MODIFIED APPROXIMATE PROXIMAL POINT ALGORITHMS FOR FINDING ROOTS OF MAXIMAL MONOTONE OPERATORS

§1　Introduction and preliminariesA set T Rn×Rnis called a monotone operator on Rn,if T has the property(x,y) ,(x′,y′)∈T 〈x -x′,y -y′〉≥0 ,where〈·,·〉denotes the inner product on Rn.T is maximal if(considered as a graph) itis not strictly contained in any other monotone operator on Rn.It is well known that thetheory of maximal monotone operators plays an important role in the study of convexprogramming and variational inequalities since itcan provide a powerful general framework…     

Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups

Let X be a Banach space with a weak uniform normal structure and C a non–empty convexweakly compact subset of X. Under some suitable restriction, we prove that every asymptoticallyregular semigroup T = {T(t) : t ∈¸ S} of selfmappings on C satisfying

${\mathop {\lim \inf }\limits_{S \mathrel\backepsilon t \to \infty } }{\left| {{\left\| {T(t)} \right\|}} \right|} < {\text{WCS}}(X)$

has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and\({\left| {{\left\| {T(t)} \right\|}} \right|}\) is the exact Lipschitz constant of T(t).     

Composite Legendre-Laguerre pseudospectral approximation in unbounded domains

A composite Legendre–Laguerre pseudospectral approximationin unbounded domains is developed. Some approximation resultsare obtained. As an application, a composite pseudospectralscheme is proposed for the Burgers equation on the half-line.The stability and convergence of the scheme are proved. By choosingappropriate base functions, the resulting system of this methodhas a sparse structure and can be solved in parallel. Numericalresults are given to show the efficiency of this new method.     

The Natural Morphisms between Toeplitz Algebras on Discrete Groups

Let G be a discrete group and (G, G₊) be a quasi-ordered group.Set G₊(G₊)^–1 and G₁= (G₊\){e}. Let F^G₁(G) andF^G₊(G) be the corresponding Toeplitz algebras. In the paper,a necessary and sufficient condition for a representation ofF^G₊(G) to be faithful is given. It is proved that when G isabelian, there exists a natural C*-algebra morphism from F^G₁(G)to F^G₊(G). As an application, it is shown that when G = Z² andG₊ = Z₊ x Z, the K-groups K₀(F^G₁(G)) Z², K₁(F^G₁(G)) Z andall Fredholm operators in F^G₁(G) are of index zero.     

The fluorescence of polyamidoamine dendrimers peripherally modified with 1,8-naphthalimide groups: Effect of the rare earth ions and protons

We report the absorption spectra, fluorescent spectra and photophysical properties of G 2.0 polyamidoamine dendrimers with peripheral 1,8-naphthalimide groups with the hydrogen ions, the rare earth ions (Er³⁺, Tb³⁺, Nb³⁺, Eu³⁺, Yb³⁺ and Gd³⁺) and the mixture of the rare earth metal and hydrogen ions. The presence of the rare earth ions and hydrogen ions was found to enhance the fluorescence owing to the coordination between the rare earth metal or hydrogen ions and internal amido groups of polyamidoamine (PAMAM) from dendrimer. The result from the 3D isogram of the fluorescence spectra for the dendrimers with peripheral 1,8-naphthalimide groups show that it was obtained for the different emission fluorescence intensity and scope by varying the excitation wavelength and the different rare earth ions as well as its concentration. The results obtained reveal that the capacities of these systems might have acted as a sensitive label agent of the rare earth cations and protons.     

Synthesis and luminescent properties of Y6W2O15:Eu phosphors

In this paper, a novel phosphor, Y₆W₂O₁₅:Eu³⁺ was synthesized by thermal decomposition and phase transition of its decatungstate gel precursor. With stepwise increase of temperature to 750 °C, a crystalline phase of Y₆W₂O₁₅:Eu³⁺forms that gives intense red emission when excited at 466 nm, the emission is attributed to the Eu³⁺ ions transitions from ⁵D₀ excited states to ⁷F_J (J=0-4) ground states. The long excitation wavelength proves the Eu³⁺ transition follows the photoexcitation of the oxygen-metal (O→W lmct) charge transfer bands in yttrium tungstate. Some structural information regarding Y₆W₂O₁₅ provided by luminescence is in accord with that characterized by X-ray diffraction (XRD) and scanning electron microscope (SEM). The long-wavelength excitation properties of this material may find application in the production of red phosphors for white light-emitting diodes (LEDs).     

An Affine Scaling Interior Trust Region Method via Optimal Path for Solving Monotone Variational Inequality Problem with Linear Constraints

Based on a differentiable merit function proposed by Taji et al. in ＂Math. Prog. Stud., 58, 1993, 369-383＂, the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints. By using the eigensystem decomposition and affine scaling mapping, the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem. Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.     

On S-Shaped Bifurcation Curves for a Class of Perturbed Semilinear Equations

By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.     

Synchronization of delayed fuzzy cellular neural networks based on adaptive control

This Letter studies synchronization of delayed fuzzy cellular neural networks with all the parameters unknown. To enhance the coupled strength dynamically and be more suitable for the reality, we add fuzzy theory to the traditional cellular neural networks. By the Lyapunov-Lasall principle of functional differential equations, some new stability criteria are obtained via adaptive control. To the best of our knowledge, there has few work studying fuzzy cellular neural networks. Moreover, the approaches developed here extend the ideas and techniques derived in recent literatures. In the end, an example and its simulation were given to illustrate the simpleness and effectiveness of our main results.