...$v _ { \infty } ( f ) = - \operatorname { log } | f |$, is similar to the Cauchy residue formula
...s good functoriality properties and is equipped with a graded intersection product, at least after tensoring it by $\mathbf{Q}$.
8 KB (1,219 words) - 21:00, 13 July 2020
obtained by taking the product of $ n $
is Cauchy in $ {\mathsf P} $-
11 KB (1,627 words) - 06:28, 26 March 2023
...onsidered to be the cord of the sector; its area is therefore equal to the product of the length of the cord and one-half of the radius; if these areas are su
...nt must be credited to J.L. Lagrange (1736–1813), and was finally fixed by Cauchy; the latter also gave a rigorous definition of an integral as a limit of su
22 KB (3,357 words) - 17:34, 1 January 2021
...ial of degree greater than zero and with real coefficients factorizes as a product of polynomials of degrees one and two with real coefficients" (Euler, J. d
...), and K. Weierstrass (1872). Here Cantor and Meray used [[Cauchy sequence|Cauchy sequences]] of rational numbers, Dedekind used cuts in the field of rationa
23 KB (3,482 words) - 08:03, 6 June 2020
...(areas, volumes, angles) were represented by the lengths of lines and the product of two such quantities was represented by a rectangle with sides representi
...the absolute value $|x|$ (K. Weierstrass, 1841), the vector $\vec{v}$ (A. Cauchy, 1853), the determinant
18 KB (2,697 words) - 13:11, 13 December 2013
If one solves the Cauchy problem for it on $ 0 \leq \lambda \leq 1 $
with the new scalar product
20 KB (2,830 words) - 19:25, 9 January 2024
As a substitute for the resolvent one can take a continuous operator whose product with $ A - \lambda I $,
<TR><TD valign="top">[8]</TD> <TD valign="top"> J. Chazarain, "Problèmes de Cauchy abstraits et applications à quelques problèmes mixtes" ''J. Funct. Anal.'
34 KB (5,024 words) - 09:12, 21 January 2024
...ion of problems for ordinary differential equations. These studies applied Cauchy's method of contour integration to the resolvent.
...$ n $-fold completeness is, naturally, connected with the solution of the Cauchy problem for the non-stationary equation corresponding to (1).
35 KB (5,059 words) - 04:12, 9 May 2022
...work of J. Fourier, N.I. Lobachevskii, P. Dirichlet, B. Bolzano, and A.L. Cauchy, where the notion of a function as a correspondence between two sets of num
is called the product of the sets $ X $
34 KB (5,509 words) - 22:06, 28 January 2020
...he hydrodynamics of a viscous fluid. The uniqueness of the solution of the Cauchy problem for them has not been proved (proofs have only been found for two-d
...w is played here by the so-called potential vorticity, which is the scalar product of the vorticity of the absolute velocity and the gradient of the entropy.
21 KB (3,004 words) - 08:26, 6 June 2020
...ram that came to be known as the [[Arithmetization of analysis]], Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, and others succeeded in “reducing” anal
* ''Cartesian product'' of $A$ and $B$, denoted $A \times B$, is the set whose members are all po
189 KB (29,059 words) - 14:31, 19 March 2023