UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.

Hermite Non-Uniformly Correlated Array Beams and Its Propagation Properties

We study the evolution of spectral intensity and degree of coherence of a new class of partially coherent beams,Hermite non-uniformly correlated array beams,in free space and in turbulence,based on the extended Huygens–Fresnel integral.Such beams possess controllable rectangular grid distributions due to multi-self-focusing propagation property.Furthermore,it is demonstrated that adjusting the initial beam parameters,mode order,shift parameters,array parameters and correlation width plays a role in resisting intensity and degree of coherence degradation effects of the turbulence.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY L-LIPSCHITZIAN MAPPINGS

The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].

Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

MARTINGALE REPRESENTATION IN NEARLY UNIFORMLY CONVEX SPACES

In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.

Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).

A UNIFORMLY CONVERGENT DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF A HIGH ORDER ELLIPTIC DIFFERENTIAL EQUATION

In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.

UNIFORMLY HIGHER ORDER ACCURATE EXTRAPOLATIONS TO SOLUTIONS OF UNIFORMLY CONVERGENT DISCRETIZATION METHODS FOR SINGULARLY PERTURBED PROBLEMS

We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.

A UNIFORMLY CONVERGENT FINITE DIFFERENCE METHOD FOR A SINGULARLY PERTURBED INITIAL VALUE PROBLEM

Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh, which gives first_order uniform convergence in the sense of discrete maximum norm. Numerical results are also presented.

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.

Effects of La^(3+) Non-Uniformly Doping in TiO_2 Films on Photocatalytic Activities

TiO2 thin films non-uniformly doped by La^3＋ were prepared by sol-gel method. The comparison of thin film activities, which was characterized by photocatalytic degradation of methyl orange, shows that doping modes have great activities. The non-uniformly effects on photocatalytic doped TiO2 films resuh in good photocatalytic activities with an optimal concentration; about 0. 5% （ atom fraction ）. UV-Vis transmittance spectra indicate that the absorption edges of these TiO2 thin films shift to ward longer wave- lengths remarkably, and electrochemical behavior also reveales that e^- -h^＋ pairs are prone to formation and separation under UV irradiation. The mechanism of photocatalytic activities are enhanced by La^3＋ non-uniformly doping was discussed on the analogy of the theory of “window effect” of solar cell heterojunction.

ITERATIVE APPROXIMATION OF FIXED POINTS FOR MULTIVALUED OPERATORS OF THE MONOTONE TYPE IN UNIFORMLY SMOOTH BANACH SPACES

In this paper, let K be a nonempty subset of a uniformly smooth Banach space X, and T:K→2~k be a multivalued operator of the monotone type. The iterative sequence which converges strongly to the unique fixed point of T is given. Our results are the extension and improvements of the results obtained previously by several authors including Dunn, Chidume, Deng and Ding.

THE MODULUS OF CONVEXITY AND THE EQUIVALENT CONDITIONS OF UNIFORMLY NON-SQUARE SPACES

This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.

Uniformly Illuminated Efficient Daylighting System

Different approaches have been introduced for the daylighting system to reduce energy consumption, but they were not populated due to complex, high cost, and insufficient designs. There has been a recent problem in achieving uniform distribution of sunlight at a destination deep inside the building. Therefore, we propose a system to achieve high illumination by illuminating the surface of the absorber (optical fibers) uniformly. To capture sunlight, parabolic reflector and Fresnel lens are used. Different reflectors and lenses are considered, compared, and investigated to direct uniform light, which solves the heat problem, into the optical fibers. In addition, this study includes comparison between fiber-based daylighting systems. The proposed system has been verified through simulation and experimental results.

Frost deformation and microstructure evolution of porous rock under uniform and unidirectional freeze-thaw conditions

The frost deterioration and deformation of porous rock are commonly investigated under uniform freeze-thaw(FT)conditions.However,the unidirectional FT condition,which is also prevalent in engineering practice,has received limited attention.Therefore,a comparative study on frost deformation and microstructure evolution of porous rock under both uniform and unidirectional FT conditions was performed.Firstly,frost deformation experiments of rock were conducted under cyclic uniform and unidirectional FT action,respectively.Results illustrate that frost deformation of saturated rock exhibits isotropic characteristics under uniform FT cycles,while it shows anisotropic characteristics under unidirectional FT condition with both the frost heaving strain and residual strain along FT direction much higher than those perpendicular to FT direction.Moreover,the peak value and residual value of cumulative frost strain vary as logarithmic functions with cycle number under both uniform and unidirectional FT conditions.Subsequently,the microstructure evolution of rock suffered cyclic uniform and unidirectional FT action were measured.Under uniform FT cycles,newly generated pores uniformly distribute in rock and pore structure of rock remains isotropic in micro scale,and thus the frost deformation shows isotropic characteristics in macro scale.Under unidirectional FT cycles,micro-cracks or pore belts generate with their orientation nearly perpendicular to the FT direction,and rock structure gradually becomes anisotropic in micro scale,resulting in the anisotropic characteristics of frost deformation in macro scale.

Uncertainty Analysis of the Residual Strength of Non-Uniformly Loaded Casingsin Deep Wells

An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non-uniform load is considered.The distribution of multi-source parameters related to the residual anti extrusion strength and residual anti internal pressure strength of the casing after wear are determined using the probability theory.Considering the technical casing of X101 well in Xinjiang Oilfield as an example,it is shown that the randomness of casing wear depth,formation elastic modulus and formation Poisson’s ratio are the main factors that affect the uncertainty of residual strength.The wider the confidence interval is,the greater the uncertainty range is.Compared with the calculations resulting from the proposed uncertainty analysis method,the residual strength obtained by means of traditional single value calculation method is either larger or smaller,which leads to the conclusion that the residual strength should be considered in terms of a range of probabilities rather than a single value.

Relativistic Paradox of a Uniformly Charged Sphere Moving with Constant Velocity

A magneto-electric field appearing in a laboratory due to moving charges has unusual properties. In particular, such a field of kinematical origin does not obey the wave equation with a non-relativistic velocity instead of light speed;so, its movement resembles that of a rigid body. In this paper the field of a uniformly charged sphere moving at constant velocity is considered. Relativistic axiom, implicitly used in the derivation of formulas describing a kinematic deformation for the proper spherical field from the point of view of a fixed observer, is revealed. A discrepancy was found between the generally accepted idea of the configuration of a deformed field and its real geometry. It is shown that the correct interpretation of known formulas leads to a logical contradiction, which cannot be eliminated within the framework of the theory of relativity. A scheme of a decisive experiment is proposed.

PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL

We present an overview of the properties of the pseudohyperbolic metric in several real dimensions and study uniformly discrete sequences for the real unit ball in R^n.

Construction of Dynamic Alloy Interfaces for Uniform Li Deposition in Li-Metal Batteries

It is well accepted that a lithiophilic interface can effectively regulate Li deposition behaviors,but the influence of the lithiophilic interface is gradually diminished upon continuous Li deposition that completely isolates Li from the lithiophilic metals.Herein,we perform in-depth studies on the creation of dynamic alloy interfaces upon Li deposition,arising from the exceptionally high diffusion coefficient of Hg in the amalgam solid solution.As a comparison,other metals such as Au,Ag,and Zn have typical diffusion coefficients of 10-20 orders of magnitude lower than that of Hg in the similar solid solution phases.This difference induces compact Li deposition pattern with an amalgam substrate even with a high areal capacity of 55 mAh cm^(-2).This finding provides new insight into the rational design of Li anode substrate for the stable cycling of Li metal batteries.