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We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis to algebras generated by semi-algebraic functions. In which case the standard…
This note introduces the concept of a partially specified prior distribution for certain post hoc inference problems, where a finite population is sampled once in order to make a decision on the presence or complete absence of some…
We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.
In this paper, we show that half of non-zero coefficients of the spinor zeta function of a Siegel cusp form of genus 2 are positive and half are negative.
We prove that the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents are partial $\gamma$-positive, thereby confirming a recent conjecture posed by Lin, Ma…
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for…
In this article, using a twisted version of H\"ormander's $L^2$-estimate, we give new characterizations of notions of partial positivity, which are uniform $q$-positivity and RC-positivity. We also discuss the definition of uniform…
We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.
The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A special case of relative categoricity is identified (almost…
The class of MB(MB0)-tensors, which is a generation of B(B0)-tensors and quasi-double B(B0)-tensors, is proposed. And we prove that an even order symmetric MB(MB0)-tensor is positive (semi-)definite. This provides a positive answer for the…
The purpose of this paper is to revisit the proof of the Gearhart-Pr\"uss-Huang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on the…
The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the…
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
The use of compositions simplifies some aspects of the theory of numerical semigroups. We illustrate this by giving a new proof for the asymptotic number C((1 + $\sqrt$ 5)/2) g of numerical semigroups of genus g and by describing the…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain norms or seminorms. One example is the norms on $\Z/N\Z$ introduced by Gowers in his proof of Szemer\'edi's…
We revisit one of Zilber's early results in model-theoretic algebra, viz. definability in Schur's lemma. This takes place in a broader context than the original version from the seventies. The present exposition contains results extracted…
In this note we introduce and define half Cauchy sequences. We prove that a sequence of real numbers is convergent if and only if it is bounded and half Cauchy. We also provide an example of how the concept may be used.