In this article we survey the existence of best proximity points for a class of non-self mappings which‎ satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [‎A‎. ‎Abkar‎, ‎M‎. ‎Gabeleh‎, Best proximity points of non-self mappings‎, ‎Top‎, ‎21, (2013)‎, ‎287-295]‎ which guarantees the existence of best proximity points for nonex...

In this paper, we deal with the subdierential concept onHadamard spaces. Flat Hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in Hadamard spaces is nonempty. Proximal subdierentialin Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdierential set is established.

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

We show that, typically, lower semicontinuous functions on a Banach space densely inherit lower subderivatives of the same degree of smoothness as the norm. In particular every continuous convex function on a space with a Gâteaux (weak Hadamard, Fréchet) smooth renorm is densely Gâteaux (weak Hadamard, Fréchet) differentiable. Our technique relies on a more powerful analogue of Ekeland's variat...

We start the discussion of the free Bose gas on Robertson-Walker space-times by introducing a new state on the Weyl algebra of the free massive Klein-Gordon eld on Robertson-Walker space-times. This state approximates a thermal equilibrium state and opens the possibility to do quantum statistical mechanics on expanding universes. We explain why this state is believed to be a physically relevant...

This paper is devoted to the study of four integral operators that are basic generalizations and modifications of fractional integrals of Hadamard, in the space X c of Lebesgue measurable functions f on R+ = (0,∞) such that ∞ ∫ 0 ∣∣ucf (u)∣∣p du u <∞ (1 p <∞), ess sup u>0 [ u ∣∣f (u)∣∣]<∞ (p =∞), for c ∈ R = (−∞,∞), in particular in the space Lp(0,∞) (1 p ∞). Formulas for the Mellin transforms ...

Automatic generation of fast Hadamard transform (FHT) algorithms through genetic programming is studied. The design of FHT algorithms is viewed as a search in the space of linear algorithms employing restricted types of coefficients. A generic circuit that can realize all algorithms belonging to this space is proposed. The goal is to automatically find an algorithm that can perform Hadamard tra...

A logic network to produce the sequency ordered Hadamard matrix H based on the property of gray code and orthogonal group codes is developed. The network uses a counter to generate Rademacher function such that the output of H will be in sequency. A general purpose shift register with output logic is used to establish a sequence of period P corresponding to a given value of order m of the Hadam...

§0 Introduction. In a paper of Wan [W], he proved that for each holomorphic quadratic differential defined on the Euclidean 2-disk, D, there exists a harmonic diffeomorphism from the real hyperbolic plane H R into itself, such that its Hopf differential is the given holomorphic quadratic differential after representing H R by the Poincaré model. In addition, he also proved that this corresponde...

Spectral unraveling by space-selective Hadamard spectroscopy (SUSHY) enables recording of NMR spectra of multiple samples loaded in multiple sample tubes in a modified spinner turbine and a regular 5mm liquids NMR probe equipped with a tri-axis pulsed field gradient coil. The individual spectrum from each sample is extracted by adding and subtracting data that are simultaneously obtained from a...