September 2022 - 10 articles
We consider the inhomogeneous Wiener–Hopf equation whose kernel is a nonarithmetic probability distribution with positive mean. The inhomogeneous term behaves like a submultiplicative function. We establish asymptotic properties of the solution...
A mathematical description of catastrophe in complex systems modeled as a network is presented with emphasis on network topology and its relationship to risk and resilience. We present mathematical formulas for computing risk, resilience, and likelih...
A general population model with variable carrying capacity consisting of a coupled system of nonlinear ordinary differential equations is proposed, and a procedure for obtaining analytical solutions for three broad classes of models is provided. A pa...
Let X⊂Pr be an integral and non-degenerate variety. A “cost-function” (for the Zariski topology, the semialgebraic one, or the Euclidean one) is a semicontinuous function w:=[1,+∞)∪+∞ such that w(a)=1 for a non-empty o...
In this paper, we develop local expansions for the ratio of the centered matrix-variate T density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several probability metri...
We review several one-dimensional problems such as those involving linear Schrödinger equation, variable-coefficient Helmholtz equation, Zakharov–Shabat system and Kubelka–Munk equations. We show that they all can be reduced to solvi...
Shor’s algorithm for prime factorization is a hybrid algorithm consisting of a quantum part and a classical part. The main focus of the classical part is a continued fraction analysis. The presentation of this is often short, pointing to text b...
Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green’s function. In a paper, the problem is treated in dist...
New definitions for fractional integro-differential operators are presented and referred to as delayed fractional operators. It is shown that delayed fractional derivatives give rise to the notion of functional order differentiation. Functional diffe...
This work focuses on the structure and properties of the triangular numbers modulo m. The most important aspect of the structure of these numbers is their periodic nature. It is proven that the triangular numbers modulo m forms a 2m-cycle for any m....
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