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We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.

Commutative Algebra · Mathematics 2024-05-01 Mircea Cimpoeas

A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…

Logic · Mathematics 2013-11-11 Jesse Alama

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

Statistics Theory · Mathematics 2024-11-22 Sandra Fortini , Sonia Petrone

In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.

Combinatorics · Mathematics 2008-01-08 Fabien Durand

We construct a prequential test of probabilistic forecasts that does not reject correct forecasts when the data-generating processes is exchangeable and is not manipulable by a false forecaster.

Statistics Theory · Mathematics 2014-07-21 Alvaro Sandroni , Eran Shmaya

Ichikawa et al. [Phys. Rev. A 78, 052105 (2008)] showed that exchange symmetry gives rise to simple characterization of whether multipartite pure quantum states being either globally entangled or fully separable. In this Brief Report, we…

Quantum Physics · Physics 2010-06-01 Tzu-Chieh Wei

We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…

Category Theory · Mathematics 2013-01-03 Olivia Caramello

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

Algebraic Geometry · Mathematics 2020-10-07 Ciro Ciliberto

In this paper, we introduce the notion of binomial edge ideals of a clutter and obtain results similar to those obtained for graphs by Rauf \& Rinaldo in \cite{raufrin}. We also answer a question posed in their paper.

Commutative Algebra · Mathematics 2021-05-03 Kamalesh Saha , Indranath Sengupta

This paper investigates the strict comparison theorem under the framework of $G$-expectation, i.e., let $X\leq Y$ q.s., if $X,Y$ satisfy some additional conditions, then $\E[X]<\E[Y]$.

Probability · Mathematics 2010-02-26 Xinpeng Li

We give an elementary proof to Hasse theorem.

General Mathematics · Mathematics 2012-12-12 Jianhua Chen , Debiao He , Zhijin Hu , Yitao Chen , Hao Hu

We introduce a novel notion of pasting shapes for iterated Segal spaces which classify particular arrangements of composing cells in d-uple Segal spaces. Using this formalism, we then continue to prove a pasting theorem for these iterated…

Category Theory · Mathematics 2024-05-24 Jaco Ruit

The article presents the proof of Casas-Alvero conjecture.

Number Theory · Mathematics 2017-05-09 Edward Dobrowolski

We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…

Probability · Mathematics 2009-09-08 Gert de Cooman , Erik Quaeghebeur , Enrique Miranda

In this article we prove several reciprocity theorems for some infinite-dimensional dual pairs of representations on Bargmann-Segal-Fock spaces.

Representation Theory · Mathematics 2007-05-23 Tuong Ton-That

This work is about the structure of the symbolic Rees algebra of the base ideal of a Cremona map. We give sufficient conditions under which this algebra has the "expected form" in some sense. The main theorem in this regard seemingly covers…

Commutative Algebra · Mathematics 2014-07-25 Barbara Costa , Zaqueu Ramos , Aron Simis

We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.

Commutative Algebra · Mathematics 2014-04-30 Amnon Yekutieli

The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…

Quantum Physics · Physics 2007-05-23 Anthony Rizzi

In this paper we state and prove the analogous of the principal ideal theorem of algebraic number theory for the case of 3-manifolds from the point of view of arithmetic topology.

Geometric Topology · Mathematics 2007-06-13 Dimoklis Goundaroulis , Aristides Kontogeorgis

The purpose of this paper is to give an elementary proof to the theorem due to Avramov on certain determinantal ideals of linear type.

Commutative Algebra · Mathematics 2013-06-06 kosuke Fukumuro
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