Related papers: On the Summability Problem of Multivariate Rationa…
Iterating Newton's method symbolically for the general quadratic yields a rational function, the numerator and denominator of which are polynomials with highly composite coefficients.
We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
For a rational matrix function R of one variable in general position, the matrix functions R(x)/R(y) and R(y)\R(x) of two variables are considered. For these matrix functions of two variables, representations which are analogous to the…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
The analogue of Hilbert's tenth problem over $\mathbb{Q}$ asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as one of the main open problems in the area of undecidability…
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…
We use a function field version of the circle method to prove that a positive proportion of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of minimal degree from $\mathbb{F}_q[t]$, assuming a suitable form of the…
The classical Ritt's Theorems state several properties of univariate polynomial decomposition. In this paper we present new counterexamples to Ritt's first theorem, which states the equality of length of decomposition chains of a…
We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate…
We give quantitative bounds for the number of quasi-integral points in orbits of semigroups of rational maps under some conditions, generalizing previous work of L. C. Hsia and J. Silverman (2011) for orbits generated by the iterations of…
Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…
For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded…
We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial…
An algorithm for computing the limit of a quotient of bivariate real analytic functions has been developed by one of the authors in (Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, 50, 2013, 197…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
In the direction towards the question when mixed multiplicities are equal to the Hilbert-Samuel multiplicity of joint reductions, this paper not only generalizes [28, Theorem 3.1] that covers the Rees's theorem [13, Theorem 2.4], but also…