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In the News (Wed 21 Aug 19)

 Modular form - Wikipedia, the free encyclopedia
Modular form theory is a special case of the more general theory of automorphic forms, and therefore can now be seen as just the most concrete part of a rich theory of discrete groups.
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation and growth condition.
By "holomorphic at the cusp", it is meant that the modular form is holomorphic as /wiki/Modular_forms

 Variation (music) - Wikipedia, the free encyclopedia
Variation form, or theme and variation, is a musical form where a theme is repeated in altered form or accompanied in a different manner.
A favorite form of variations in Renaissance music was divisions, a type in which the basic rhythmic beat is successively divided into faster and faster intervals.
In music, variation is a formal technique where material is altered during repetition; reiteration with changes. /wiki/Theme_and_variation   (763 words)

 sonata form
The crucial elements that lead to the sonata form are: the weakening of the difference between binary and ternary form; the shift of texture away from full polyphony, many voices in imitation, to homophony, or a single dominant voice and supporting harmony; and the increasing reliance on juxtaposing different keys and textures.
The term "sonata form" is also applied to the use the layout of all of the movements, for example, Schumann relabelled a piano work as a "sonata" only when he included a fourth dance movement.
The sonata form is a guide to composers as to the schematic for their works, for interpreters to understand the grammar and meaning of a work, and listeners to understand the significance of musical events. /sonata_form.html   (5468 words)

 Quadratic equation - Wikipedia, the free encyclopedia
This equation may be resolved directly or with a simple substitution, using the methods that are available for the quadratic, such as factoring (also called factorising), the quadratic formula, or completing the square.
The quadratic formula is derived by the method of completing the square.
The equation is now in a form in which we can conveniently complete the square. /wiki/Quadratic_equation   (871 words)

 Newton's laws of motion - Wikipedia, the free encyclopedia
The weak form is a valuable mathematical abstraction, because it allows one to study concepts such as the center of mass in the presence of arbitrary forces.
For an example in electrostatics where the strong form is not obeyed, consider the interaction between a point charge and a perfect dipole aligned in a direction perpendicular to the line connecting the charge and the dipole.
The law of conservation of momentum, which Newton derived as a corollary of his second and third laws, was the first conservation law to be discovered. /wiki/Newton's_laws_of_motion   (871 words)

 Efficient market hypothesis - Wikipedia, the free encyclopedia
Some economists, mathematicians and market practitioners cannot believe that man-made markets are strong-form efficient when there are prima facie reasons for inefficiency including the slow diffusion of information, the relatively great power of some market participants (e.g.
Opponents of the EMH sometimes cite examples of market movements that seem inexplicable in terms of conventional theories of stock price determination, for example the stock market crash of October 1987 where most stock exchanges crashed at the same time.
The efficient market hypothesis implies that it is not possible to consistently outperform the market - appropriately adjusted for risk - by using any information that the market already knows, except through luck or obtaining and trading on inside information. /wiki/Efficient_market_hypothesis   (1278 words)

 Logarithmic spiral - Wikipedia, the free encyclopedia
Logarithmic spirals are self-similar in that they are self-congruent under all similarity transformations (scaling them gives the same result as rotating them).
The logarithmic spiral was first described by Descartes and later extensively investigated by Jakob Bernoulli, who called it Spira mirabilis, "the marvelous spiral", and wanted one engraved on his headstone.
The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the arms of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant. /wiki/Logarithmic_spiral   (734 words)

 Complex number - Wikipedia, the free encyclopedia
In mathematics, a complex number is an expression of the form a + bi, where a and b are real numbers, and i stands for one of the square roots of negative one (−1).
The conjugate of the complex number z corresponds to the transformation which rotates through the same angle as z but in the opposite direction, and scales in the same manner as z; this can be described by the transpose of the matrix corresponding to z.
In mathematics, the adjective "complex" means that the field of complex numbers is the underlying number field considered, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. /wiki/Complex_number   (3516 words)

 Binary - Wikipedia, the free encyclopedia
Binary (music), a musical form that consists of two parts.
Binary (chemical weapon), one that contains two capsules, each of which contains a chemical, that when combined with the contents of the other, will react to make a toxic agent.
Binary star, a stellar system consisting of two nearby stars that revolve around a common center of mass. /wiki/Binary   (288 words)

 Online Enzyklopädie 1911 Britannica
IKONE (durch die Form Latinized, vom Gr.-eixiav, vom Portrait, vom Bild)
Sturm; die Wurzel ist vermutlich die, die in "gesehen wird, sich rühren," zum rouse, Bewegung, stören, cf.
IMPOST (durch das O.-Feld vom Lat.-impositum, eine Sache gelegt nach anderen; die modernen Franzosen sind impot) /de/II1_ISS/index.html   (741 words)

 Rondo - Wikipedia, the free encyclopedia
Rondo, and its French equivalent rondeau, is a word that has been used in music in a number of ways, most often in reference to a musical form, but also in reference to a character-type that is distinct from the form.
A common expansion of rondo form is to combine it with sonata form, to create the sonata rondo form.
Rondo as a character-type (as distinct from the form) equates to music that is fast and vivacious—normally allegro. /wiki/Rondo   (300 words)

 Info and facts on 'Quadratic form'
Quadratic forms over the ring of integers are called integral quadratic forms or integral lattice (Framework consisting of an ornamental design made of strips of wood or metal) s.
The kernel of the bilinear form B consists of the elements that are orthogonal to all elements of V, and the kernel of the quadratic form Q consists of all elements u of the kernel of B with Q(u)=0.
Note that general quadratic function (additional info and facts about quadratic function) s and quadratic equation (An equation in which the highest power of an unknown quantity is a square) s are not examples of quadratic forms. /encyclopedia/q/qu/quadratic_form.htm   (841 words)

 Ode - Wikipedia, the free encyclopedia
The poets of the Pleiad recognized in the ode one of the forms of verse with which French prosody should be enriched, but they went too far in their use of Greek words crudely introduced.
Early in the 19th century the form was resumed, and we have the odes composed between 1817 and 1824 by Victor Hugo, the philosophical and religious odes of Lamartine, and the brilliant Odes funambulesques of Theodore de Banville (1857).
This article is about the poetic and musical form of ode. /wiki/Ode   (1082 words)

 Platonic realism - Wikipedia, the free encyclopedia
According to Platonic realism, universals exist in a "realm" (often so called) that is separate from space and time; one might say that universals have a sort of ghostly or heavenly mode of existence, but, at least in more modern versions of Platonism, such a description is probably more misleading than helpful.
Indeed, probably the most popular argument for Platonic realism says that universals explain best the meaning general terms have; on this argument, when we speak of 'applehood' or 'redness', the best way to understand what such terms mean is to say that they refer to Platonic forms.
The forms are supposed to exist in a special realm of the universe, apart from space and time. /wiki/Platonic_realism   (1239 words)

Form (biology) In biology a form is a trinomial nomenclature notation is: Genusname speciesname forma formname.
Legendre form In mathematics, the Legendre forms of elliptic integrals, F(φ,k), E(φ,k) and P(φ,k,n) are def...
Form of government A form of government (also referred to as a system of government or a political system) is a system b... /topics/form.html   (1239 words)

Form (biology) In biology a form is a trinomial nomenclature notation is: Genusname speciesname forma formname.
Legendre form In mathematics, the Legendre forms of elliptic integrals, F(φ,k), E(φ,k) and P(φ,k,n) are def...
Carlson symmetric form In mathematics, the Carlson symmetric forms of elliptic integrals, RC(x,y), RD(x,y,z), RF(x,y,z)... /topics/form.html   (1239 words)

 Canonical - Wikipedia, the free encyclopedia
Canonical can also mean "part of the canon", i.e., one of the books comprising the biblical canon, as opposed to apocryphal books.
Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics.
This word is used by theologians and canon lawyers to refer to the canons of the Eastern Orthodox and Roman Catholic churches, adopted by ecumenical councils. /wiki/Canonical   (578 words)

 Cyclic group - Wikipedia, the free encyclopedia
This makes a cyclic group one of the simplest groups to study and a number of nice properties are known.
In group theory, a cyclic group is a group that can be generated by a single element, in the sense that the group has an element a (called a "generator" of the group) such that, when written multiplicatively, every element of the group is a power of a (or na when the notation is additive).
The cycle graphs of finite cyclic groups are all n-sided polygons with the elements at the vertices. /wiki/Cyclic_group   (1318 words)

 Form (disambiguation) - Wikipedia, the free encyclopedia
Differential form, a mathematical concept in the fields of multivariate calculus, differential topology and tensors.
Form (document), a document (printed or electronic) with spaces in which to write or enter data.
Modular form, a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. /wiki/Form_(disambiguation)   (330 words)

 Differential form
Differential Forms in Electromagnetic Theory The differential forms research group at BYU is investigating the use of the calculus of differential forms in teaching and research.
In differential geometry, a differential form of degree k is a smooth section of the k th exterior power of the cotangent bundle of a manifold.
Differential forms of degree k are integrated over k dimensional chain s. /encyclopedia/article-Differential_form.html   (330 words)

 Degeneracy (mathematics) - Wikipedia, the free encyclopedia
A point is a degenerate case of a circle, namely one with radius 0.
The line is a degenerate form of a parabola if the parabola resides on a tangent plane.
In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. /wiki/Mathematical_degeneracy   (330 words)

 Cusp - Wikipedia, the free encyclopedia
Note, however, that hyperbolic geometry, Riemann surfaces and modular forms are related; in this case, a cusp can be visualized as a cone-shaped protrusion, and be given a precise geometrical definition through a cusp neighborhood.
More literally, a cusp is a sharp point or apex, such as occurs in two dimensions at the end of a crescent, or in three dimensions at the tip of a cone or horn.
The term cusp form in modular form theory refers to the third of these meanings, implying a form that vanishes at cusps. /wiki/Cusp   (274 words)

 Strophic form - Wikipedia, the free encyclopedia
Strophic form, or chorus form, is a sectional and/or additive way of structuring a piece of music based on the repetition of one formal section or block played repeatedly.
Most folk and popular songs are strophic in form, including the twelve bar blues, all of which may be in simple verse or simple verse-chorus form.
The "verse-chorus-verse" (verse-chorus form) of most popular music songs may be interpreted as parts of a larger a strophic verse-refrain form. /wiki/Strophic   (219 words)

 Static single assignment form - Wikipedia, the free encyclopedia
Converting ordinary code into SSA form is primarily a simple matter of replacing the target of each assignment with a new variable, and replacing each use of a variable with the "version" of the variable reaching that point.
SSA form is a relatively recent development in the compiler community.
As SSA form is no longer useful for direction execution, it is frequently used "on top of" another IR with which it remains in direct correspondence. /wiki/SSA_(compilers)   (219 words)

 History of sonata form
Another area where the sonata form expanded was in the realm of "tone poems" or "symphonic poems", which would often use the first movement form, and greatly extended their length versus traditional overtures.
The crucial elements that lead to the sonata form are: the weakening of the difference between binary and ternary form; the shift of texture away from full polyphony, many voices in imitation, to homophony, or a single dominant voice and supporting harmony; and the increasing reliance on juxtaposing different keys and textures.
Properly speaking, the "Sonata Form" does not exist in the Baroque period, however, the forms which lead to the standard defintion are present, and, in fact, there are a greater variety of harmonic patterns in Baroque works labelled "Sonata" than in the classical period that is to follow.   (2481 words)

Religion may thus be defined as the voluntary subjection of oneself to God, that is to the free, supernatural Being (or beings) on whom man is conscious of being dependent, of whose powerful help he feels the need, and in whom he recognizes the source of his perfection and happiness.
Religion in its simplest form implies the notion of being bound to God; the same notion is uppermost in the word religion in its most specific sense, as applied to the life of poverty, chastity, and obedience to which individuals voluntarily bind themselves by vows more or less solemn.
In the Christian religion there are numerous instances of sudden conversions from a life of vice to one of virtue, from a state of spiritual depression to one of enthusiastic zeal. /cathen/12738a.htm   (2481 words)

 PlanetMath: quadratic form
Quadratic forms can be defined on other algebraic objects, such as modules or algebras over rings (of scalars), or even non-associative algebras over commutative rings (of scalars).
This is version 15 of quadratic form, born on 2002-02-13, modified 2005-04-12.
is the field of real numbers, we say that a quadratic form is positive definite, negative definite, or positive semidefinite if the same can be said of the corresponding bilinear form. /encyclopedia/QuadraticForm.html   (257 words)

 Charles Hermite - Wikipedia, the free encyclopedia
Hermite polynomials, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor.
Charles Hermite (pronounced "air meet", or, in IPA, /ˌʃaʁl ɛʁˈmit/) (December 24, 1822 - January 14, 1901) was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
He was the first to prove that e, the base of natural logarithms, is a transcendental number. /wiki/Charles_Hermite   (257 words)

 Talk:Glucose - Wikipedia, the free encyclopedia
Similar to with cyclic alpha formation the double bond between the C and O is broken and the H from the 5th carbon leaves the hydroxyl group to join with the O. Many oligosaccharides have structures that are dependant on the structure of glucose because glucose plays a major role in the makeup of them.
Maltose is formed with an alpha-d-glucose and a beta-glucose and catalyzing the reaction with an enzyme.
The conversion from straight chain to cyclic alpha-glucose, the double bond between the C and O is broken and the H from the 5th carbon leaves the hydroxyl group to join with the O. If the aldehyde is in O=C-H form it will become beta (Figure-12) when it becomes cyclic. /wiki/Talk:Glucose   (4034 words)

 Sixth form college - Wikipedia, the free encyclopedia
The first comprehensive intake Sixth Form Colleges in England were established at the end of the 1960s and they have since proved popular with students, their parents, and other groups in the community.
A sixth form college is an educational institution in England, Wales or Northern Ireland where students aged 16 to 18 complete post-compulsory further education qualifications, such as A-levels.
Those wishing to continue may either stay on at a secondary school with an attached sixth form, transfer to a local Sixth Form College, or go to a more vocationally-orientated further education college (depending on geographical location there may be little choice as to which of these options can be taken). /wiki/Sixth_form_college   (347 words)

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