Results 41 to 50 of about 12,887 (176)

Applications of hypercomplex automorphic forms in Yang-Mills gauge theories [PDF]

, 2013
In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds.
Krausshar, Rolf Soeren, Tolksdorf, Jürgen   +1 more
core  

UNVEILING THE POWER OF CAUCHY'S RESIDUE THEOREM FOR EVALUATING THE INTEGRATION OF DIFFERENT TYPES OF COMPLEX FUNCTIONS

JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2022
Cauchy's residue theorem gives a relatively general form for a complex integral along a simple closed contour. With the help of Cauchy's residue theorem, an appropriate closed contour can be chosen to calculate some abnormal definite integrals that might be very complicated and difficult to solve by conventional methods.
openaire   +2 more sources

New Generalised Semi‐Analytical Approach for the Multidimensional Nonlinear Collisional Fragmentation Equations

International Journal for Numerical Methods in Fluids, EarlyView.
This work aims to develop a generalised and efficient semi‐analytical method that combines the Laplace decomposition method with Pade approximation (LDMPA) to solve multidimensional nonlinear integro‐partial differential equation. For a one‐dimension case, explicit (closed‐form) solutions for the number density functions are derived for the first time.
Somveer Keshav, Ashok Das, Sukhjit Singh, Randhir Singh, Mehakpreet Singh   +4 more
wiley   +1 more source

Jacobi Identity for Vertex Algebras in Higher Dimensions

, 2005
Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance.
Bakalov B., Bakalov B., Bakalov B., Bojko Bakalov, Borcherds R. E., Borcherds R. E., Dong C., Fattori D., Frenkel E., Frenkel I. B., Frenkel I. B., Goddard P., Kac V. G., Kapustin A., Li H., Li H., Mossberg G., Nikolay M. Nikolov, Nikolov N. M., Nikolov N. M., Primc M., Todorov I. T.   +21 more
core   +3 more sources

Estimating Interaction Effects With Panel Data

Journal of Applied Econometrics, EarlyView.
ABSTRACT This paper analyzes how interaction effects can be consistently estimated under economically plausible assumptions in linear panel models with a fixed T$$ T $$‐dimension. We advocate for a correlated interaction term effects (CITE) estimator and show that it is consistent under conditions that are not sufficient for consistency of the ...
Chris Muris, Konstantin M. Wacker
wiley   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

Trigonometric integrals evaluated in terms of Riemann zeta and Dirichlet beta functions

Open Mathematics
Three classes of trigonometric integrals involving an integer parameter are evaluated by the contour integration and the residue theorem. The resulting formulae are expressed in terms of Riemann zeta function and Dirichlet beta function.
Li Jing, Chu Wenchang
doaj   +1 more source

Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo, Delfina Gómez, Maria‐Eugenia Pérez‐Martínez   +2 more
wiley   +1 more source

Analytical Solutions of Systems of Linear Delay Differential Equations by the Laplace Transform: Featuring Limit Cycles

Mathematical and Computational Applications
In this paper we develop an approach for obtaining the solutions to systems of linear retarded and neutral delay differential equations. Our analytical approach is based on the Laplace transform, inverse Laplace transform and the Cauchy residue theorem ...
Gilbert Kerr, Nehemiah Lopez, Gilberto González-Parra   +2 more
doaj   +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, Gentili, Graziano, Sabadini, Irene   +2 more
core   +1 more source