Closed-form

	Closed-form Closed form may refer to: Mathematics * Closed-form expression, a finitary expression * Closed differential form In mathematics, especially vector calculus and differential topology, a closed form is a differential form ''α'' whose exterior derivative is zero (); and an exact form is a differential form, ''α'', that is the exterior derivative of another di ..., a differential form \alpha whose exterior derivative d\alpha is the zero form 0, meaning d\alpha = 0. Poetry * In poetry analysis, a type of poetry that exhibits regular structure, such as meter or a rhyming pattern * Trobar clus, an allusive and obscure style adopted by some 12th-century troubadours {{disambig Mathematics disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Closed-form Expression In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. Commonly, the basic functions that are allowed in closed forms are ''n''th root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions. The ''closed-form problem'' arises when new ways are introduced for specifying mathematical objects, such as limits, series, and integrals: given an object specified with such tools, a natural problem is to find, if possible, a ''closed-form expression'' of this object; that is, an expression of this object in terms of previous ways of specifying it. Example: roots of polynomials The quadratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Poetry Analysis Poetry analysis is the process of investigating the form of a poem, content, structural semiotics, and history in an informed way, with the aim of heightening one's own and others' understanding and appreciation of the work. The words ''poem'' and ''poetry'' derive from the Greek ''poiēma'' (to make) and ''poieo'' (to create). One might think of a poem as, in the words of William Carlos Williams, a "machine made of words." A reader analyzing a poem is akin to a mechanic taking apart a machine in order to figure out how it works. There are many different reasons to analyze poetry. A teacher might analyze a poem in order to gain a more conscious understanding of how the poem achieves its effects, in order to communicate this to their students. A writer learning the craft of poetry might use the tools of poetry analysis to expand and strengthen their own mastery. A reader might use the tools and techniques of poetry analysis in order to discern all that the work has to offer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Closed Differential Form In mathematics, especially vector calculus and differential topology, a closed form is a differential form ''α'' whose exterior derivative is zero (); and an exact form is a differential form, ''α'', that is the exterior derivative of another differential form ''β'', i.e. . Thus, an ''exact'' form is in the ''image'' of ''d'', and a ''closed'' form is in the '' kernel'' of ''d'' (also known as null space). For an exact form ''α'', for some differential form ''β'' of degree one less than that of ''α''. The form ''β'' is called a "potential form" or "primitive" for ''α''. Since the exterior derivative of a closed form is zero, ''β'' is not unique, but can be modified by the addition of any closed form of degree one less than that of ''α''. Because , every exact form is necessarily closed. The question of whether ''every'' closed form is exact depends on the topology of the domain of interest. On a contractible domain, every closed form is exact by the Poincaré lemma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Trobar Clus ''Trobar clus'' (), or closed form, was a complex and obscure style of poetry used by troubadours for their more discerning audiences, and it was only truly appreciated by an elite few. It was developed extensively by Marcabru and Arnaut Daniel, but by 1200 its inaccessibility had led to its disappearance. Among the imitators of Marcabru were Alegret and Marcoat, who claimed himself to write ''vers contradizentz'' (contradictory verses), indicative of the incomprehensibility of the ''trobar clus'' style. Below is a sample of the style from Marcoat's '' sirventes'' ''Mentre m'obri eis huisel'', wherein the poet himself remarks on his ''moz clus'' (closed words): :''Mon ''serventes'' no val plus,'' :''que faitz es de bos moz clus'' :''apren lo, Domeing Sarena.''Chambers, 91. Among the late twelfth-century practitionars of ''trobar clus'' was Peire d'Alvernhe, an imitator of Marcabru, while Raimbaut d'Aurenga of the '' trobar ric'' style was influenced by Marcoat. The only troba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]