Related papers: Explicit solutions of the multi-loop integral recu…
For a family of Riemann problems for systems of conservation laws, we construct a flux function that is scalar and is capable of describing the Riemann solution of the original system.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
A recurrence relations for sums of powers of complex functions can be written as a system of linear equation AX=B. Using properties of determinant and Cramer's rule for solving systems of linear equation, this paper presents an absolutely…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
General one-loop integrals with arbitrary mass and kinematical parameters in $d$-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects $(n+1)$-point to $n$-point functions. In…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…
We consider the exactly solvable quantum mechanical systems whose eigenfunctions are described by the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the recurrence relations with…
Numerous exact relations exist that relate the effective elastic properties of composites to the elastic properties of their components. These relations can not only be used to determine the properties of certain composites, but also…
The history of linear differential equations is over 350 years. By using Frobenius method and putting the power series expansion into linear differential equations, the recursive relation of coefficients starts to appear. There can be…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
Multi-view depth estimation plays a critical role in reconstructing and understanding the 3D world. Recent learning-based methods have made significant progress in it. However, multi-view depth estimation is fundamentally a…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass…
We establish a systematic way to calculate multiloop amplitudes of infrared safe massless models with Implicit Regularization (IR), with a direct cancelation of the fictitious mass introduced by the procedure. The ultraviolet content of…
We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the…
Renormalization Group Equations in integro-differential form describing the evolution of cascades or resumming logarithmic scaling violations have been known in quantum field theory for a long time. These equations have been traditionally…
In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…