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## Otimização de forma de cascas via deformação livre de forma baseado em NURBS; Shape optimization of shell via free-form deformation NURBSbased

Fonte: Universidade Federal do Rio Grande do Sul
Publicador: Universidade Federal do Rio Grande do Sul

Tipo: Dissertação
Formato: application/pdf

POR

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#Elementos finitos#NURBS#Free-form deformation#Otimização matemática#Estruturas (Engenharia)#Mathematical optimization#Finite element method

Neste trabalho buscou-se consolidar a união entre três áreas do conhecimento: a parametrização de curvas e superfícies do tipo B-spline racionais não-uniformes (NURBS), a otimização matemática e a análise estrutural por elementos finitos. A união destas três áreas é realizada neste trabalho através da otimização de formas de cascas, devido ao fato de que as características mecânicas dos materiais devem refletir-se na forma da estrutura e sua distribuição de espessura expressando um máximo desempenho. Estas variáveis, forma e distribuição de espessura, possuem um rol dominante nos projetos de engenharia, já que mínimas quantidades de materiais, uma frequência específica, um estado puro de tensões de membrana são típicos objetivos de projeto. Neste contexto, obter a forma e a distribuição de espessura adequadas são conceitos intrínsecos à otimização estrutural. Portanto, implementaram-se técnicas para modificar a geometria de cascas, sem perder a parametrização, sem a necessidade de gerar uma nova malha de elementos finitos ao se modificar a forma e ainda ter controle sobre a distorção da malha para evitar erros numéricos inaceitáveis. A modificação de forma é fomentada pelo código de otimização...

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## Mathematical Models of Rigid Solid Objects

Fonte: University of Rochester. Production Automation Project
Publicador: University of Rochester. Production Automation Project

Tipo: Relatório

ENG

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#TM-28#geometry, solid mathematical models#geometric modelling theory#solids mathematical models#production engineering mathematical models

Computational models of solid objects are potentially useful in a variety of scientific and engineering fields, and in particular in the field of design and manufacturing automation for the mechanical industries. In recent years a multitude of modelling systems have been implemented both by research laboratories and commercial vendors, but little attention has been paid to the fundamental theoretical issues in geometric modelling. This has led to severe difficulties in assessing current and proposed systems, and in distinguishing essential capabilities and limitations from user conveniences and efficiency considerations. This paper seeks a sharp mathematical characterization of "rigid solids" in a manner that is suitable for studies in design and production automation. It draws heavily on established results in modern geometry and topology. Relevant results scattered throughout the mathematical literature are placed in a coherent framework and presented in a form accessible to engineers and computer scientists. A companion paper is devoted to a discussion of representational issues in the contest set forth by this paper.

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## Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

Fonte: Université de Montréal
Publicador: Université de Montréal

Tipo: Artigo de Revista Científica
Formato: 267450 bytes; application/pdf

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#Time series#VARMA#stationary#invertible#echelon form#estimation#asymptotic normality#bootstrap#Hannan-Rissanen#[JEL:C3] Mathematical and Quantitative Methods - Econometric Methods: Multiple#Simultaneous Equation Models

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.

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## Mathematical models of cell migration and self-organization in embryogenesis

Fonte: La Sapienza Universidade de Roma
Publicador: La Sapienza Universidade de Roma

Tipo: Tese de Doutorado

EN

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#Mathematical Biology#Modelling and Numerical Simulations#Collective Motion#Self-organization#Hybrid Models#Morphogenesis#Cell Migration#Cellular Signalling#Partial Differential Equations#Numerical Methods#Settori Disciplinari MIUR::Scienze matematiche e informatiche

In this thesis we deal with mathematical models and numerical simulations for cell migration and self-organization in embryogenesis. The part of biology which studies the formation and development of the embryo from fertilization until birth is called embryology. Morphogenesis is then the part of embryology which is concerned with the development of patterns and forms. It is well known that although morphogenesis processes are controlled at the genetic scale, genes themselves cannot create the pattern. In general a series of biological mechanisms of self-organization intervene during the early development and the formation of particular biological structures can not be anticipated solely by genetic information. This needs to be taken into account in the choice of a suitable mathematical formulation of such phenomena.
Two main main topics will be investigated: we will analyze and mathematically model the self-organizing cell migration in the morphogenesis of the lateral line in the zebrafish (Danio rerio); in a second part, starting from this model, we will propose, and will study both from the analytical and the numerical point of view, a mathematical model of collective motion under only alignment and chemotaxis effects.
The present thesis is organized in four chapters.
In Chapter 1 we will introduce biological elements about the morphogenetic process occurring in the development of the lateral line in a zebrafish. After a first discussion on the lateral line system and on its fundamental relevance in the current scientific research...

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## Exterior and evolutionary skew-symmetric differential forms and their role in mathematical physics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/10/2003

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At present the theory of skew-symmetric exterior differential forms has been
developed. The closed exterior forms possess the invariant properties that are
of great importance. The operators of the exterior form theory lie at the basis
of the differential and integral operators of the field theory. However, the
theory of exterior forms, being invariant one, does not answer the questions
related to the evolutionary processes. In the work the readers are introduced
to the skew-symmetric differential forms that possess evolutionary properties.
They were called evolutionary ones. The radical distinction between the
evolutionary forms and the exterior ones consists in the fact that the exterior
forms are defined on manifolds with closed metric forms, whereas the
evolutionary forms are defined on manifolds with unclosed metric forms. The
mathematical apparatus of exterior and evolutionary forms allows description of
discrete transitions, quantum steps, evolutionary processes, generation of
various structures. These are radically new possibilities of the mathematical
physics. A role of exterior and evolutionary forms in the mathematical physics
is conditioned by the fact that they reflect properties of the conservation
laws and allow elucidate a mechanism of evolutionary processes in material
media...

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## Pair and Impar, Even and Odd Form Fields and Electromagnetism

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper after reviewing the Schouten and de Rham definition of impair
and pair differential form fields (not to be confused with differential form
fields of even and odd grades) we prove that in a relativistic spacetime it is
possible (despite claims in contrary) to coherently formulate electromagnetism
(and we believe any other physical theory) using only pair form fields or, if
one wishes, using pair and impair form fields together, in an appropriate way.
Those two distinct descriptions involve only a mathematical choice and do not
seem to lead to any observable physical consequence if due care is taken.
Moreover, we show in details that a formulation of electromagnetic theory in
the Clifford bundle formalism of differential forms where the two Maxwell
equations of the so called free metric approach becomes a single equation is
compatible with both formulations of electromagnetism just mentioned above.
Moreover we derive directly from Maxwell equation the density of force
(coupling of the electromagnetic field with the charge current) that is a
postulate in the free metric approach to electromagnetism. We recall also a
formulation of the engineering version of Maxwell equations using electric and
magnetic fields as objects of the same nature...

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## Supplementary balance laws and the entropy principle

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/08/2010

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In this work we study the mathematical aspects of the development in the
continuum thermodynamics known as the "Entropy Principle". It started with the
pioneering works of B.Coleman, W.Noll and I. Muller in 60th of XX cent. and got
its further development mostly in the works of G. Boillat, I-Shis Liu and
T.Ruggeri. "Entropy Principle" combines in itself the structural requirement on
the form of balance laws of the thermodynamical system (denote such system
$(\mathcal{C})$) and on the entropy balance law with the convexity condition of
the entropy density. First of these requirements has pure mathematical form
defining so called "supplementary balance laws" (shortly SBL) associated with
the original balance system. Vector space of SBL can be considered as a kind of
natural "closure" of the original balance system. This space includes the
original balance laws, the entropy balance, the balance laws corresponding to
the symmetries of the balance system and some other balance equations. We
consider the case of Rational Extended Thermodynamics where densities, fluxes
and sources of the balance equations do not depend on the derivatives of
physical fields $y^i$. We present the basic structures of RET: Lagrange-Liu
equations,"main fields"...

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## Unified Form Language: A domain-specific language for weak formulations of partial differential equations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Computer Science - Mathematical Software#Computer Science - Numerical Analysis#Computer Science - Symbolic Computation#97N80#G.4#G.1.8#G.1.4

We present the Unified Form Language (UFL), which is a domain-specific
language for representing weak formulations of partial differential equations
with a view to numerical approximation. Features of UFL include support for
variational forms and functionals, automatic differentiation of forms and
expressions, arbitrary function space hierarchies for multi-field problems,
general differential operators and flexible tensor algebra. With these
features, UFL has been used to effortlessly express finite element methods for
complex systems of partial differential equations in near-mathematical
notation, resulting in compact, intuitive and readable programs. We present in
this work the language and its construction. An implementation of UFL is freely
available as an open-source software library. The library generates abstract
syntax tree representations of variational problems, which are used by other
software libraries to generate concrete low-level implementations. Some
application examples are presented and libraries that support UFL are
highlighted.; Comment: To appear in ACM Transactions on Mathematical Software

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## Energy and electromagnetism of a differential form

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#General Relativity and Quantum Cosmology#Mathematical Physics#Mathematics - Differential Geometry#53A55, 83C40

Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric
g, and let T be the electromagnetic energy tensor associated to a 2-form F. In
this paper we characterize this tensor T as the only 2-covariant natural tensor
associated to a lorentzian metric and a 2-form that is independent of the unit
of scale and satisfies certain condition on its divergence. This
characterization is motivated on physical grounds, and can be used to justify
the Einstein-Maxwell field equations. More generally, we characterize in a
similar manner the energy tensor associated to a differential form of arbitrary
order k. Finally, we develop a generalized theory of electromagnetism where
charged particles are not punctual, but of an arbitrary fixed dimension p. In
this theory, the electromagnetic field F is a differential form of order 2+p
and its electromagnetic energy tensor is precisely the energy tensor associated
to F.; Comment: 28 pages. Referee's suggestions added. To appear in Journal of
Mathematical Physics

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## First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-form

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/04/2009

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We show that in analogy to the introduction of Poisson structures twisted by
a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional
sigma models with Wess-Zumino term leads in a likewise way to twisting of
Courant algebroid structures by closed 4-forms H.
The presentation is kept pedagogical and accessible to physicists as well as
to mathematicians, explaining in detail in particular the interplay of field
transformations in a sigma model with the type of geometrical structures
induced on a target. In fact, as we also show, even if one does not know the
mathematical concept of a Courant algebroid, the study of a rather general
class of 3-dimensional sigma models leads one to that notion by itself.
Courant algebroids became of relevance for mathematical physics lately from
several perspectives - like for example by means of using generalized complex
structures in String Theory. One may expect that their twisting by the
curvature H of some 3-form Ramond-Ramond gauge field will become of relevance
as well.; Comment: 25 pages, invited contribution to the Wolfgang Kummer memorial volume

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## Skew-symmetric forms: On integrability of equations of mathematical physics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/10/2009

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The study of integrability of the mathematical physics equations showed that
the differential equations describing real processes are not integrable without
additional conditions. This follows from the functional relation that is
derived from these equations. Such a relation connects the differential of
state functional and the skew-symmetric form. This relation proves to be
nonidentical, and this fact points to the nonintegrability of the equations. In
this case a solution to the equations is a functional, which depends on the
commutator of skew-symmetric form that appears to be unclosed. However, under
realization of the conditions of degenerate transformations, from the
nonidentical relation it follows the identical one on some structure. This
points out to the local integrability and realization of a generalized
solution.
In doing so, in addition to the exterior forms, the skew-symmetric forms,
which, in contrast to exterior forms, are defined on nonintegrable manifolds
(such as tangent manifolds of differential equations, Lagrangian manifolds and
so on), were used.
In the present paper, the partial differential equations, which describe any
processes, the systems of differential equations of mechanics and physics of
continuous medium and field theory equations are analyzed.; Comment: 8 pages...

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## On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Quantum Algebra#Mathematical Physics#Mathematics - Representation Theory#15A66#17B37#81R25#81R50

Clifford algebras are naturally associated with quadratic forms. These
algebras are Z_2-graded by construction. However, only a Z_n-gradation induced
by a choice of a basis, or even better, by a Chevalley vector space isomorphism
Cl(V) <-> \bigwedge V and an ordering, guarantees a multi-vector decomposition
into scalars, vectors, tensors, and so on, mandatory in physics. We show that
the Chevalley isomorphism theorem cannot be generalized to algebras if the
Z_n-grading or other structures are added, e.g., a linear form. We work with
pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which
we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford
algebras'. It turns out, that in this sense, all multi-vector Clifford algebras
of the same quadratic but different bilinear forms are non-isomorphic. The
usefulness of such algebras in quantum field theory and superconductivity was
shown elsewhere. Allowing for arbitrary bilinear forms however spoils their
diagonalizability which has a considerable effect on the tensor decomposition
of the Clifford algebras governed by the periodicity theorems, including the
Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which
can be decomposed in the symmetric case into a tensor product Cl_{p-1...

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## Assumptions and Axioms: Mathematical Structures to Describe the Physics of Rigid Bodies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/05/2010

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This paper challenges some of the common assumptions underlying the
mathematics used to describe the physical world. We start by reviewing many of
the assumptions underlying the concepts of real, physical, rigid bodies and the
translational and rotational properties of such rigid bodies. Nearly all
elementary and advanced texts make physical assumptions that are subtly
different from ours, and as a result we develop a mathematical description that
is subtly different from the standard mathematical structure. Using the
homogeneity and isotropy of space, we investigate the translational and
rotational features of rigid bodies in two and three dimensions. We find that
the concept of rigid bodies and the concept of the homogeneity of space are
intrinsically linked. The geometric study of rotations of rigid objects leads
to a geometric product relationship for lines and vectors. By requiring this
product to be both associative and to satisfy Pythagoras' theorem, we obtain a
choice of Clifford algebras. We extend our arguments from space to include
time. By assuming that ct=l and rewriting this in Lorentz invariant form as
c^2t^2-x^2-y^2-z^2=0 we obtain a generalization of Pythagoras to spacetime.
This leads us directly to establishing that the Clifford algebra CL(1...

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## Reduction formula of form factors for the integrable spin-s XXZ chains and application to the correlation functions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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For the integrable spin-s XXZ chain we express explicitly any given spin-$s$
form factor in terms of a sum over the scalar products of the spin-1/2
operators. Here they are given by the operator-valued matrix elements of the
monodromy matrix of the spin-1/2 XXZ spin chain. In the paper we call an
arbitrary matrix element of a local operator between two Bethe eigenstates a
form factor of the operator. We derive all important formulas of the fusion
method in detail. We thus revise the derivation of the higher-spin XXZ form
factors given in a previous paper. The revised method has several interesting
applications in mathematical physics. For instance, we express the spin-$s$ XXZ
correlation function of an arbitrary entry at zero temperature in terms of a
sum of multiple integrals.; Comment: 41 pages, no figures

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## On the Integrated Form of the BBGKY Hierarchy for Hard Spheres

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/05/2006

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In my book ``Large Scale Dynamics of Interacting Particles'' [S] I refer to
an unpublished note from early 1985 on the BBGKY hierarchy for hard spheres. My
main point there was to provide a direct probabilistic proof for the
time-integrated version of the hierarchy. Over recent years there has been
repeated interest in this derivation, which encourages me to make my note
public. I decided to leave it in its original form including likely
inaccuracies. The work of R. Illner and M. Pulvirenti [IP] appeared in
September 1985, see also the book by C. Cercignani, R. Illner, and M.
Pulvirenti [CIP], who prove the same result using special flow representation
and methods from the theory of differential operators. [S] H. Spohn, Large
Scale Dynamics of Interacting Particles, Texts and Monographs in Physics,
Springer-Verlag, Heidelberg, 1991. [IP] R. Illner and M. Pulvirenti, A
derivation of the BBGKY-hierarchy for hard sphere particle systems, Transport
Theory and Stat. Phys. \textbf{16}, 997--1012 (1987), preprint DM-388-IR,
September 1985. [CIP] C. Cercignani, R. Illner, and M. Pulvirenti, The
Mathematical Theory of Dilute Gases, Applied Mathematical Sciences
\textbf{106}, Springer-Verlag, New York, 1994.

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## General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Starting with minimal requirements from the physical experience with higher
gauge theories, i.e. gauge theories for a tower of differential forms of
different form degrees, we discover that all the structural identities
governing such theories can be concisely recombined into a so-called
Q-structure or, equivalently, a Lie infinity algebroid. This has many technical
and conceptual advantages: Complicated higher bundles become just bundles in
the category of Q-manifolds in this approach (the many structural identities
being encoded in the one operator Q squaring to zero), gauge transformations
are generated by internal vertical automorphisms in these bundles and even for
a relatively intricate field content the gauge algebra can be determined in
some lines only and is given by the so-called derived bracket construction.
This article aims equally at mathematicians and theoretical physicists; each
more physical section is followed by a purely mathematical one. While the
considerations are valid for arbitrary highest form-degree p, we pay particular
attention to p=2, i.e. 1- and 2-form gauge fields coupled non-linearly to
scalar fields (0-form fields). The structural identities of the coupled system
correspond to a Lie 2-algebroid in this case and we provide different axiomatic
descriptions of those...

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## A new mathematical representation of Game Theory, I

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper, we introduce a framework of new mathematical representation of
Game Theory, including static classical game and static quantum game. The idea
is to find a set of base vectors in every single-player strategy space and to
define their inner product so as to form them as a Hilbert space, and then form
a Hilbert space of system state. Basic ideas, concepts and formulas in Game
Theory have been reexpressed in such a space of system state. This space
provides more possible strategies than traditional classical game and
traditional quantum game. So besides those two games, more games have been
defined in different strategy spaces. All the games have been unified in the
new representation and their relation has been discussed. General Nash
Equilibrium for all the games has been proposed but without a general proof of
the existence. Besides the theoretical description, ideas and technics from
Statistical Physics, such as Kinetics Equation and Thermal Equilibrium can be
easily incorporated into Game Theory through such a representation. This
incorporation gives an endogenous method for refinement of Equilibrium State
and some hits to simplify the calculation of Equilibrium State. The more
privileges of this new representation depends on further application on more
theoretical and real games. Here...

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## Analysis of the equations of mathematical physics and foundations of field theories with the help of skew-symmetric differential forms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/12/2005

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In the paper it is shown that, even without a knowledge of the concrete form
of the equations of mathematical physics and field theories, with the help of
skew-symmetric differential forms one can see specific features of the
equations of mathematical physics, the relation between mathematical physics
and field theory, to understand the mechanism of evolutionary processes that
develop in material media and lead to emergency of physical structures forming
physical fields. This discloses a physical meaning of such concepts like
"conservation laws", "postulates" and "causality" and gives answers to many
principal questions of mathematical physics and general field theory.
In present paper, beside the exterior forms, the skew-symmetric differential
forms, whose basis (in contrast to the exterior forms) are deforming manifolds,
are used. Mathematical apparatus of such differential forms(which were named
evolutionary ones) includes nontraditional elements like nonidentical relations
and degenerate transformations and this enables one to describe discrete
transitions, quantum steps, evolutionary processes, and generation of various
structures.; Comment: 36 pages

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## Equivalence of Two Mathematical Forms for the Bound Angular Momentum of the Electromagnetic Field

Fonte: Taylor & Francis Group
Publicador: Taylor & Francis Group

Tipo: Artigo de Revista Científica

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It is shown that the mathematical form obtained in a recent paper for the angular momentum of the electromagnetic field in the vicinity of electric charge is equivalent to another form obtained previously.

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## On the Structure of Rationality in the Thought and Invention or Creation of Physical Theories; On the Structure of Rationality in the Thought and Invention or Creation of Physical Theories

Fonte: Federal University of Santa Catarina – UFSC
Publicador: Federal University of Santa Catarina – UFSC

Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ;
Formato: application/pdf

Publicado em 24/02/2012
POR

Relevância na Pesquisa

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#Epistemologia#Filosofia da ciência#Creative thought#general theory of relativity#intuitive grasp#mathematical form#logistic foundational program#mathematical thought#physical content#physical thought#quantum theory

We want to consider anew the question, which is recurrent along the history of philosophy, of the relationship between rationality and mathematics, by inquiring to which extent the structuration of rationality, which ensures the unity of its function under a variety of forms (and even according to an evolution of these forms), could be considered as homeomorphic with that of mathematical thought, taken in its movement and made concrete in its theories. This idea, which is as old as philosophy itself, although it has not been dominant, has still been present to some degree in the thought of modern science, in Descartes as well as in Kant, Poincaré or Einstein (and a few other scientists and philosophers). It has been often harshly questioned, notably in the contemporaneous period, due to the failure of the logistic programme, as well as to the variety of “empirical” knowledges, and, in a general way, to the character of knowledges that show them as transitory, evolutive and mind-built. However, the analysis of scientific thought through its inventive and creative processes leads to characterize this thought as a type of rational form whose configurations can be detailed rather precisely. In this work we shall propose, first, a quick sketch of some philosophical requirements for such a research programme...

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