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A modified backward Euler scheme for the diffusion equation subject to purely integral conditions
Diffusion equation Modified backward Euler method
2010/9/25
In this paper, a modified backward Euler scheme is developped for obtaining approximate solution to the initial-boundary value problem for one-dimensional diffusion equation with purely integral condi...
On two inequalities similar to Hardy-Hilbert's integral inequality
Hardy-Hilbert inequality weight function
2010/9/20
Two new inequalities similar to Hardy- Hilbert’s inequality are given.
A note on integral transforms and partial differential equations
Laplace transform Sumudu transform convolution
2010/9/20
In this study, we apply double integral transforms to solve partial differential equation namely double Laplace and Sumudu transforms, in particular the wave and poisson’s equations were solved by dou...
The expansions approach for solving Cauchy integral equation of the first kind
Cauchy integral equation Chebyshev polynomials
2010/9/27
In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determine...
Aim of this work is a broad-band study with INTEGRAL, Swift and XMM-Newton satellites of a sample of 9 blazars (7 FSRQ and 2 BL Lac) with redshift up to about 4. The spectral analysis has shown clear ...
Integral Octonions, Octonion XY-Product, and the Leech Lattice
Integral Octonions Octonion XY-Product
2010/12/23
The integral octonions arise from the octonion XY-product. A parallel is shown to exist with the quaternion Z-product. Connections to the laminated lattices, $\Lambda_{4}$, $\Lambda_{8}$, $\Lambda_{16...
A note on the vector Schwinger Model with the photon mass term: Gauge invariant reformulation, operator solution and path integral formulation
vector Schwinger Model photon mass term
2010/12/23
Vector Schwinger model is reinvestigated with the mass like term for gauge field. Phase space structure has been determined in this situation. It has been found that mass of the gauge boson acquires ...
A Symbolic Summation Approach to Feynman Integral Calculus
Symbolic Summation Feynman Integral Calculus
2010/12/27
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Lauren...
A Symbolic Summation Approach to Feynman Integral Calculus
Symbolic Summation Feynman Integral Calculus
2010/12/27
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent...
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter. In the odd case, int...
Jacob's ladders, Bessel's functions and the asymptotic solutions of a new class of nonlinear integral equations
Jacob's ladders Bessel's functions the asymptotic solutions
2010/11/19
It is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the Bessel's functions. In this direction, a new class of the nonlinear integral equations is introduce...
Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory
the Borwein-Broadhurst conjecture dilogarithmic integral arising quantum field theory
2010/11/8
Borwein and Broadhurst, using experimental-mathematics techniques, in 1998 identified numerous hyperbolic 3-manifolds whose volumes are rationally related to values of various Dirichlet L series $\te...
INTEGRAL observations of the GeV blazar PKS1502+106 and of the hard X-ray bright Seyfert Galaxy Mkn841
galaxies active – quasars individual PKS 1502+106 – Galaxies Seyfert – galaxies individual Mkn 841 – radiation
2010/11/16
Context. Extragalactic nuclear activity is best explored with observations at high energies, where the most extreme flux and spectral variations are expected to occur, witnessing changes in the accret...
Integral Menger curvature for sets of arbitrary dimension in $\mathbb{R}^n$. Part I: Uniform Ahlfors regularity
Integral Menger curvature math
2010/11/15
We propose the notion of integral Menger curvature for $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies Ahlfors regularity with constant depe...
Multivalued stochastic partial differential-integral equations via backward doubly stochastic differential equations driven by a Lévy process
partial differential-integral equations stochastic differential equations
2010/11/19
In this paper, we deal with a class of backward doubly stochastic differential equations (BDSDEs, in short) involving subdifferential operator of a convex function and driven by Teugels martingales a...