410 research outputs found
Magnetic Backgrounds from Generalised Complex Manifolds
The magnetic backgrounds that physically give rise to spacetime
noncommutativity are generally treated using noncommutative geometry. In this
article we prove that also the theory of generalised complex manifolds contains
the necessary elements to generate B-fields geometrically. As an example, the
Poisson brackets of the Landau model (electric charges on a plane subject to an
external, perperdicularly applied magnetic field) are rederived using the
techniques of generalised complex manifolds.Comment: Some refs. adde
Skew compact semigroups
[EN] Skew compact spaces are the best behaving generalization of compact Hausdorff spaces to non-Hausdorff spaces. They are those (X ; Ï„ ) such that there is another topology Ï„* on X for which Ï„ V Ï„* is compact and (X; Ï„ ; Ï„*) is pairwise Hausdorff; under these conditions, Ï„ uniquely determines Ï„ *, and (X; Ï„*) is also skew compact. Much of the theory of compact T2 semigroups extends to this wider class. We show:
A continuous skew compact semigroup is a semigroup with skew compact topology τ, such that the semigroup operation is continuous τ2→ τ. Each of these contains a unique minimal ideal which is an upper set with respect to the specialization order.
A skew compact semigroup which is a continuous semigroup with respect to both topologies is called a de Groot semigroup. Given one of these, we show:
It is a compact Hausdorff group if either the operation is cancellative, or there is a unique idempotent and S2 = S.
Its topology arises from its subinvariant quasimetrics.
Each *-closed ideal ≠S is contained in a proper open ideal.Kopperman, RD.; Robbie, D. (2003). Skew compact semigroups. Applied General Topology. 4(1):133-142. doi:10.4995/agt.2003.2015.SWORD1331424
Topological Test Spaces
A test space is the set of outcome-sets associated with a collection of
experiments. This notion provides a simple mathematical framework for the study
of probabilistic theories -- notably, quantum mechanics -- in which one is
faced with incommensurable random quantities. In the case of quantum mechanics,
the relevant test space, the set of orthonormal bases of a Hilbert space,
carries significant topological structure. This paper inaugurates a general
study of topological test spaces. Among other things, we show that any
topological test space with a compact space of outcomes is of finite rank. We
also generalize results of Meyer and Clifton-Kent by showing that, under very
weak assumptions, any second-countable topological test space contains a dense
semi-classical test space.Comment: 12 pp., LaTeX 2e. To appear in Int. J. Theor. Phy
Difração e refração de ondas: uma análise por meio de elementos finitos e infinitos
In the present work the phenomena of diffraction and refraction of gravitational surface waves is treated by using a two-dimensional formulation, given by Berkhoff's equation. The Finite Element Method is used in the
solution of the numerical problem. However, the main objective of this thesis is the formulation and implementation of a computational program with elements that model an infinite domain: they are called Infinite Elements. By studying the existing Infinite Elements it was possible to formulate a new and efficient one. Its geometrical characteristics are the same as for the Isoparametric Finite Element, but the integration is over an unbounded domain. Because the wave potencital is a complex function, a series of difficulties appear in the program development. The program structure for the solution of a real linear system is maintained. The Sky-line technique is used in the storage of the system global matrix. The programming language is FORTRAN.O presente trabalho trata do fenômeno de Difração e Refração de ondas gravitacionais de superfÃcie, através
de uma formulação bi-dimensional, dada pela equação de Berkhoff. O Método dos Elementos Finitos é utilizado na resolução numérica do problema. No entanto, o principal objetivo desta tese é a formulação e implementação de um programa computacional com elementos capazes de modelar um domÃnio infinito:
estes são conhecidos como Elementos Infinitos. A partir de um estudo feito com os Elementos Infinitos existentes na literatura, foi possÃvel formular e implementar um novo e eficiente elemento. Este tem as caracterÃsticas geométricas de um Elemento Finito Isoparamétrico, sendo no entanto integrado em um domÃnio aberto. O potencial da onda, sendo urna função complexa, leva a urna série de dificuldades na programação. É mantida a estrutura de um programa para solução de sistemas com equações lineares reais. O armazenamento da matriz do sistema é feito em perfil ("sky-line"). A programação é feita em linguagem
FORTRAN
Bandgaps in the propagation and scattering of surface water waves over cylindrical steps
Here we investigate the propagation and scattering of surface water waves by
arrays of bottom-mounted cylindrical steps. Both periodic and random
arrangements of the steps are considered. The wave transmission through the
arrays is computed using the multiple scattering method based upon a recently
derived formulation. For the periodic case, the results are compared to the
band structure calculation. We demonstrate that complete band gaps can be
obtained in such a system. Furthermore, we show that the randomization of the
location of the steps can significantly reduce the transmission of water waves.
Comparison with other systems is also discussed.Comment: 4 pages, 3 figure
Partial order and a -topology in a set of finite quantum systems
A `whole-part' theory is developed for a set of finite quantum systems
with variables in . The partial order `subsystem'
is defined, by embedding various attributes of the system (quantum
states, density matrices, etc) into their counterparts in the supersystem
(for ). The compatibility of these embeddings is studied. The
concept of ubiquity is introduced for quantities which fit with this structure.
It is shown that various entropic quantities are ubiquitous. The sets of
various quantities become -topological spaces with the divisor topology,
which encapsulates fundamental physical properties. These sets can be converted
into directed-complete partial orders (dcpo), by adding `top elements'. The
continuity of various maps among these sets is studied
- …