Related papers: Finite Difference Calculus for Alternating Permuta…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
We introduce a finite-time detailed fluctuation theorem for the environmental entropy of the form $\tilde P(\Delta S_{env}) = e^{\Delta S_{env}} \tilde P(-\Delta S_{env})$ for an appropriately weighted probability density of the external…
The theory of differential equations has an arithmetic analogue in which derivatives of functions are replaced by Fermat quotients of numbers. Many classical differential equations (Riccati, Weierstrass, Painlev\'{e}, etc.) were previously…
The purpose of [1] was as follows. ?We consider special sets of continuants which occur in applications. For these sets we solve the problem of finding maximal and minimal continuants. There are several methods for finding extremum such as…
We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that…
This work provides an effective algorithm for distinguishing finite quotients between two non-isomorphic finitely generated Fuchsian groups $\Gamma$ and $\Lambda$. It will suffice to take a finite quotient which is abelian, dihedral, a…
Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.
Differentiation is an important task in control, observation and fault detection. Levant's differentiator is unique, since it is able to estimate exactly and robustly the derivatives of a signal with a bounded high-order derivative.…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
From a transfer formula in multivariate finite operator calculus, comes an expansion for the determinant similar to Ryser's formula for the permanent. Although this one contains many more terms than the usual determinant formula. To prove…
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource…
We present a new alternative theorems for sequences of functions. As applications, we extend recent results in the literature related to first-order necessary conditions for optimality problems. Our contributions involve extending…
Conditional specification of distributions is a developing area with increasing applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…