Related papers: Solutions to some problems on unique representatio…

A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…

We present three simple and efficient protocol constructions to solve Yao's Millionaire Problem when the parties involved are non-colluding and semi-honest. The first construction uses a partially homomorphic Encryption Scheme and is a…

We give a sharply-vertex-transitive solution of each of the nine Hamilton-Waterloo problems left open by Danziger, Quattrocchi and Stevens.

Fake coin problems using balance scales to identify one fake coin and its type among n coins (n > 2) were solved by Dyson in 1946. Dyson gave adaptive solutions with the minimum number of weighings where later weighings may be dependent on…

We resolve three long-standing open problems, namely the (algorithmic) decidability of network coding, the decidability of conditional information inequalities, and the decidability of conditional independence implication among random…

We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…

We consider a natural generalization of the Nagell-Ljunggren equation to the case where the qth power of an integer y, for q >= 2, has a base-b representation that consists of a length-l block of digits repeated n times, where n >= 2.…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

In the paper we presnt a solution of problem 31 of chaptr 8 of the monograph of K. Denecke and S. L. Wismath: Hypridentities and clones, Gordon & Breach, 2000, by presnting two main theorems on hyperbasis for hypervarieties and…

By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…

All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…

In this work, we will prove a uniqueness result for Calder\'on's inverse problem via some integral representation formulas for solutions of the Vekua equation in the framework of Clifford analysis.

We prove that integer programming with three quantifier alternations is $NP$-complete, even for a fixed number of variables. This complements earlier results by Lenstra and Kannan, which together say that integer programming with at most…

We give formulas for the number of representations of non negative integers by various quadratic forms. We also give evaluations in the case of sum of two cubes (cubic case) and the quintic case, as well. We introduce a class of generalized…

We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor…

Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity,…

We reformulate the Cheeger N partition problem as a minimization among a suitable class of BV functions. This allows us to obtain a new existence proof for the Cheeger-N-problem. Moreover, we derive some connections between the Cheeger-2-…

The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a…

Solutions to the Yang-Baxter equation - an important equation in mathematics and physics - and their afforded braid group representations have applications in fields such as knot theory, statistical mechanics, and, most recently, quantum…

We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give…