B A R ; B A B ; A B A R ; where R is the refrain. Swinburne had published a book A Century of Roundels.Algernon Charles Swinburne, A Century of Roundels (London: Chatto & Windus, 1883) Kindle ebook 2011, ASIN B004TP1MWW .

Both genres intend to portray the illustrious or non-illustrious deeds and doings of persons in the contexts of mighty wars. Thus Aristagoras personally can be called a “coward.” The lying that they do is metis, “cunning,” an admired Greek virtue practised by the greatest hero of them all, the crafty Odysseus. The literary tradition of it went on. Virgil could include the half-line Timeo Graecos dona ferentes, “I fear Greeks bearing Gifts,” in the Aeneid.

A half-space in a one-dimensional space is called a half-line or ray. A half-space may be specified by a linear inequality, derived from the linear equation that specifies the defining hyperplane. A strict linear inequality specifies an open half-space: :a_1x_1+a_2x_2+\cdots+a_nx_n>b A non-strict one specifies a closed half-space: :a_1x_1+a_2x_2+\cdots+a_nx_n\geq b Here, one assumes that not all of the real numbers a1, a2, ..., an are zero.

After the scoring team returns to their half, the scored-on team may cross the half line and resume play. The game continues until a team reaches either a limit of a predetermined length of time, depending on the format. 3v3 games are typically 10–15 minutes, while Squad games are typically 30–40 minutes. A player who "dabs", (touches a horizontal surface with their foot), must undertake some form of remedial penalty before making contact with the ball again.

Olsson argues that the 837/8 evidence marks only the beginning of a long and difficult official Judaization that concluded some decades later. A 9th-century Jewish traveller, Eldad ha-Dani, is said to have informed Spanish Jews in 883 that there was a Jewish polity in the East, and that fragments of the legendary Ten Lost Tribes, part of the line of Simeon and half-line of Manasseh, dwelt in "the land of the Khazars", receiving tribute from some 25 to 28 kingdoms.

The three lines of double points intersect at a triple point which lies on the origin. The triple point cuts the lines of double points into a pair of half-lines, and each half-line lies between a pair of lobes. One might expect from the preceding statements that there could be up to eight lobes, one in each octant of space which has been divided by the coordinate planes. But the lobes occupy alternating octants: four octants are empty and four are occupied by lobes.

This theorem has been generalised to semisimple Lie groups.. If is supported on the half-line , then is said to be "causal" because the impulse response function of a physically realisable filter must have this property, as no effect can precede its cause. Paley and Wiener showed that then extends to a holomorphic function on the complex lower half-plane which tends to zero as goes to infinity.. The converse is false and it is not known how to characterise the Fourier transform of a causal function..

Being 17 () is a 2016 French drama film directed by André Téchiné and starring Kacey Mottet Klein, Corentin Fila and Sandrine Kiberlain. The script was written by Téchiné in collaboration with Céline Sciamma. The plot follows the romantic and sexual awakening of two seventeen-year-old boys as their initial animosity, expressed in violence, morphs into love. Being 17 borrows its title from the second half-line of the first verse of Roman, (1870) by Arthur Rimbaud: On n'est pas sérieux quand on a dix-sept ans.

A hemistich (; via Latin from Greek , from "half" and "verse") is a half-line of verse, followed and preceded by a caesura, that makes up a single overall prosodic or verse unit. In Latin and Greek poetry, the hemistich is generally confined to drama. In Greek tragedy, characters exchanging clipped dialogue to suggest rapidity and drama would speak in hemistichs (in hemistichomythia). The Roman poet Virgil employed hemistichs in the Aeneid to indicate great duress in his characters, where they were incapable of forming complete lines due to emotional or physical pain.

Most of the poem is in alliterative verse of very uneven quality.Ideally, '[t]he long line is divided into two by a strong caesura, and the halves, each of which has two major stresses, are linked by alliteration—that is, by the identity of initial sounds—in some of these stresses. The most important stress is that on the first beat of the second half-line' (Murdoch 1983, 59). Though found elsewhere in Old High German and Old Saxon, this form is much better represented in Old English and Old Norse.

This need became apparent when trying to fit known theoretical models to observed data that exhibited skewness. Pearson's examples include survival data, which are usually asymmetric. In his original paper, Pearson (1895, p. 360) identified four types of distributions (numbered I through IV) in addition to the normal distribution (which was originally known as type V). The classification depended on whether the distributions were supported on a bounded interval, on a half-line, or on the whole real line; and whether they were potentially skewed or necessarily symmetric.

In skaldic poetry, the dróttkvætt stanza had eight lines, each having three "lifts" produced with alliteration or assonance. In addition to two or three alliterations, the odd- numbered lines had partial rhyme of consonants with dissimilar vowels, not necessarily at the beginning of the word; the even lines contained internal rhyme in set syllables (not necessarily at the end of the word). Each half- line had exactly six syllables, and each line ended in a trochee. The arrangement of dróttkvætts followed far less rigid rules than the construction of the individual dróttkvætts.

The verses of the skalds contain a great profusion of kennings, the fixed metaphors found in most Northern European poetry of the time. Kennings are devices ready to supply a standard image to form an alliterating half-line to fit the requirements of dróttkvætt, but the substantially greater technical demands of skaldic verse required the devices to be multiplied and compounded to meet its demands for skill and wordplay. The images can therefore become somewhat hermetic, at least to those who fail to grasp the allusions that are at the root of many of them.

Stephanos (1881) He also represented Laguerre's oriented spheres by quaternions (1883).Stephanos (1883) Lines, circles, planes, or spheres with radii of certain orientation are called by Laguerre half-lines, half-circles (cycles), half-planes, half-spheres, etc. A tangent is a half- line cutting a cycle at a point where both have the same direction. The transformation by reciprocal directions transforms oriented spheres into oriented spheres and oriented planes into oriented planes, leaving invariant the "tangential distance" of two cycles (the distance between the points of each one of their common tangents), and also conserves the lines of curvature.

Interlacing divides the frame into two fields, each containing half the number of lines. Each field is scanned in 1/60 second under the 525-line system (or 480i – often incorrectly referred to as NTSC) or 1/50 of a second under the 625-line system (or 576i – often incorrectly referred to as the PAL). With interlaced systems there are an odd number of lines in each frame. This means that there is a half line offset between the fields, therefore the lines in the second field will be positionally interleaved with the lines in the first field.

His poem, Namby Pamby (1725), satirized Ambrose Philips who was a frequent and famous target of Alexander Pope's wrath. Philips had written a series of odes to "all persons", from Robert Walpole to the mother in the nursery, and the latter provided the occasion for Carey to exaggerate. Philips had employed a 2.5' iambic line, and Carey devastatingly claimed that the half-line matched Philips's halfwitted conception. The poem was so successful that Carey himself began to be known as "Namby Pamby Carey" (while Philips became known as "Namby Pamby"), and the poem even came to be used as children's literature.

The line above illustrates the principle: note that there is a natural pause after 'hondum' and that the first stressed syllable after that pause begins with the same sound as a stressed line from the first half-line (the first halfline is called the a-verse and the second is the b-verse).Bradley, S.A.J. Anglo-Saxon Poetry. New York: Everyman Paperbacks, 1995. There is very strong evidence that Anglo-Saxon poetry has deep roots in oral tradition, but keeping with the cultural practices seen elsewhere in Anglo-Saxon culture, there was a blending between tradition and new learning.

Bisection of an angle using a compass and straightedge An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The exterior or external bisector is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles.

Economic agents face a sequence of budget sets, one at each date-state. Item (2) introduces the concept of incomplete markets, formulated in terms of net trade, the budget set is contained in a half space intersecting the positive cone of contingent goods at zero net trade only (this is called absence of arbitrage). This is because without transaction cost agents will demand an infinite amount of any trade promising positive consumption in some state and no negative net trade against that in any other good and state. This half space, containing the budget set and separating it from the free lunch cone, corresponds to a half line of positive prices.

In association football, a player is an offside position if they are beyond the half-line, beyond the second to last defender and beyond the ball at the moment when their teammate touches the ball, excluding when the teammate is engaged in a goal kick, throw-in, or corner kick. They are committing an infringement if they are in an offside position and are interfering with an opponent, interfering with play or gaining an advantage from being in an offside position. In futsal, there is no comparable offside rule, although a portion of the Laws of the Game is dedicated to indicating that there is no offside rule.

A scalar field source is another scalar field that contributes a term to the (Lorentz) Lagrangian: : \int h(x) \phi(x)\, d^dx = \int h(k) \phi(k)\, d^dk \, In the Feynman expansion, this contributes H terms with one half-line ending on a vertex. Lines in a Feynman diagram can now end either on an vertex, or on an vertex, and only one line enters an vertex. The Feynman rule for an vertex is that a line from an with momentum gets a factor of . The sum of the connected diagrams in the presence of sources includes a term for each connected diagram in the absence of sources, except now the diagrams can end on the source.

As an offensive playmaker, he was a brilliant passer, two-footed, had remarkable field vision, and was noted for his balance and agility on the ball, as well as his control, turns and spins. His trademark goals were ones where he would collect the ball at the half-line, dribble through several opponents with a series of twinkle-toed shuffles, and turns, until arriving in front of the goal, where he would stop and invite the goalkeeper to attack him like a matador, before faking a shot, then dribbling past the beaten goalkeeper to slot home easily. In away games, the defenders would often foul and hack him to avoid being humiliated.Paolo Facchinetti, La Grande Ambrosiana.

The hymn uses classical metres: the Sapphic stanza consisting of three Sapphic hendecasyllables followed by an adonius (a type of dimeter). The chant is useful for teaching singing because of the way it uses successive notes of the scale: the first six musical phrases of each stanza begin on a successively higher notes of the hexachord, giving ut–re–mi–fa–so–la; though ut is replaced by do in modern solfège. The naming of the notes of the hexachord by the first syllable of each hemistich (half line of verse) of the first verse is usually attributed to Guido of Arezzo. Guido, who was active in the eleventh century, is regarded as the father of modern musical notation.

Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point O of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point P of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains P. A line with a chosen Cartesian system is called a number line. Every real number has a unique location on the line.

In this formula P is the sub-portfolio of risky assets at the tangency with the Markowitz bullet, F is the risk-free asset, and C is a combination of portfolios P and F. By the diagram, the introduction of the risk-free asset as a possible component of the portfolio has improved the range of risk-expected return combinations available, because everywhere except at the tangency portfolio the half-line gives a higher expected return than the hyperbola does at every possible risk level. The fact that all points on the linear efficient locus can be achieved by a combination of holdings of the risk-free asset and the tangency portfolio is known as the one mutual fund theorem, where the mutual fund referred to is the tangency portfolio.

Another is when three external lines end on an , and the remaining half- line joins up with another , and the remaining half-lines of this run off to external lines. These are all also forest diagrams (as every tree is a forest); an example of a forest that is not a tree is when eight external lines end on two s. It is easy to verify that in all these cases, the momenta on all the internal lines is determined by the external momenta and the condition of momentum conservation in each vertex. A diagram that is not a forest diagram is called a loop diagram, and an example is one where two lines of an are joined to external lines, while the remaining two lines are joined to each other.

To prove the existence of the Angenent torus, Angenent first posits that it should be a surface of revolution. Any such surface can be described by its cross-section, a curve on a half-plane (where the boundary line of the half- plane is the axis of revolution of the surface). Following ideas of Huisken, Angenent defines a Riemannian metric on the half-plane, with the property that the geodesics for this metric are exactly the cross-sections of surfaces of revolution that remain self-similar and collapse to the origin after one unit of time. This metric is highly non-uniform, but it has a reflection symmetry, whose symmetry axis is the half-line that passes through the origin perpendicularly to the boundary of the half-plane.

Three of the Brigade commanders on Operation Thursday (two of whom had also served in the first Chindit expedition) subsequently wrote autobiographies, which contained their comments on the Chindits' concept and practice of operations. Bernard Fergusson, originally an enthusiastic supporter of Wingate, later came to feel that Wingate lacked both consistency and flexibility in his plans, which contributed to Fergusson's long, pointless march from Ledo and his defeat at Indaw. John Masters, who was a close friend and supporter of Lentaigne, felt that the Chindits' mobility was sacrificed in holding fixed defensive positions or attacking strong Japanese positions, without the necessary support. In criticism of the whole Chindit concept, he pointed out that the Chindit force had the infantry strength of two and a half line divisions, but, without supporting arms, it had the fighting strength of less than one.

In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moments :m_n = \int_0^1 x^n\,d\mu(x) of some Borel measure supported on the closed unit interval . In the case , this is equivalent to the existence of a random variable supported on , such that . The essential difference between this and other well-known moment problems is that this is on a bounded interval, whereas in the Stieltjes moment problem one considers a half-line , and in the Hamburger moment problem one considers the whole line . The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions (indeterminate moment problem) whereas a Hausdorff moment problem always has a unique solution if it is solvable (determinate moment problem).

The unaccented syllables typically occur before the first stress in the half-line, and most often in the b-verse. The Hildebrandslied, lines 4–5: The Heliand, line 3062: :Sâlig bist thu Sîmon, quað he, sunu Ionases; ni mahtes thu that selbo gehuggean ::Blessed are you Simon, he said, son of Jonah; for you did not see that yourself (Matthew 16, 17) This leads to a less dense style, no doubt closer to everyday language, which has been interpreted both as a sign of decadent technique from ill- tutored poets and as an artistic innovation giving scope for additional poetic effects. Either way, it signifies a break with the strict Sievers typology. In more recent times, Richard Wagner sought to evoke old German models and what he considered a more natural and less over-civilised style by writing his Ring poems in Stabreim.

If we are comparing positive quantities X and Y using the ratio X / Y, then if X < Y, the ratio is in the interval (0,1), whereas if X > Y, the ratio is in the half-line (1,∞), where the ratio of 1 corresponds to equality. In an analysis where X and Y are treated symmetrically, the log-ratio log(X / Y) is zero in the case of equality, and it has the property that if X is K times greater than Y, the log-ratio is the equidistant from zero as in the situation where Y is K times greater than X (the log-ratios are log(K) and −log(K) in these two situations). If values are naturally restricted to be in the range 0 to 1, not including the end-points, then a logit transformation may be appropriate: this yields values in the range (−∞,∞).

Nearly all Old English poetry (whether or not it was written or sung) follows the same general verse form, its chief characteristic being alliteration. As was common with poetry of the period, the nine lines of the Hymn are divided into eighteen half-lines by a medial caesura (pause or break in the middle of the line); the four principal stresses of each line are in turn divided evenly, allotting each half line with two stresses. It is generally acknowledged that the text can be separated into two rhetorical sections (although some scholars believe it could be divided into three), based on theme, syntax and pacing; the first being lines one to four and the second being lines five to nine. Bede himself stated (in regards to his own Latin translation of Cædmon's Hymn) that "it is impossible to make a literal translation, no matter how well written, of poetry into another language without losing some of the beauty and dignity" of the piece.