Related papers: Fischer type determinantal inequalities for accret…

This paper provides a characterization of when two expansive matrices yield the same anisotropic local Hardy and inhomogeneous Triebel-Lizorkin spaces. The characterization is in terms of the coarse equivalence of certain quasi-norms…

We consider a natural filtration $\boldsymbol{\operatorname{Bad}}(\delta) \subset \boldsymbol{\operatorname{Bad}}(\delta')$ for $\delta \geq \delta'>0$ on the set of badly approximable numbers to complement the filtration of the well…

Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice.…

We give a short and elementary proof of a theorem of Procesi, Schacher and (independently) Gondard, Ribenboim that generalizes a famous result of Artin. Let $A$ be an $n \times n$ symmetric matrix with entries in the polynomial ring…

Given a matrix $A\in \R^{n\times n}$ and a tall rectangular matrix $B \in \R^{n\times q}$, $q < n$, we consider the problem of making the pair $(A,B)$ dissipative, that is the determination of a {\it feedback} matrix $K \in \R^{q\times n}$…

We study the multiplication operation of square matrices over lattices. If the underlying lattice is distributive, then matrices form a semigroup; we investigate idempotent and nilpotent elements and the maximal subgroups of this matrix…

We prove that every partially ordered set on $n$ elements contains $k$ subsets $A_{1},A_{2},\dots,A_{k}$ such that either each of these subsets has size $\Omega(n/k^{5})$ and, for every $i<j$, every element in $A_{i}$ is less than or equal…

In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dY(t)= -AY(t)dt -f_0(t,Y(t))dt -f_1(t,Y(t),Z(t))dt + Z(t)dW(t) on the interval [0,T], with given final condition at time T, in an infinite…

Let $\mathbb{F}$ be a field, and $n \geq r>0$ be integers, with $r$ even. Denote by $\mathrm{A}_n(\mathbb{F})$ the space of all $n$-by-$n$ alternating matrices with entries in $\mathbb{F}$. We consider the problem of determining the…

A general lattice Boltzmann (LB) model is proposed for solving nonlinear partial differential equations with the form $\partial_t \phi+\sum_{k=1}^{m} \alpha_k \partial_x^k \Pi_k (\phi)=0$, where $\alpha_k$ are constant coefficients, and…

Let $F \subseteq [0,1]$ be a set that supports a probability measure $\mu$ with the property that $ |\widehat{\mu}(t)| \ll (\log |t|)^{-A}$ for some constant $ A > 0 $. Let $\mathcal{A}= (q_n)_{n\in \mathbb{N}} $ be a sequence of natural…

We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…

We continue the study initiated by H. S. Shapiro on Fischer decompositions of entire functions, showing that such decomposition exist in a weak sense (we do not prove uniqueness) under hypotheses regarding the order of the entire function…

The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2)…

Let $X$ be a connected component of the maximal orthogonal grassmannian of a generic $n$-dimensional quadratic form $q$ with trivial Clifford invariant. Consider the canonical epimorphism $\phi$ from the Chow ring of $X$ to the associated…

We recall the well-known Chern-Terng theorem concerning affine minimal surfaces. Next we formulate some complementary (with transversal fields necessarily not parallel) affine B\"acklund theorem. We describe some geometrical conditions…

We consider the problem of the reconstruction of a Schwarz matrix from exactly one given eigenvalue. This inverse eigenvalue problem leads to the Jacobi orthogonal polynomials~$\{P_k^{(-n,n)}\}_{k=0}^{n-1}$ that can be treated as a discrete…

Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we produce discrete fractional Taylor formulae for the first time, and we estimate their…

We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…

We consider a Markov chain X_1, X_2, ..., X_n belonging to a class of iterated random functions, which is "one-step contracting" with respect to some distance d. If f is any separately Lipschitz function with respect to d, we use a well…