Some suggestions concerning a geometric definition of the symmetry group of non-rigid molecules

A geometric definition of Gabrielov numbers

Revista Matemática Complutense ◽

10.1007/s13163-013-0139-x ◽

2013 ◽

Vol 27 (2) ◽

pp. 447-460 ◽

Cited By ~ 1

Author(s):

Wolfgang Ebeling ◽

Atsushi Takahashi

Keyword(s):

Definition Of ◽

Gabrielov Numbers ◽

Geometric Definition

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Conformal mapping of the Misner–Sharp mass from gravitational collapse

International Journal of Modern Physics D ◽

10.1142/s0218271816500814 ◽

2016 ◽

Vol 25 (07) ◽

pp. 1650081 ◽

Cited By ~ 9

Author(s):

Fayçal Hammad

Keyword(s):

Conformal Mapping ◽

Gravitational Collapse ◽

Conformal Transformation ◽

Conformal Mappings ◽

Conformal Transformations ◽

Theories Of Gravity ◽

Definition Of ◽

Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

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On the geometric definition of quasiconformality

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2021.62.502 ◽

2021 ◽

Vol 62 (5) ◽

pp. 965-982

Author(s):

V. V. Aseev

Keyword(s):

Definition Of ◽

Geometric Definition

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Multisymplectic Reduction for Proper Actions

Canadian Journal of Mathematics ◽

10.4153/cjm-2004-029-8 ◽

2004 ◽

Vol 56 (3) ◽

pp. 638-654 ◽

Cited By ~ 1

Author(s):

Jędrzej Śniatycki

Keyword(s):

Symmetry Group ◽

Dense Subset ◽

Variational Problems ◽

Open Dense Subset ◽

Proper Action ◽

Partial Derivatives ◽

Proper Actions ◽

Reduced Equations ◽

Definition Of

AbstractWe consider symmetries of the Dedonder equation arising from variational problems with partial derivatives. Assuming a proper action of the symmetry group, we identify a set of reduced equations on an open dense subset of the domain of definition of the fields under consideration. By continuity, the Dedonder equation is satisfied whenever the reduced equations are satisfied.

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Empleo de simulaciones dinámicas en matlab como parte del proceso de enseñanza-aprendizaje de las matemáticas con aplicación al cálculo diferencial e integral.

Revista Científica y Tecnológica UPSE ◽

10.26423/rctu.v5i1.306 ◽

2018 ◽

Vol 5 (1) ◽

pp. 36-41

Author(s):

Miguel Lema Carrera

Keyword(s):

Learning Process ◽

Definite Integral ◽

Integral Calculus ◽

Dynamic Simulations ◽

Student Community ◽

Basic Ideas ◽

Definition Of ◽

Teaching Learning ◽

Disk Method ◽

Geometric Definition

La matemática en todos los tiempos ha tenido como principal fuente de inspiración la visualización, jugando un papel importante en el desarrollo de conceptos, nociones e ideas básicas del cálculo diferencial e integral. El presente trabajo proporciona herramientas y métodos básicos de uso relativamente sencillo, desarrollados en el paquete computacional MATLAB, trabajando temas como la definición geométrica de derivada, la integral definida y cálculo de volúmenes de revolución utilizando el método de discos, que permite obtener resultados muy poderosos en simulaciones dinámicas “animadas” que sirvan de soporte y recurso didáctico facilitador en el proceso de enseñanza-aprendizaje del cálculo. Modificando y renovando en una primera instancia la forma tradicional de enseñanza de esta asignatura en los primeros años del ciclo básico universitario en esta institución y porque no del país, además, se espera que este trabajo, permita desterrar el paradigma entorno a la comunidad estudiantil, que ha relacionado al cálculo matemático con una idea pura y completamente algebraizada, estática y memorística. ABSTRACT The mathematics of all time has had as the main source of inspiration the visualization, playing an important role in the development of concepts, notions and basic ideas of the differential and integral calculus. The present work provides tools and basic methods of use relatively simple, developed in the computational package Matlab, working topics such as the geometric definition of derivative, the definite integral and calculation of volumes of revolution using the disk method, which allows to obtain very powerful results in "animated" dynamic simulations that serve as support and facilitating didactic resource in the teaching-learning process of calculus. Modifying and renewing in the first instance the traditional way of teaching this subject in the first years of the basic university cycle in this institution and why not in the country, in addition, it is expected that this work, to banish the paradigm around the student community, that has related to the calculus with a pure and completely algebraic, static and rote idea.

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On the geometric definition of the quasi-conformality

Annales Polonici Mathematici ◽

10.4064/ap-39-1-31-36 ◽

1981 ◽

Vol 39 (1) ◽

pp. 31-36

Author(s):

Cabiria Andreian Cazacu

Keyword(s):

Definition Of ◽

Geometric Definition

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On the Geometric Definition of Quasiconformality

Siberian Mathematical Journal ◽

10.1134/s0037446621050025 ◽

2021 ◽

Vol 62 (5) ◽

pp. 782-795

Author(s):

V. V. Aseev

Keyword(s):

Definition Of ◽

Geometric Definition

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Transfer principles for pseudo real closed e-fold ordered fields

Journal of Symbolic Logic ◽

10.2307/2273910 ◽

1986 ◽

Vol 51 (4) ◽

pp. 981-991 ◽

Cited By ~ 3

Author(s):

Şerban A. Basarab

Keyword(s):

Elementary Theory ◽

Field Extension ◽

Equivalent Model ◽

Ordered Field ◽

Ordered Fields ◽

Order Language ◽

Irreducible Variety ◽

Famous Paper ◽

Definition Of ◽

Geometric Definition

In his famous paper [1] on the elementary theory of finite fields Ax considered fields K with the property that every absolutely irreducible variety defined over K has K-rational points. These fields have been called pseudo algebraically closed (pac) and also regularly closed, and extensively studied by Jarden, Éršov, Fried, Wheeler and others, culminating with the basic works [8] and [11].The above algebraic-geometric definition of pac fields can be put into the following equivalent model-theoretic version: K is existentially complete (ec) relative to the first order language of fields into each regular field extension of K. It has been this characterization of pac fields which the author extended in [2] to ordered fields. An ordered field (K, <) is called in [2] pseudo real closed (prc) if (K, <) is ec in every ordered field extension (L, <) with L regular over K. The concept of pre ordered field has also been introduced by McKenna in his thesis [15] by analogy with the original algebraic-geometric definition of pac fields.Given a positive integer e, a system K = (K; P1, …, Pe), where K is a field and P1, …, Pe are orders of K (identified with the corresponding positive cones), is called an e-fold ordered field (e-field). In his thesis [9] van den Dries developed a model theory for e-fields. The main result proved in [9, Chapter II] states that the theory e-OF of e-fields is model con. panionable, and the models of the model companion e-OF are explicitly described.

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