Using recent results of Berman and Boucksom [BB2] we show that for a non-pluripolar compact set K ⊂ C d and an admissible weight function w = e −φ any sequence of so-called optimal measures converges weak-* to the equilibrium measure µ K,φ of (weighted) Pluripotential Theory for K, φ.

We construct a Cantor set ̂ of limit-periodic Jacobi operators having the spectrum on the Julia set J of the quadratic map z ι-> z + E for large negative real numbers E. The density of states of each of these operators is equal to the unique equilibrium measure μ on J. The Jacobi operators in $ are defined over the von Neumann-Kakutani system, a group translation on the compact topological group...

In this paper, we describe some topological properties of dualistic partial metric spaces and establish some fixed point theorems for weak contraction mappings of rational type defined on dual partial metric spaces. These results are generalizations of some existing results in the literature. Moreover, we present examples to illustrate our result.

Abstract. We consider the integrability of φ(f∗) for various maximal functions f∗ and various increasing functions φ. We show that for some of the standard maximal functions arising in harmonic analysis and ergodic theory, there is never integrability of φ(f∗) for all Lebesgue integrable functions f except in cases where the growth of φ is slow enough so that the integrability follows from the ...

In this paper, we prove that into isometries and disjointness preserving linear maps from C0(X) into C0(Y ) are essentially weighted composition operators Tf = h · f ◦ φ for some continuous map φ and some continuous scalar-valued function h.

This paper proves the estimate ‖uε − u‖L1(QT ) ≤ Cε , where, for all ε > 0, uε is the weak solution of (uε)t + div(q f(uε)) − ∆(φ(uε)+εuε) = 0 with initial and boundary conditions, u is the entropy weak solution of ut + div(qf(u)) − ∆(φ(u)) = 0 with the same initial and boundary conditions, and C > 0 does not depend on ε. The domain Ω is assumed to be regular and T is a given positive value.

Abstract In this paper, fixed point and coincidence results are presented for multivalued generalized φ-weak contractive mappings on complete metric spaces, where φ : [0, +∞) −→ [0, +∞) is a lower semicontinuous function with φ(0) = 0 and φ(t) > 0 for all t > 0. Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969), and Daffer and Kaneko (1995).

In this note we prove that an extended-real-valued lower semi-continuous convex function Φ defined on a reflexive Banach space X achieves its supremum on every nonempty bounded and closed convex set of its effective domain Dom Φ, if and only if the restriction of Φ to Dom Φ is sequentially continuous with respect to the weak topology on the underlying space X .

Ciphers y = C(x, k) and  = (, ) are isomorphic if there exists invertible computable in both directions map y ↔ , x ↔ , k ↔ . Cipher is vulnerable if and only if isomorphic cipher is vulnerable. Instead of computing the key of a cipher it is sufficient to find suitable isomorphic cipher and compute its key. If φ is arbitrary substitution and T is round substitution, its conjugate  = φTφ...