相关论文: Hall's Condition for Partial Latin Squares
A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$.…
In this paper we give solutions to Hamburger moment problems with missing entries. The problem of completing partial positive sequences is considered. The main result is a characterization of positive definite completable patterns, namely…
Partial difference sets (for short, PDSs) with parameters ($n^2$, $r(n-\epsilon)$, $\epsilon n+r^2-3\epsilon r$, $r^2-\epsilon r$) are called Latin square type (respectively negative Latin square type) PDSs if $\epsilon=1$ (respectively…
A commutative ring R is said to be coverable if it is the union of its proper subrings and said to be finitely coverable if it is the union of a finite number of them. In the latter case, we denote by {\sigma}(R) the minimal number of…
In this paper, we consider the explicit expressions of the normwise condition number for the scaled total least squares problem. Some techniques are introduced to simplify the expression of the condition number, and some new results are…
We study bilayer Fractional Quantum Hall State also known as Halperin state. We prove that for any filling fractions (positive rational numbers), there are infinite solutions that imply that infinite topological states are corresponding to…
We study the following problem: Determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a…
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
The study of the complexity of the equation satisfiability problem in finite groups had been initiated by Goldmann and Russell (2002) where they showed that this problem is in polynomial time for nilpotent groups while it is NP-complete for…
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The condition number is with respect to the least-squares…
We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp…
Let $D$ be a digraph on $p\geq 5$ vertices with minimum degree at least $p-1$ and with minimum semi-degree at least $p/2-1$. For $D$ (unless some extremal cases) we present a detailed proof of the following results [12]: (i) $D$ contains…
Does a given a set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
Quantum Latin squares are a generalization of classical Latin squares in quantum field and have wide applications in unitary error bases, mutually unbiased bases, $k$-uniform states and quantum error correcting codes. In this paper, we put…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two…
We show that any good moduli space $\pi : \mathcal{X} \to Y$ has a splitting after a proper, generically finite covering of $Y$. As an application we generalize Koll\'ar's ampleness lemma to give a criterion for projectivity of a good…
We show how to generate an expression for the number of k-line Latin rectangles for any k. The computational complexity of the resulting expression, as measured by the number of additions and multiplications required to evaluate it, is on…
To get another from a given latin square, we have to change at least 4 entries. We show how to find these entries and how to change them.