Related papers: A Robin formula for the Fekete-Leja transfinite di…
Some elementary algebraic points regarding the Green function for a localised flux tube are developed. A calculation of the effective action density is included.
We show that a finite set of integers $A \subseteq \mathbb{Z}$ with $|A+A| \le K |A|$ contains a large piece $X \subseteq A$ with Fre\u{i}man dimension $O(\log K)$, where large means $|A|/|X| \ll \exp(O(\log^2 K))$. This can be thought of…
In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…
An extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3. These closed…
We study a Robin boundary problem for degenerate parabolic equation. We suggest a notion of entropy solution and propose a result of existence and uniqueness. Numerical simulations illustrate some aspects of solution behaviour.…
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal form, also known as Jacobi matrix form. This Jacobi matrix structure involves a continued fraction representation for the…
This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and can be understood as that of giving…
Existence and global regularity results for boundary-value problems of Robin type for harmonic and polyharmonic functions in $n$-dimensional half-spaces are offered. The Robin condition on the normal derivative on the boundary of the…
In this paper, we prove a generalization of Green's Hyperplane Restriction Theorem to the case of modules over the polynomial ring, providing in particular an upper bound for the Hilbert function of the general linear restriction of a…
Let E be an elliptic curve over Q with complex multiplication by the ring of integers of an imaginary quadratic field K. In 1991, by studying a certain special value of the Katz two-variable p-adic L-function lying outside the range of…
A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean <J_ij> = Jo. Incorporation of a quadrupolar interaction term…
The inverse Robin problem covers the determination of the Robin parameter in an elliptic partial differential equation posed on a domain $\Omega$. Given the solution of the Robin problem on a subdomain $\omega \subset \Omega$ together with…
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions. The main result is that the convolution of most arithmetic functions…
We find an explicit upper bound for general $L$-functions on the critical line, assuming the Generalized Riemann Hypothesis, and give as illustrative examples its application to some families of $L$-functions and Dedekind zeta functions.…
The incompressible fluid dynamics is reformulated as dynamics of closed loops $C$ in coordinate space. This formulation allows to derive explicit functional equation for the generating functional $\Psi[C]$ in inertial range of spatial…
We give an explicit formula for the arithmetic intersection number of CM cycles on Lubin-Tate spaces for all levels. We prove our formula by formulating the intersection number on the infinite level. Our CM cycles are constructed by…
The type $A$ Kostant partition function is an important combinatorial object with various applications: it counts integer flows on the complete directed graph, computes Hilbert series of spaces of diagonal harmonics, and can be used to…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
For the case of finite life-time broadening the standard Kubo-formula for the optical conductivity tensor is rederived in terms of Green's functions by using contour integrations, whereby finite temperatures are accounted for by using the…
The connection formulae provide a systematic way to compute physical quantities, such as the quasinormal modes, Green functions, in blackhole perturbation theories. In this work, we test whether it is possible to consistently take the…