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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…

In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.

A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$…

The literature in persistent homology often refers to a "structure theorem for finitely generated graded modules over a graded principal ideal domain". We clarify the nature of this structure theorem in this context.

This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.

In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.

This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…

We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision…

Writing the values of Krawtchouk polynomials as matrices, we consider weighted partial sums along columns. For the general case, we find an identity that, in the symmetric case yields a formula for such partial sums. Complete sums of…

This note presents a simple, universal closed form for the powers of any square matrix. A diligent search of the internet gave no indication that the form is known.

This paper investigates local spectral statistics of singular values for many products of independent large rectangular matrices, sampled from the ensemble of truncated unitary matrices with the invariant Haar measure. Our main contribution…

Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_X-coherent D_X-modules) on X without relying on…

This article is the second in the series and is devoted to the type G_2. The work consists of two parts. In the first part we calculate the structure constants of the complex simple Lie algebra of type G_2. All structure constants are…

This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to…

We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is…

An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…

One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair $(A, B)$ whose nonzero entries are…

This paper shows how to obtain a simple closed form for the elements of a triangular matrix raised to the nth power.

For a positive integer $m$ and a subgroup $\Lambda$ of the unit group $(\mathbb{Z}/m\mathbb{Z})^\times$, the corresponding generalized Kloosterman sum is the function $K(a,b,m,\Lambda) = \sum_{u \in \Lambda}e(\frac{au + bu^{-1}}{m})$.…

We provide exact and asymptotic formulae for the number of unrestricted, respectively indecomposable, $d$-dimensional matrices where the sum of all matrix entries with one coordinate fixed equals 2.