Related papers: Bitwise operations related to a combinatorial prob…
Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following:…
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…
Sets of $d\times d$ matrices sharing a common invariant cone enjoy special properties, which are widely used in applications. However, finding this cone or even proving its existence/non-existence is hard. This problem is known to be…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
In this note, we intend to produce all latin squares from one of them using suitable move which is defined by small trades and do the similar work on 4-cycle systems. These problems, reformulate as finding basis for the kernel of special…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…
This paper introduces the study of occurrence of symmetries in binary differential equations (BDEs). These are implicit differential equations given by the zeros of a quadratic 1-form, $a(x,y)dy^2 + b(x,y)dxdy + c(x,y)dx^2 = 0,$ for $a, b,…
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar…
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss…
We use computational linear algebra and commutative algebra to study spaces of relations satisfied by quadrilinear operations. The relations are analogues of associativity in the sense that they are quadratic (every term involves two…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…