NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OF U-CONVEXITY IN BANACH SPACES

We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.

ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE

In this article, the authors study a generalized modulus of convexity, δ（α） （ε）. Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^（α）（1＋ε ） 〉 （1- α）ε.

UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION

The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich＇ s open question is given. The results presented extend and improve Zhang Shisheng＇ s recent ones in the following aspects ： （i） Zhang＇ s stronger condition that the sequence of iterative parameters converges to zero is removed; （ii） Zhang＇ s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; （iii） Zhang＇ s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.

ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES

In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized Garc′?a-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.

Measurement of pore diffusion factor of porous solid materials

Internal diffusion of molecules in porous materials plays an important role in many chemical processes.However, the pore diffusion capacity of porous materials cannot be measured by conventional catalyst characterization methods. In the present paper, a pore diffusion factor, the ratio of the diffusionconstriction factor to the pore tortuosity of the porous materials, was proposed to measure the diffusion ability of pores inside solid materials, and a method was proposed for measuring the diffusion factor using a well-defined and uniform pore size material as a reference. The diffusion factor was calculated based on the effective diffusion coefficients and the diffusion-constriction factor and pore tortuosity of the reference porous materials. The pore diffusion factor measurement can be performed at room temperature and atmospheric pressure. The pore diffusion factor of conventional porous materials was found to be much smaller than 1, indicating that there is a lot of room for improving the diffusion ability of the conventional catalysts and adsorbents, and could be significantly increased through adding small number of fibers into the conventional porous materials as template.

COVERING PROPERTIES ON H-SPACES AND APPLICATIONS

Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.

Erratum to "Uniform Coverage of Fibres over Open-contoured Freeform Structure Based on Arc-length Parameter" [Chinese Journal of Aeronautics 21(2008)571-577]

It is regretted that the author corrections requested at the proof stage were not made accurately. There are some incorrect typings in two equations which will lead to inaccurate results if readers perform calculations directly

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 convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying

Localized Electrons Accelerated Ionic and Charge Transfer for Superior Lithium Storage

The electrochemical energy storage performance is greatly determined by the charge transfer and ion transportation occurring in the electrode materials.Therefore,the enhancement of electric conductivity and ionic mobility is vital for high-performing and stable metal ion batteries.Here,we report the properties of oxygen vacancies(VO)and carbon co-doped TiO_(2) hollow spheres(HS-TiO_(2))and compared them with fully oxidized white TiO_(2) hollow spheres(W-TiO_(2)).Theoretical calculations and experimental results revealed that the introduction of carbon dopant and VO in anatase TiO_(2) reduced the bandgap and the existence of localized electrons,leading to a lower migration barrier of Li ions that promoted faster ion diffusion kinetics,enabling the HS-TiO_(2) with higher reversibility during the insertion and extraction of Li ions than the W-TiO_(2).This HS-TiO_(2) delivered superior lithium storage properties with a specific discharge capacity of 214.6 mAh g^(-1) for the 100th cycle at 200 mA g^(-1) and 116.3 mAh g^(-1) over 2000 cycles at a high rate of 2 A g^(-1).

A new FPGA architecture suitable for DSP applications

A new FPGA architecture suitable for digital signal processing applications is presented. DSP modules can be inserted into FPGA conveniently with the proposed architecture, which is much faster when used in the field of digital signal processing compared with traditional FPGAs. An advanced 2-level MUX （multiplexer） is also proposed. With the added SLEEP MODE PASS to traditional 2-level MUX, static leakage is reduced. Furthermore, buffers are inserted at early returns of long lines. With this kind of buffer, the delay of the long line is improved by 9.8% while the area increases by 4.37%. The layout of this architecture has been taped out in standard 0.13 μm CMOS technology successfully. The die size is 6.3 × 4.5 mm^2 with the QFP208 package. Test results show that performances of presented classical DSP cases are improved by 28.6%-302% compared with traditional FPGAs.