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Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and lattices

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Chinese Physics B 2009年第7期18卷 2634-2641页

作者：傅景礼聂宁明黄健飞 Jiménez Salvador 唐贻发 Vzquez Luis 赵维加 Institute of Mathematical Physics Zhejiang Sci-Tech University State Key Laboratory of Scientific and Engineering Computing ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences department of Mathematics Qingdao University departamento de matema'tica Aplicada TTII E.T.S.I.Telecomunicacio'nUniversidad Polit'ecnica de Madrid28040-MadridSpain departamento de matemática Aplicada Facultad de MatemáticasInstituto de Matemática Interdisciplinar(IMI)Universidad Complutense de Madrid28040-MadridSpain departamento de matemática Aplicada Facultad de InformáticaInstituto de Matemática Interdisciplinar(IMI)Universidad Complutense de Madrid28040-MadridSpain

This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange Maxwell equations in differences which correspond to mechanico-electrical systems,by adapting existing differential *** particular,it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical *** an application,it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.

关键词： Lagrange Maxwell equation Lie point symmetry discrete mechanico-electrical system conserved quantity

Liouvillian and Analytic Integrability of the Quadratic Vector Fields Having an Invariant Ellipse

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Acta Mathematica Sinica,English Series 2014年第3期30卷 453-466页

作者： Jaume LLIBRE Claudia VALLS departament de matemàtiques Universitat Autònoma de Barcelona departamento de matemtica Instituto Superior TcnicoUniversidade Tcnica de Lisboa

We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant *** precisely,a quadratic system having an invariant ellipse can be written into the form x=x2＋y2-1＋y（ax＋by＋c）,y=x（ax＋by＋c）,and the ellipse becomes x2＋y2=*** prove that（i） this quadratic system is analytic integrable if and only if a=0;（ii） if x2＋y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2＋y2=1 is not a limit cycle;and（iii） if x2＋y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0.

关键词： Liouvillian integrability quadratic planar polynomial vector fields invariant ellipse

The tensor embedding for a Grothendieck cosmos

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Science China Mathematics 2023年第11期66卷 2471-2494页

作者： Henrik Holm Sinem Odabasi department of Mathematical Sciences University of CopenhagenCopenhagen 02100Denmark instituto de Ciencias Físicas y matemáticas Universidad Austral de ChileValdivia 5090000Chile

While the Yoneda embedding and its generalizations have been studied extensively in the literature,the so-called tensor embedding has only received a little *** this paper,we study the tensor embedding for closed symmetric monoidal categories and show how it is connected to the notion of geometrically purity,which has recently been investigated in the works of Enochs et al.(2016)and Estrada et al.(2017).More precisely,for a Grothendieck cosmos,i.e.,a bicomplete Grothendieck category V with a closed symmetric monoidal structure,we prove that the geometrically pure exact category(V,ε■)has enough relative injectives;in fact,every object has a geometrically pure injective *** also show that for some regular cardinalλ,the tensor embedding yields an exact equivalence between(V,ε■)and the category ofλ-cocontinuous V-functors from Presλ(V)to V,where the former is the full V-subcategory ofλ-presentable objects in *** many cases of interest,λcan be chosen to be■0 and the tensor embedding identifies the geometrically pure injective objects in V with the(categorically)injective objects in the abelian category of V-functors from fp(V)to *** we explain,the developed theory applies,e.g.,to the category Ch(R)of chain complexes of modules over a commutative ring R and to the category Qcoh(X)of quasi-coherent sheaves over a(suitably nice)scheme X.

关键词： enriched functor exact category (pre)envelope (pure)injective object purity symmetric monoidal category tensor embedding Yoneda embedding

LINEAR STIELTJES EQUATION WITH GENERALIZED RIEMANN INTEGRAL AND EXISTENCE OF REGULATED SOLUTIONS

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Acta Mathematicae Applicatae Sinica 2001年第4期17卷 526-531页

作者： L.BARBANTI instituto de matemática e Estatística Departamento de Matemática Universidade de São Paulo São Paulo Brasil

In this work we establish an existence theorem of regulated solutions for a class of Stieltjes equations which involve generalized fuemann kind of integrals. The general method spplied consists in considering the continuous-time Stieltjes equation as limit of discrete processes. This approach will prove fruitful in the study of the controllability of Stieltjes systems, because it will be possible to get properties on the continuous time equation by transferring properties of the discrete ones.

关键词： Existence of regulated solutions integral equations approximation scheme in time for Stieltjes equations

Restabilization Process in Matching Markets with Workers Proposing

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Open Journal of Discrete Mathematics 2022年第4期12卷 101-112页

作者： Millán Beatriz instituto de matemática Aplicada San Luis IMASL Universidad Nacional de San Luis and CONICET San Luis Argentina departamento de matemática Universidad Nacional de San Juan San Juan Argentina

This paper is focused on the analysis, in the framework of lattice theory, of the matchings obtained from restabilization (after disruption) of stable matchings. When the disruption is due to entry workers or closure of firms the unemployed workers make offers to firms. The stable matching obtained is the firms-worst stable matching of the set of stable matchings that the firms weakly prefer to the initial stable matching (i.e., before being disrupted by changes in the population). More precisely, their position within the lattice of stable matchings is shown.

关键词： Stable Matchings Restabilization Lattice

Maximum mass of magnetic white dwarfs

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Research in Astronomy and Astrophysics 2015年第10期15卷 1735-1741页

作者： Daryel Manreza Paret Jorge Ernesto Horvath Aurora Pérez Martínez departamento de Fisica General Facultad de FísicaUniversidad de la Habana instituto de Astronomia Geofisica e Ciencias Atmosfericas USP instituto de Cibernética Matemática y Física(ICIMAF)

We revisit the problem of the maximum masses of magnetized white dwarfs （WDs）. The impact of a strong magnetic field on the structure equations is addressed. The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components. We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure whenB ≥ 10^13 G. This fact estab- lishes an upper bound for a magnetic field and the stability of the configurations in the （quasi） spherical approximation. Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the val- ues of the magnetic field needed for them are higher than this bound. To proceed into the anisotropic regime, we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work. From the solutions of the structure equations in cylindrical symmetry we have con- firmed the same bound for B- 10^13 G, since beyond this value no physical solutions are possible. Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.

关键词： magnetic fields -- white dwarfs -- equation of state

Anisotropic stellar structure equations for magnetized strange stars

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Research in Astronomy and Astrophysics 2015年第7期15卷 975-985页

作者： Daryel Manreza Paret Jorge Ernesto Horvath Aurora Pérez Mart'nez departamento de F'sica General Facultad de F'sica Universidad de la Habana instituto de Astronomia Geofisica e Ciencias Atmosfericas USP instituto de Cibernética Matemática y Física (ICIMAF)

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark *** assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.

关键词： magnetic fields -- stars: neutron -- equation of state

A generalization of the half-normal distribution

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Applied Mathematics(A Journal of Chinese Universities) 2016年第4期31卷 409-424页

作者： Yolanda M. Gomez Ignacio Vidal departamento de matemáticas facultad de ciencias universidad de católica del norte Antofagasta Chile instituto de matemática y física universidad de talca Chile

In this paper we introduce an extension of the half-normal distribution in order to model a great variety of non-negative data. Its hazard rate function can be decreasing or increasing, depending on its parameters. Some properties of this new distribution are presented. For example, we give a general expression for the moments and a stochastic representation. Also, the cumulative distribution function, the hazard rate function, the survival function and the quantile function can be easily evaluated. Maximum likelihood estimators can be computed by using numerical procedures. Finally, a real-life dataset has been presented to illustrate its applicability.

关键词： half-normal distribution generalized half-normal distribution maximum likelihood estimate

ASYMPTOTIC RAREFACTION WAVES FOR BALANCE LAWS WITH STIFF SOURCES

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Acta Mathematica Scientia 2009年第6期29卷 1613-1628页

作者： W. Lambert D. Marchesin 1-instituto Nacional de matemtica Pura e Aplicada Estrada Dona Castorina 11022460-320 Rio de Janeiro RJ Brazil instituto de matemtica Pura e Aplicada Estrada Dona Castorina 11022460-320 Rio de Janeiro RJ Brazil

We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.

关键词： balance laws asymptotic expansion rarefaction waves compositional models