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pro vyhledávání: '"Glasser, M L"'
Autor:
Glasser, M. L.
An $n$-dimensional generalization of the Onsager Ising partition function integral is reduced to a single integral and applied to evaluate the partition function and residual entropy of an eight vertex model.
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/2307.06854
Autor:
Glasser, M. L.
This short note investigates a number of index integrals of products of the Lommel functions $s_{\mu,\nu}(a)$ and uncovers an integral relationship. between this function and the Tchebyshev polynomials $T_{2n}(x)$.
Comment: 5 Pages
Comment: 5 Pages
Externí odkaz:
http://arxiv.org/abs/2203.03395
Autor:
Glasser, M. L.
It is proposed that the validity, or not, of the Riemann Hypothesis might be established on the basis of the integral $$\int\frac{\xi(2s)}{\xi(s)}ds$$ where $$\xi(s)=(s-1)\pi^{-s/2}\Gamma(1+s/2)\zeta(s).$$
Comment: 3pages
Comment: 3pages
Externí odkaz:
http://arxiv.org/abs/2108.06860
In this work we analyze the statistical thermodynamics of Diced lattice carriers employing a Greens function formulation to examine the grand potential, Helmholtz free energy, the grand and ordinary partition functions and entropy. This facilitates t
Externí odkaz:
http://arxiv.org/abs/2008.05113
Autor:
Glasser, M. L.
In this note a one-dimensional band model is proposed based on a periodic Dirac comb having an identical mass distribution $m(x)$ . in each unit cell. The mass function is represented as a Hermitian, non-local separable operator. Two specific cases--
Externí odkaz:
http://arxiv.org/abs/1910.00549
Autor:
Glasser, M. L.
This note investigates a number of integrals of and integral equations satisfied by Riemann's $\xi-$function. A different, less restrictive, derivation of one of his key identities is provided. This work centers on the critical strip and it is argued
Externí odkaz:
http://arxiv.org/abs/1901.07011
Publikováno v:
Journal of Integer Sequences 22 (2019), article 19.4.7, 16 pp
Let $f_0(z) = \exp(z/(1-z))$, $f_1(z) = \exp(1/(1-z))E_1(1/(1-z))$, where $E_1(x) = \int_x^\infty e^{-t}t^{-1}{\,d}t$. Let $a_n = [z^n]f_0(z)$ and $b_n = [z^n]f_1(z)$ be the corresponding Maclaurin series coefficients. We show that $a_n$ and $b_n$ ma
Externí odkaz:
http://arxiv.org/abs/1812.00316
Autor:
Glasser, M. L.
The Moll-Arias de Reyna integral [1] $$\int_0^{\infty}\frac{dx}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi(x)+\sqrt{\varphi(x)}}}$$ $$\varphi(x)=1+\frac{4}{3}\left(\frac{x}{x^2+1}\right)^2$$ is generalised and several values are given.
Comment: 4 page
Comment: 4 page
Externí odkaz:
http://arxiv.org/abs/1802.10564
We decorate the one-dimensional conic oscillator $\frac{1}{2} \left[-\frac{d^{2} }{dx^{2} } + \left|x \right| \right]$ with a point impurity of either $\delta$-type, or local $\delta'$-type or even nonlocal $\delta'$-type. All the three cases are exa
Externí odkaz:
http://arxiv.org/abs/1706.04916
Autor:
Glasser, M. L.
The exact Green function is constructed for a quantum system, with known Green function, which is decorated by two delta function impurities.It is shown that when two such impurities coincide they behave as a single singular potential with combined a
Externí odkaz:
http://arxiv.org/abs/1702.05111