Search results for "Pure Mathematics"
showing 10 items of 2106 documents
An Integral Version of Ćirić’s Fixed Point Theorem
2011
We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.
Star-products and phase space realizations of quantum groups
1992
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
Some Problems on Homomorphisms and Real Function Algebras
2001
In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra.
Fuzzy algebras as a framework for fuzzy topology
2011
The paper introduces a variety-based version of the notion of the (L,M)-fuzzy topological space of Kubiak and Sostak and embeds the respective category into a suitable modification of the category of topological systems of Vickers. The new concepts provide a common framework for different approaches to fuzzy topology and topological systems existing in the literature, paving the way for studying the problem of interweaving algebra and topology in mathematics, which was raised by Denniston, Melton and Rodabaugh in their recent research on variable-basis topological systems over the category of locales.
Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds
2003
For appropriate triples (M, g, M), where M is an (in general non-compact) manifold, g is a metric on T*M, and M is a weight function on T* M, we developed in [5] a pseudo-differential calculus on.A.4 which is based on the S(M, g)-calculus of L. Hormander [30] in local models. Here we prove that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [21] in \( \mathcal{L}\left( {{L^2}\left( M \right)} \right)\). For the basic calculus we generalized the concept of E. Schrohe [40] of so-called SG-compatible manifolds. In the proof of the existence of “order reducing operators” we apply a method from [4], and the proof of spectral invariance and sub…
Convergence-theoretic mechanisms behind product theorems
2000
Abstract Commutation of the topologizer with products, quotientness of product maps, preservation of some properties by products, topologicity of continuous convergence, continuity of complete lattices are facets of the same quest. A new method of multifilters is used to establish (in terms of core-contour-compactness) sufficient and necessary conditions for these properties in the framework of general convergences. The relativized Antoine reflector plays here an important role. Several classical results (of Whitehead, Michael, Boehme, Cohen, Day and Kelly, Hofmann and Lawson, Schwarz and Weck, Kent and Richardson, and others) are extended or refined.
Faithful representations of left C*-modules
2010
The existence of a faithful modular representation of a left module $$ \mathfrak{X} $$ over a C*-algebra $$ \mathfrak{A}_\# $$ possessing sufficiently many traces is proved.
Nondivisibility among character degrees II: Nonsolvable groups
2007
We say that a finite group G is an NDAD-group (no divisibility among degrees) if for any 1 < a < b in the set of degrees of the complex irreducible characters of G, a does not divide b. In this article, we determine the nonsolvable NDAD-groups. Together with the work of Lewis, Moreto and Wolf (J. Group Theory 8 (2005)), this settles a problem raised by Berkovich and Zhmud’, which asks for a classification of the NDAD-groups.
Algebraic Results on Quantum Automata
2004
We use tools from the algebraic theory of automata to investigate the class of languages recognized by two models of Quantum Finite Automata (QFA): Brodsky and Pippenger’s end-decisive model, and a new QFA model whose definition is motivated by implementations of quantum computers using nucleo-magnetic resonance (NMR). In particular, we are interested in the new model since nucleo-magnetic resonance was used to construct the most powerful physical quantum machine to date. We give a complete characterization of the languages recognized by the new model and by Boolean combinations of the Brodsky-Pippenger model. Our results show a striking similarity in the class of languages recognized by th…
Double point curves for corank 2 map germs from C2 to C3
2012
Abstract We characterize finite determinacy of map germs f : ( C 2 , 0 ) → ( C 3 , 0 ) in terms of the Milnor number μ ( D ( f ) ) of the double point curve D ( f ) in ( C 2 , 0 ) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f t : ( C 2 , 0 ) → ( C 3 , 0 ) is equivalent to the constancy of both μ ( D ( f t ) ) and μ ( f t ( C 2 ) ∩ H ) with respect to t , where H ⊂ C 3 is a generic plane.