相关论文: Fuchsian differential equation for the perimeter g…
In this manuscript, we elaborate on a procedure to derive $\epsilon$-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms. We…
Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a…
The discovery of new crystalline materials calls for generative models that handle periodic boundary conditions, crystallographic symmetries, and physical constraints, while scaling to large and structurally diverse unit cells. We propose a…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;\alpha)$. We call it fractional Fourier series of the order $\alpha$. Extending the basis functions of the linear space…
A formula is derived that provides generating functions for any multi-j-symbol, such as the 3-j-symbol, the 6-j-symbol, the 9-j-symbol, etc. The result is completely determined by geometrical objects (loops and curves) in the graph of the…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…
The subject of this paper are polynomials in multiple non-commuting variables. For polynomials of this type orthogonal with respect to a state, we prove a Favard-type recursion relation. On the other hand, free Sheffer polynomials are a…
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
We first show how, from the general 3rd order ODE of the form z'''=F(z,z',z'',s), one can construct a natural Lorentzian conformal metric on the four-dimensional space (z,z',z'',s). When the function F(z,z',z'',s) satisfies a special…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational R\'{e}dei functions. A complete characterization of their compositional inverses is also given. These…
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
Since their introduction by Andrews, generalized Frobenius partitions have interested a number of authors, many of whom have worked out explicit formulas for their generating functions in specific cases. This has uncovered interesting…
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
We solve the time evolution of the density matrix both for fermions and bosons in the presence of a homogeneous but time dependent external electric field. The number of particles produced by the external field, as well as their…
In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating function some well-known and new identities for the Euler…
We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…