A choice of time-slicing in classical general relativity permits the construction of time-dependent wave functions in the “frozen time” Chern-Simons formulation of (2 + 1)-dimensional quantum gravity. Because of operator ordering ambiguities, however, these wave functions are not unique. It is shown that when space has the topology of a torus, suitable operator orderings give rise to wave funct...

Starting with a W ∗-algebra M we use the inverse system obtained by cutting down M by its (central) projections to define an inverse limit of W ∗-algebras , and show that how this pro-W ∗-algebra encodes the local structure of M . For the C∗-algebras we do the same thing using their atomic enveloping W ∗-algebras . We investigate the relation of these ideas to the Akemann-Giles-Kummer non commu...

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator, or equivalently, as the index of Neuberger’s lattice Dirac operator, is shown to have analogous properties to Lüscher’s geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum lim...

The prediction of the topology of transmembrane proteins is an important foundation in the research of bioinformatics. In this paper, information fusion theory has been introduced to locate the transmembrane regions and find their orientation. The proposed method, which is on the basis of the power average operator and a kind of similarity degree of interval numbers, considers a transmembrane r...

In this paper, we propose a stress-based crossover (SX) operator to solve the checkerboardlike material distributation and disconnected topology that is common for simple genetic algorithm (SGA) to structural topology optimization problems (STOPs). A penalty function is defined to evaluate the fitness of each individual. A number of constrained problems are adopted to experiment the effectivene...

Let l be a length function on a group G, and let Ml denote the operator of pointwise multiplication by l on l(G). Following Connes, Ml can be used as a “Dirac” operator for C ∗ r (G). It defines a Lipschitz seminorm on C∗ r (G), which defines a metric on the state space of C∗ r (G). We show that if G is a hyperbolic group and if l is a word-length function on G, then the topology from this metr...

In this article, the spectral theory is considered, we study families and their correspondence to operators on reflexive Banach spaces; assume A a well-bounded operator Lebesgue spaces then scalar type operator. The main goals are obtain characterization of in terms associated family topology dual pairing construct continuous functional calculus for space.

The paper describes the structure of a linear continuous operator on space functions in topology pointwise convergence. corresponding theorem is generalization A.V.Arkhangel'skii's general form functional such spaces.