Related papers: Boolean Inner product Spaces and Boolean Matrices
In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical…
A bilinear quadrature numerically evaluates a continuous bilinear map, such as the $L^2$ inner product, on continuous $f$ and $g$ belonging to known finite-dimensional function spaces. Such maps arise in Galerkin methods for differential…
Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers for arbitrary formal languages of finite words over finite…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
Pierce identified 3 invariants of a compact metrisable Boolean space, derived from its Cantor-Bendixson sequence, that determine the space up to homeomorphism. For locally compact spaces we define an additional invariant, the compact rank,…
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.
Some preliminary results are reported on the equivalence of any n-queens problem with the roots of a Boolean valued quadratic form via a generic dimensional reduction scheme. It is then proven that the solutions set is encoded in the…
In this paper, we first explore exponential stability by using Monotonicity inequality and use this information to obtain the existence of Invariant measure for linear Stochastic PDEs with potential in the space of tempered distributions.…
We formulate conjectures regarding the maximum value and maximizing matrices of the permanent and of diagonal products on the set of stochastic matrices with bounded rank. We formulate equivalent conjectures on upper bounds for these…
New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…
Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…
In this article, we study spectral Barron spaces whose elements are made up of some vector-valued functions on a compact group whose Fourier transforms admit a certain summability property. We investigate their functional properties and…
Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector spaces. Some special classes of ordered locally convex…
The main aim of this work is to apply the study of the asymptotic behaviour of generalized eigenvalues between infinite Hermitian definite positive matrices in an important question regarding the location of zeros of Sobolev orthogonal…
A bistochastic matrix B of size N is called unistochastic if there exists a unitary U such that B_ij=|U_{ij}|^{2} for i,j=1,...,N. The set U_3 of all unistochastic matrices of order N=3 forms a proper subset of the Birkhoff polytope, which…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli…