Related papers: A novel approach to the discovery of binary BBP-ty…
In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than that using the expression of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving…
A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
In this paper, we introduce two primality tests based on new divisibility properties of binomial coefficients. These new properties were enunciated and proved in previous work. We also study two similar tests that can be obtained from…
This paper proposes some simple propagation rules which give rise to new binary constant-weight codes.
In this work, tests of symmetry for bivariate copulas are introduced and studied using empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a multiplier bootstrap…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
In this paper, we study the complexity of solving generic over-determined bilinear systems over a finite field $\mathbb{F}$. Given a generic bilinear sequence $B \in \mathbb{F}[\mathbf{x},\mathbf{y}]$, with respect to a partition of…
In the paper, the author elementarily unifies and generalizes eight identities involving the functions $\frac{\pm1}{e^{\pm t}-1}$ and their derivatives. By one of these identities, the author establishes two explicit formulae for computing…
In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…
In this paper, we give a new discovery of conversion of generalized singular values. New formulation is proposed.
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming…
Yang-Baxter system related to quantum doubles is introduced and large class of both continuous and discrete symmetries of the solution manifold are determined. Strategy for solution of the system based on the symmetries is suggested and…
A numerical scheme based on backward differentiation formula (BDF) and generalized differential quadrature method (GDQM) has been developed. The proposed scheme has been employed to investigate three cases of Burgers equation,…