Results 21 to 30 of about 12,886 (197)
Application of Cauchy’s Residue Theorem in Several Improper Integrals
Highlights in Science, Engineering and Technology, 2023 Calculating definite integrals in complex functions requires the Cauchy's residue theorem, which is a key concept in the complex variables. It is based on several ideas, including the isolated singular points theory, the Laurent theorem, and the Cauchy integral theorem.
openaire +1 more source
Applications of Cauchy’s Residue Theorem in Computing Improper Integral
Highlights in Science, Engineering and Technology, 2023 An improper integral is a definite integral that either has an infinite interval or has the integrand that is not defined on some points in the interval. Many improper integrals are difficult to compute by using real analysis methods, especially those containing infinity.
openaire +1 more source
Analytical Solution for the Problem of Point Location in Arbitrary Planar Domains
AlgorithmsThis paper presents a general analytical solution for the problem of locating points in planar regions with an arbitrary geometry at the boundary. The proposed methodology overcomes the traditional solutions used for polygonal regions.
Vitor Santos
doaj +1 more source
General Variational Formulas for Abelian Differentials
, 2018 We use the jump problem technique developed in a recent paper by Grushevsky, Krichever and the second author to compute the variational formula of any stable differential and its periods to arbitrary precision in plumbing coordinates.
Hu, Xuntao, Norton, Chaya
core +1 more source
Revisiting stress propagation in a three-dimensional elastic sphere under diametric loading
Nihon Kikai Gakkai ronbunshuThe stress propagation for a three-dimensional elastic sphere under a diametric loading condition in the framework of the linear elastodynamics is revisited. By describing displacements in terms of scalar and vector potentials using the Helmholtz theorem,
Yosuke SATO, Satoshi TAKADA
doaj +1 more source
Advanced Science, EarlyView.A universal laser absorption model based on spectral integration enables the design of ultrabroadband dielectric multilayer reflectors for laser protection. The model reveals exponential decay of absorption characterized by two coefficients, and a design that prioritizes short‐wavelength reflection minimizes heating.
Yukang Feng +8 more
wiley +1 more source
Subuniformity of harmonic mean p$$ p $$‐values
Canadian Journal of Statistics, EarlyView.Abstract We obtain several inequalities on the generalized means of dependent p$$ p $$‐values. In particular, the weighted harmonic mean of p$$ p $$‐values is strictly subuniform under several dependence assumptions of p$$ p $$‐values, including independence, negative upper orthant dependence, the class of extremal mixture copulas, and some Clayton ...
Yuyu Chen +3 more
wiley +1 more source
Highlights in Science, Engineering and Technology, 2023 Integration is a useful mathematical tool which is applied in a wide range of studies and assists people to solve many problems. Despite methods of real analysis, complex integrations in complex analysis are more beneficial and more convenient than real integrations under certain circumstances.
openaire +1 more source
Asymptotic properties of cross‐classified sampling designs
Canadian Journal of Statistics, EarlyView.Abstract We investigate the family of cross‐classified sampling designs across an arbitrary number of dimensions. We introduce a variance decomposition that enables the derivation of general asymptotic properties for these designs and the development of straightforward and asymptotically unbiased variance estimators.
Jean Rubin, Guillaume Chauvet
wiley +1 more source
A Cauchy kernel for slice regular functions
, 2009 In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula.
Colombo, Fabrizio +2 more
core +1 more source