‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

A continuous function f with domain X and range f(X) in R n is weakly univalent if there is a sequence of continuous one-to-one functions on X converging to f uniformly on bounded subsets of X. In this article, we establish, under certain conditions, the connectedness of an inverse image f ?1 (q). The univalence results of Radulescu-Radulescu, Mor e-Rheinboldt, and Gale-Nikaido follow from our ...

We consider the Laplacian on a rooted metric tree graph with branching number K ≥ 2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generali...

We propose a uni ed analysis of a whole spectrum of no-arbitrage conditions for nancial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation of all no-arbitrage conditions, linking their validity to the existence and to ...

We have studied quantum coherent oscillations of two qubits under continuous measurement by a symmetrically coupled mesoscopic detector. The analysis is based on a Bayesian formalism that is applicable to individual quantum systems. Measurement continuously collapses the two-qubit system to one of the subspaces of the Bell basis. For a detector with linear response this corresponds to measureme...

Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T 〈Tx, y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be esta...

We consider crossovers with respect to the weak convergence theorems from a discretetime quantum walk (DTQW). We show that a continuous-time quantum walk (CTQW) and discreteand continuous-time random walks can be expressed as DTQWs in some limits. At first we generalize our previous study [Phys. Rev. A 81, 062129 (2010)] on the DTQW with position measurements. We show that the position measurem...