相关论文: On the sign patterns of entrywise positivity prese…

We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set $A$ whose indicator function is 'approximately multiplicative' and uniformly distributed on short…

Let $f$ be a holomorphic or Maass Hecke cusp form for the full modular group and write $\lambda_f(n)$ for the corresponding Hecke eigenvalues. We are interested in the signs of those eigenvalues. In the holomorphic case, we show that for…

The classical as well as non commutative Korovkin-type theorems deal with convergence of positive linear maps with respect to modes of convergences such as norm convergence and weak operator convergence. In this article, Korovkin-type…

We show the following version of the Schur's product theorem. If $M=(M_{j,k})_{j,k=1}^n\in{\mathbb R}^{n\times n}$ is a positive semidefinite matrix with all entries on the diagonal equal to one, then the matrix $N=(N_{j,k})_{j,k=1}^n$ with…

We consider a large class of piecewise expanding maps T of [0,1] with a neutral fixed point, and their associated Markov chain Y_i whose transition kernel is the Perron-Frobenius operator of T with respect to the absolutely continuous…

The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the closures of these orbits have polynomial representatives…

For a half integral weight modular form $f$ we study the signs of the Fourier coefficients $a(n)$. If $f$ is a Hecke eigenform of level $ N$ with real Nebentypus character, and $t$ is a fixed square-free positive integer with $a(t)\neq 0$,…

In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…

For any closed $K\subseteq\mathbb{R}^n$, in [P.\ J.\ di\,Dio, K.\ Schm\"udgen: $K$-Positivity Preserver and their Generators, SIAM J.\ Appl.\ Algebra Geom.\ 9 (2025), 794--824] all $K$-positivity preserver have been characterized, i.e., all…

We study the recurrence coefficients of the monic polynomials $P_n(z)$ orthogonal with respect to the deformed (also called semi-classical) Freud weight \begin{equation*} w_{\alpha}(x;s,N)=|x|^{\alpha}{\rm…

In a previous paper, dealing with "Applications in $\mathbb{R}^1$," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications…

Given a positive integer $r$ and a prime power $q$, we estimate the probability that the characteristic polynomial $f_{A}(t)$ of a random matrix $A$ in $\mathrm{GL}_{n}(\mathbb{F}_{q})$ is square-free with $r$ (monic) irreducible factors…

Consider an m by N matrix Phi with the Restricted Isometry Property of order k and level delta, that is, the norm of any k-sparse vector in R^N is preserved to within a multiplicative factor of 1 +- delta under application of Phi. We show…

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…

We study singularities f in K[[x_1,...,x_n]] over an algebraically closed field K of arbitrary characteristic with respect to right respectively contact equivalence, and we establish that the finiteness of the Milnor respectively the…

Let $f\in S_k(\Gamma_{0}(N))$ be a normalized Hecke eigenform of even integral weight $k$ and level $N$. Let $j\ge1$ be a positive integer. We prove that for almost all primes $p$, $p\nmid N$, and for all characters $\chi_{0}=\pm 1\pmod N$,…

In this paper we study the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup…

The field of compressed sensing has become a major tool in high-dimensional analysis, with the realization that vectors can be recovered from relatively very few linear measurements as long as the vectors lie in a low-dimensional structure,…

We will show that if $\sM$ is a factor, then for any pair $\f, \p\in\sMdsup$ of normal positive linear functionals on $\sM$, the inequality: $$ \lrnorm{\f}\leq \lrnorm{\p} $$ is equivalent to the fact that there exist a countable family…

In this paper we study the positive definiteness of meet and join matrices using a novel approach. When the set $S_n$ is meet closed, we give a sufficient and necessary condition for the positive definiteness of the matrix $(S_n)_f$. From…