Search results for "Linear"
showing 10 items of 7165 documents
A candidate for a noncompact quantum group
1996
A previous letter (Bidegain, F. and Pinczon, G:Lett. Math. Phys.33 (1995), 231–240) established that the star-product approach of a quantum group introduced by Bonneau et al. can be extended to a connected locally compact semisimple real Lie group. The aim of the present Letter is to give an example of what a noncompact quantum group could be. From half of the discrete series ofSL(2,\(\mathbb{R}\)), a new type of quantum group is explicitly constructed.
Partial *-algebras of closable operators: A review
1996
This paper reviews the theory of partial *-algebras of closable operators in Hilbert space (partial O*-algebras), with some emphasis on partial GW*-algebras. First we discuss the general properties and the various types of partial *-algebras and partial O*-algebras. Then we summarize the representation theory of partial *-algebras, including a generalized Gel’fand-Naimark-Segal construction; the main tool here is the notion of positive sesquilinear form, that we study in some detail (extendability, normality, order structure, …). Finally we turn to automorphisms and derivations of partial O*-algebras, and their mutual relationship. The central theme here is to find conditions that guarante…
VECTOR MEASURES WITH VARIATION IN A BANACH FUNCTION SPACE
2003
Let E be a Banach function space and X be an arbitrary Banach space. Denote by E(X) the Kothe-Bochner function space defined as the set of measurable functions f : Ω → X such that the nonnegative functions ‖f‖X : Ω → [0,∞) are in the lattice E. The notion of E-variation of a measure —which allows to recover the pvariation (for E = Lp), Φ-variation (for E = LΦ) and the general notion introduced by Gresky and Uhl— is introduced. The space of measures of bounded E-variation VE(X) is then studied. It is shown, among other things and with some restriction of absolute continuity of the norms, that (E(X))∗ = VE′ (X ∗), that VE(X) can be identified with space of cone absolutely summing operators fr…
Generalized ``transition probability''
1975
An operationally meaningful symmetric function defined on pairs of states of an arbitrary physical system is constructed and is shown to coincide with the usual “transition probability” in the special case of systems admitting a quantum-mechanical description. It can be used to define a metric in the set of physical states. Conceivable applications to the analysis of certain aspects of Quantum Mechanics and to its possible modifications are mentioned.
An example concerning the zero set of the Jacobian
2006
AbstractLet f∈W1,1(Ω,Rn) be a homeomorphism of finite distortion K. It is known that if K1/(n−1)∈L1(Ω), then the Jacobian Jf of f is positive almost everywhere in Ω. We will show that this integrability assumption on K is sharp in any Orlicz-scale: if α is increasing function (satisfying minor technical assumptions) such that limt→∞α(t)=∞, then there exists f such that K1/(n−1)/α(K)∈L1(Ω) and Jf vanishes in a set of positive measure.
Construction of chaotic dynamical system
2010
The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic. First published online: 09 Jun 2011
Representable linear functionals on partial *-algebras
2012
A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.
Periodic and Chaotic Orbits of a Neuron Model
2015
In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
Improved constructions of quantum automata
2008
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use \frac{4}{\epsilon} \log 2p + O(1) states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of \log p than the previously known construction of Ambainis and Freivalds (quant-ph/9802062). Similarly to Ambainis and Freivalds, our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction.