Related papers: On p-power freeness in positive characteristic
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools come from the well-known de Rham-Kodaira decomposing theorem on the harmonic…
We study the microstate free entropy of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of their…
We discuss possibilities to test physics beyond the Standard Model in $\vert\Delta c\vert=\vert\Delta u\vert= 1$ semileptonic, hadronic and missing energy decay modes. Clean null test observables such as angular observables, CP-asymmetries…
We study certain physical observables of isoscalar heavy baryons using potential models based on hadronic degrees of freedom. The goal is to compare these results with those from an effective theory obtained in a combined heavy quark and…
We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
We pursue the current developments in random tensor theory by laying the foundations of a free probability theory for tensors and establish its relevance in the study of random tensors of high dimension. We give a definition of freeness…
Given positive integers $m_1, m_2, ..., m_n$, and $n$ general points $p_i$ of ${\bf CP}^2$, bounds are given for the least degree $t$ among plane curves passing through each point $p_i$ with multiplicity at least $m_i$, and for the least…
We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different characterizations of such rings and present conditions for…
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to…
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of…
This paper investigates two feature-scoring criteria that make use of estimated class probabilities: one method proposed by \citet{shen} and a complementary approach proposed below. We develop a theoretical framework to analyze each…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
Let $f\in \mathbb{Z}\lbrack x\rbrack$ be a polynomial of degree $d\geq 3$ without roots of multiplicity $d$ or $(d-1)$. Erd\H{o}s conjectured that, if $f$ satisfies the necessary local conditions, then $f(p)$ is free of $(d-1)$th powers for…
In this article we study limits of models that contain a dimensionful parameter such as the mass of the relativistic point-particle. The limits are analogous to the massless limit of the particle and may be thought of as high energy limits.…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…
We study divided power structures on finitely generated $k$-algebras, where $k$ is a field of positive characteristic $p$. As an application we show examples of $0$-dimensional Gorenstein $k$-schemes that do not lift to a fixed noetherian…
We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for…
In this paper, we proved that, for a semi-stable fibration of a proper smooth surface to a proper smooth curve over a filed of positive characteristic, if the p-rank of the generic fiber is 0, then the base change of the fibration by a…