Related papers: A differential equation for a class of correlation…
The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…
The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…
We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels…
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which…
For a 0-dimensional scheme $\mathbb{X}$ in $\mathbb{P}^n$ over a perfect field $K$, we first embed the homogeneous coordinate ring $R$ into its truncated integral closure $\widetilde{R}$. Then we use the corresponding map from the module of…
We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…
We consider the algebra of N x N matrices as a reduced quantum plane on which a finite-dimensional quantum group H acts. This quantum group is a quotient of U_q(sl(2,C)), q being an N-th root of unity. Most of the time we shall take N=3; in…
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions $K_{0}(b r)$ and $K_{1}(b r)$. This central…
In this article, the existence of global classical solutions to the discrete coagulation equations with collisional breakage is established for collisional kernel having linear growth whereas the uniqueness is shown under additional…
We derive the large distance asymptotics of the Fredholm determinant of the so-called generalised sine kernel at the critical point. This kernel corresponds to a generalisation of the pure sine kernel arising in the theory of random…
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…
Inspired by the article "Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel" (Z. Angew. Math. Phys. (2019) 70:42) which authors D. Zhao and HG. Sun studied the integro-differential equation with the…
The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
Lam\'e's differential equation is a linear differential equation of the second order with a periodic coefficient involving the Jacobian elliptic function ${\rm sn}$ depending on the modulus $k$, and two additional parameters $h$ and $\nu$.…
In this paper, we establish an integral expression for the Dunkl kernel in the context of Dihedral group of an arbitrary order by using the results in \cite{M-Y-Vk} where a construction of the Dunkl intertwining operator for a large set of…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non abelian gauge and scalar fields and for the Riemann connection in the…
It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This paper extends these multiple scales analyses to cases where…
In this manuscript we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. Then, we provide the integration by parts formula and we use $Q-$operator to confirm our results. The…
We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued…