相关论文: A Tauberian Theorem for Laplace Transforms with Ps…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
In this review we consider first order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad $e_a^I$ and a SO(3,1) connection ${\omega_{aI}}^J$. We study the most…
We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic…
The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four dimensional spacetime. The presence of a boundary breaks the Ward identities which describe the gauge symmetries of the theory, and, using standard…
Varying the gravitational Lagrangian produces a boundary contribution that has various physical applications. It determines the right boundary terms to be added to the action once boundary conditions are specified, and defines the…
We offer new Tauberian theorems for a generalized partition function as our main result. Our analysis provides insight into asymptotic behavior of power series with arithmetic functions as coefficients.
We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann on one component of the boundary. Our motivation is to find the rigorous proof…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
We consider the field theory of $N$ massless bosons which are free except for an interaction localized on the boundary of their 1+1 dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a…
The group of affine transformations with rational coefficients acts naturally on the real line, but also on the $p$-adic fields. The aim of this note is to show that, for random walks whose laws have a finite first moment, all these actions…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for…
In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…
We study the boundary theory of the $\mathbb{Z}_N$ X-cube model using a continuum perspective, from which the exchange statistics of a subset of bulk excitations can be recovered. We discuss various gapped boundary conditions that either…
In his paper "On the Number of Primes Less Than a Given Magnitude", Bernhard Riemann introduced a prime counting function F(x) which counts the number of primes under x. Riemann obtained an analytic expression for F(x) by evaluating an…
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…
The discrete Fourier transform of the greatest common divisor is a multiplicative function, if taken with respect to the same order of the primitive root of unity, which is a well known fact. As such, the transform can be expressed in the…