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In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation , Fenchel transformation , or Fenchel conjugate (after Adrien-Marie Legendre and Werner Fenchel ).
The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by I n, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example I n-1 or I n-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction ...
French grammar is the set of rules by which the French language creates statements, questions and commands. In many respects, it is quite similar to that of the other Romance languages. French is a moderately inflected language.
For example: peler (to peel) -> je p-èle (present) / je p-èlerai (futur) / je p-èlerais (conditional). In most -eler and -eter verbs, the writer must either change the e to an è before endings that start with a silent e , or change the l or t to ll or tt .
French verbs are conjugated by isolating the stem of the verb and adding an ending. In the first and second conjugation, the stem is easily identifiable from the infinitive, and remains essentially constant throughout the paradigm. For example, the stem of parler ("speak") is parl-and the stem of finir ("finish") is fin-. In the third group ...
French verbs have a large number of simple (one-word) forms. These are composed of two distinct parts: the stem (or root, or radix), which indicates which verb it is, and the ending (inflection), which indicates the verb's tense (imperfect, present, future etc.) and mood and its subject's person (I, you, he/she etc.) and number, though many endings can correspond to multiple tense-mood-subject ...
In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L p space ([,]).
Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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