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In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…

Quantum Physics · Physics 2009-11-10 Christopher A. Fuchs , Ruediger Schack , Petra F. Scudo

We determine sufficient structure for an elementary topos to emulate E. Nelson's Internal Set Theory in its internal language, and show that any topos satisfying the internal axiom of choice occurs as a universe of standard objects and…

Category Theory · Mathematics 2023-09-07 José Siqueira

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of…

Rings and Algebras · Mathematics 2021-05-14 Wesley G. Lautenschlaeger , Thaísa Tamusiunas

We begin by investigating the class of commutative unital rings in which no two distinct elements divide the same elements. We prove that this class forms a finitely axiomatizable, relatively ideal distributive quasivariety, and it equals…

Rings and Algebras · Mathematics 2019-01-21 P. N. Anh , Keith A. Kearnes , Agnes Szendrei

We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical…

Commutative Algebra · Mathematics 2026-04-17 Ignacio Ojeda

We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also…

Statistical Mechanics · Physics 2009-10-31 Etsuro Date , Shi-shyr Roan

We show that a suitable ring with a ``nice'' topology, in which convergent limits of units are units, is an \aleph_0-exchange ring. We generalize the argument to show that a semi-regular ring, R, with a ``nice'' topology, is a full exchange…

Rings and Algebras · Mathematics 2007-05-23 Pace P. Nielsen

In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.

Logic · Mathematics 2009-05-12 Karim Nour , Khelifa Saber

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

Algebraic Topology · Mathematics 2010-07-09 John R. Klein , Bruce Williams

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

Mathematical Physics · Physics 2013-11-12 Do-Hyung Kim

In this paper, we introduce the concept of ideal on CL-algebra. It is proved that this concept generalizes the notion of ideal on Residuated Lattices. Prime ideal on CL-algebra are defined and few interesting properties are obtained. It has…

Logic · Mathematics 2020-07-28 Safiqul Islam

Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…

Dynamical Systems · Mathematics 2008-01-28 V. O. Groppen

This is an exposition of Gauss's proof of Descartes's rule of signs.

History and Overview · Mathematics 2022-05-11 Melvyn B. Nathanson

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

Number Theory · Mathematics 2010-08-03 Antal Bege , Kinga Fogarasi

We prove several extensions of the Erdos-Fuchs theorem.

Number Theory · Mathematics 2016-08-31 Li-Xia Dai , Hao Pan

A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra.

Representation Theory · Mathematics 2023-05-16 Sajid Ali , Hassan Azad , Indranil Biswas , Fazal M. Mahomed

The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

Commutative Algebra · Mathematics 2026-03-09 Kazuhiko Kurano , Kazuma Shimomoto

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over…

Number Theory · Mathematics 2013-02-11 Stéphane Fischler , Mumtaz Hussain , Simon Kristensen , Jason Levesley

This is a series of lecture notes explaining topos theory and its application in physics.

Mathematical Physics · Physics 2012-07-10 Cecilia Flori

This article presents a generalization of the RSA cryptosystem for rings with commuting ideals. An analogue of the Euler function for ideals and the concept of an RSA-ideal are defined. An analog of a cryptosystem for the ring with…

Rings and Algebras · Mathematics 2023-04-03 Marat Nasrutdinov , Serge Tronin