Related papers: On the Summability Problem of Multivariate Rationa…
The invariant polytope algorithm was a breakthrough in the joint spectral radius computation, allowing to find the exact value of the joint spectral radius for most matrix families~\cite{GP2013,GP2016}. This algorithm found many…
In the present article, our aim is to examine some useful problems including the convolution problem, sufficiency criteria, coefficient estimates and Fekete-Szego type inequalities for a new subfamily of analytic and multivalent functions…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{\pi i \gamma n^2}$; Fusion of integrals, and…
Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves…
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a special case, determining the generating functions, some…
Ibeling et al. (2023). axiomatize increasingly expressive languages of causation and probability, and Mosse et al. (2024) show that reasoning (specifically the satisfiability problem) in each causal language is as difficult, from a…
Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with…
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…
Using a property of the q-shifted factorial, an identity for q-binomial coefficients is proved, which is used to derive the formulas for the q-binomial coefficient for negative arguments. The result is in agreement with an earlier paper…
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the whole sample. We propose a general framework based on the…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
We consider the problem of optimizing a multivariate quadratic function where each decision variable is constrained to be a complex $m$'th root of unity. Such problems have applications in signal processing, MIMO detection, and the…
This paper addresses automatic summarization of videos in a unified manner. In particular, we propose a framework for multi-faceted summarization for extractive, query base and entity summarization (summarization at the level of entities…
This note deals with the boundedness of the $H^\infty$ functional calculus of Ritt operators $T$ and associated square function estimates. The purpose is to give a shorter, concise and slightly more general approach towards Le~Merdy's…