Integral Identities for Polyanalytic Functions

2019 ◽  
pp. 279-291
Author(s):  
Anastasiia Minenkova ◽  
Olga Trofimenko
Keyword(s):  
Polyanalytic Functions ◽  
Integral Identities

scholarly journals Correction to: On Slice Polyanalytic Functions of a Quaternionic Variable

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Daniel Alpay ◽  
Kamal Diki ◽  
Irene Sabadini
Keyword(s):  
Polyanalytic Functions

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

scholarly journals A New Formulation of Maxwell’s Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 868
Author(s):  
Simona Fialová ◽  
František Pochylý
Keyword(s):  
Numerical Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Control Volume ◽  
Control Volume Method ◽  
Integral Forms ◽  
New Formulation ◽  
Electrical Induction ◽  
Volume Method ◽  
Integral Identities

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

scholarly journals Integral identities for fracture along imperfectly joined anisotropic ceramic bimaterials

2016 ◽  
Vol 36 (9) ◽  
pp. 2389-2402 ◽  
Author(s):  
A. Vellender ◽  
L. Pryce ◽  
A. Zagnetko
Keyword(s):  
Integral Identities

On the generalized fractional Laplacian

2021 ◽  
Vol 24 (6) ◽  
pp. 1797-1830
Author(s):  
Chenkuan Li
Keyword(s):  
Fractional Laplacian ◽  
Special Functions ◽  
Computational Techniques ◽  
Residue Theorem ◽  
End Points ◽  
Proper Subspace ◽  
Classical Sense ◽  
First Time ◽  
Cauchy’S Residue Theorem ◽  
Integral Identities

Abstract The objective of this paper is, for the first time, to extend the fractional Laplacian (−△) s u(x) over the space Ck (Rn ) (which contains S(Rn ) as a proper subspace) for all s > 0 and s ≠ 1, 2, …, based on the normalization in distribution theory, Pizzetti’s formula and surface integrals in Rn . We further present two theorems showing that our extended fractional Laplacian is continuous at the end points 1, 2, … . Two illustrative examples are provided to demonstrate computational techniques for obtaining the fractional Laplacian using special functions, Cauchy’s residue theorem and integral identities. An application to defining the Riesz derivative in the classical sense at odd numbers is also considered at the end.

Integral criteria for closed surfaces with constant mean curvature

2007 ◽  
Vol 463 (2081) ◽  
pp. 1199-1210
Author(s):  
Luca Guzzardi ◽  
Epifanio G Virga
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Second Variation ◽  
Closed Surfaces ◽  
Area Functional ◽  
Symmetric Surface ◽  
The Second Variation ◽  
Integral Identities

We propose three integral criteria that must be satisfied by all closed surfaces with constant mean curvature immersed in the three-dimensional Euclidean space. These criteria are integral identities that follow from requiring the second variation of the area functional to be invariant under rigid displacements. We obtain from them a new proof of the old result by Delaunay, to the effect that the sphere is the only closed axis-symmetric surface.

scholarly journals INVESTIGATION OF SOME RESULTS ARISING FROM POST QUANTUM CALCULUS

2020 ◽  
Vol 20 (3) ◽  
pp. 561-572
Author(s):  
GHAZALA GULSHAN ◽  
RASHIDA HUSSAIN ◽  
ASGHAR ALI
Keyword(s):  
Quantum Calculus ◽  
Special Cases ◽  
Type Integral ◽  
Integral Identities

This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and (p,q)-integrals. The purpose of this paper is to establish different type of identities for (p,q)-calculus. Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.

The Schwarz Problem for Polyanalytic Functions

2005 ◽  
pp. 341-351 ◽  
Author(s):  
Heinrich Begehr ◽  
Dieter Schmersau
Keyword(s):  
Schwarz Problem ◽  
Polyanalytic Functions
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