Implicit Iterations of Two Finite Families for Nonexpansive Mappings in Banach Spaces

The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for two finite families of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Xu and Ori, Numer. Funct. Anal. Optim. 2001; 22:767–773, Zhou and Chang, Numer. Fund. Anal. Optim. 2002; 23:911–921, Chidume and Shahzad, Nonlinear. Anal. 2005; 62: 1149–1156.     

Plastic Plate Bending Problem with Friction on the Boundary and Uncertain Input Data

A thin plate made of a plastic material obeying the Hencky–Mises stress-strain law is considered. On a part of the boundary displacements and/or rotations with friction are prescribed. The model leads to a variational inequality of the second kind with a nonlinear monotone operator. Since the material function, loading, and friction coefficients are uncertain, we employ the worst scenario method. The existence of a worst scenario and a convergence of approximate solutions is proved.     

On Formation Generalization of Some Local Theorems

In this paper we give formation generalizations of some results of the theory of finite groups concerning the normalizers of p-subgroups.     

Pure ℓ-Ideals in Lattice-Ordered Rings#

An ?-ideal I of a commutative lattice-ordered ring R with positive identity element is called a pure ?-ideal if R  =  I  + ?( x ) for each x  ∈  I , where ?(x) is the ?-annihilator of x in R . In this article, we give some results on pure ?-ideals and study the ?-ideal structure of a commutative lattice-ordered ring with positive identity element by using pure ?-ideals.     

Top Varieties of Generalized MV-Algebras and Unital Lattice-Ordered Groups

In spite of the well-know fact that the system of ?-groups with strong unit (unital ?-groups) does not form a variety, there is a categorical connection between the category of unital ?-groups and the variety of generalized MV-algebras which enables us to naturally export equational machinery and terminology like “variety” from the latter category to the former.

Using this categorical equivalence, we study varieties, or equationally defined classes, and top varieties, varieties above the normal valued variety, of both structures. We generalize Chang's Completeness Theorem for generalized MV-algebras, and formulate some open questions for both structures.     

Note on Characterization of Projective Spaces

We prove a numerical characterization of ?ⁿ for varieties with at worst isolated local complete intersection quotient singularities. In dimension 3, we prove such a numerical characterization of ?³ for normal ?-Gorenstein projective varieties.     

Brownian Motion Indexed by a Time Scale

In this article, we generalize Wiener's existence result for one-dimensional Brownian motion by constructing a suitable continuous stochastic process where the index set is a time scale. We construct a countable dense subset of a time scale and use it to prove a generalized version of the Kolmogorov–?entsov theorem. As a corollary, we obtain a local Hölder-continuity result for the sample paths of generalized Brownian motion indexed by a time scale.     

Quantum chemical studies on solvent effects,ligand–water complexes and dimer structure of 2,2ʹ-dipyridylamine

In this work, optimised structures, structural and spectroscopic properties of 2,2?-dipyridylamine (DPA) in solvent media have been investigated. Conformational structures of DPA were determined and relative population distributions of the conformations were obtained. Vibrational modes were calculated for each environment and they were compared with the experimental values. The effects of the changing solvent environments on the molecular structures were investigated and hydrogen bonded complex structures that DPA could form with water molecules were studied. As a result of this study, the effects of solvent environments on the molecular structure of DPA have been determined. Chemical reactivities of DPA which have not been studied previously have been determined. When the solid phase infrared spectrum of pure DPA was examined, it was seen that N-H stretching mode was observed at 3250 cm^?1. Since it will mean that there is bonded N-H in the structure, the dimer structure of DPA has been investigated.     

Recognition of dicarboxylates in aqueous acetonitrile by a dinuclear zinc(II) complex of 2,2’-binaphthalene-based receptor

Molecular recognition of dicarboxylates by a dinuclear zinc(II) complex of 2,2?-binaphthalene bearing di(2-pyridyl)aminomethyl groups at 8- and 8?-positions ([Zn₂L]⁴⁺) by UV-vis and fluorescence spectral titrations in an aqueous solvent was investigated. In a series of α,ω-dicarboxylate, receptor [Zn₂L]⁴⁺ showed the highest binding affinity for succinate and UV-vis and fluorescence changes were also largest upon the addition of this guest. In a series of phthalate derivatives, phthalate was strongly bound by [Zn₂L]⁴⁺. The characteristic UV-vis and fluorescence changes strongly depend on the dihedral angle of two naphthyl groups of the complex [Zn₂L]⁴⁺· dicarboxylate estimated by spectral titrations and DFT calculations.