WEIGHTED BEST LOCAL APPROXIMATION IN ORLICZ SPACE

We present a common fixed point theorem for generalized asymptotically non- expansive and noncommuting mappings in normed linear spaces.

A UNIFIED APPROACH TO CERTAIN PROBLEMS OF BEST LOCAL APPROXIMATION

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.

C^p Condition and the Best Local Approximation

In this paper, we introduce a condition weaker than the LP differentiability, which we call Cp condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation at that point. We also give a necessary and sufficient condition for that a function be LP differentiable. In addition, we study the convexity of the set of cluster points of the net of best appoximations of f, {Pε（f）} asε→0.

Weighted Best Local Approximation

In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Chui et al. in 1984 are extensively used.

Weighted Best Local Approximation

In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.

PREDICTING CHAOTIC TIME SERIES WITH IMPROVED LOCAL APPROXIMATIONS

In this paper, new approaches for chaotic time series prediction areintroduced. We first summarize and evaluate the existing local prediction models, then proposeoptimization models and new algorithms to modify procedures of local approximations. Themodification to the choice of sample sets is given, and the zeroth-order approximation is improvedby a linear programming method. Four procedures of first-order approximation are compared, andcorresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predictingaccuracy is put forward. In the end, we discuss two important examples, i.e. Lorenz system andRoessler system, and the simulation experiments indicate that the modified algorithms are effective.

SOME BEST APPROXIMATION RESULTS IN LOCALLY CONVEX SPACES

In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.

LOCAL SALINE APPROXIMATION METHODS FOR SINGULAR PRODUCT INTEGRATION

The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.

THE SIMULTANEOUS APPROXIMATION IN THE LOCALLY CONVEX SPACES

In this paper, we study the characterization of f-Chebyshev radius and f-Chebyshev centers and the existence of f-Chebyshev centers in locally convex spaces.

Geometrical optics-based ray field tracing method for complex source beam applications

Due to the fact that traditional ray field tracking approaches require a large number of geometrical optical（GO） ray tubes,they are very inefficient in many practical applications.An improved ray model scheme for a complex source beam（CSB） tracking technique is proposed in this paper.The source field can be expressed by a superposition of CSBs,then every CSB basis function has a Gaussian-type amplitude distribution and is suitable for replacing a GO ray tube in the ray tracing approach.The complex phase matching technique is adopted to find the reflected beam in the reflection point where local approximation is used to represent the curved surface in its neighborhood.A new solution to multiple reflections using the conventional right-handed reflected system is used to track the field easily.Numerical results show the accuracy of the proposed method.

First-principles calculations of structural and thermodynamic properties of BeB2 compound

The lattice parameter bulk modulus and pressure derivative of BeB2 are calculated by using the Cambridge Serial Total Energy Package （CASTEP） program in the frame of density function theory. The calculated results agree well with the average experimental data and other theoretical results. Through the quasi-harmonic Debye model, the dependences of the normalized lattice parameters a/ao, c/c0 and the normalized primitive cell volume V/Vo on pressure P, the variation of the thermal expansion coefficient ~ with pressure P and temperature T, as well as the dependences of the heat capacity Cv on pressure P and temperature T are obtained systematically.

Elastic and thermodynamic properties of c-BN from first-principles calculations

The elastic constants and thermodynamic properties of c-BN are calculated using the first-principles plane wave method with the relativistic analytic pseudopotential of the Hartwigen, Goedecker and Hutter （HGH） type in the frame of local density approximation and using the quasi-harmonic Debye model, separately, Moreover, tbe dependences of the normalized volume V/V0 on pressure P, as well as the bulk modulus B, the thermal expansion α, and the heat capacity CV on pressure P and temperature T are also successfully obtained,

Electronic structures and optical properties of monoclinic ZrO2 studied by first-principles local density approximation plus U approach

The electronic structures and optical properties of the monoclinic ZrO2 (m-ZrO2) are investigated by means of first-principles local density approximation (LDA) + U approach.Without on-site Coulomb interactions,the band gap of m-ZrO2 is 3.60 eV,much lower than the experimental value (5.8 eV).By introducing the Coulomb interactions of 4d orbitals on Zr atom (Ud) and of 2p orbitals on O atom (Up),we can reproduce the experimental value of the band gap.The calculated dielectric function of m-ZrO2 exhibits a small shoulder at the edge of the band gap in its imaginary part,while in the tetragonal ZrO2 and cubic ZrO2 it is absent,which is consistent with the experimental observations.The origin of the shoulder is attributed to the difference of electronic structures near the edge of the valence and conduction bands.

Phase transition and thermodynamic properties of TiO_2 from first-principles calculations

The pressure induced phase transitions of TiO2 from anatase to columbite structure and from rutile to columbite structure and the temperature induced phase transition from anatase to rutile structure and from columbite to rutile structure are investigated by ab initio plane-wave pseudopotential density functional theory method （DFT）, together with quasi-harmonic Debye model. It is found that the zero-temperature transition pressures from anatase to columbite and from rutile to columbite are 4.55 GPa and 19.92 GPa, respectively. The zero-pressure transition temperatures from anatase to rutile and from columbite to rutile are 950 K and 1500 K, respectively. Our results are consistent with the available experimental data and other theoretical results. Moreover, the dependence of the normalized primitive cell volume V/Vo on pressure and the dependences of thermal expansion coefficient α on temperature and pressure are also obtained successfully.

Structural,thermodynamic and electronic properties of zinc-blende AlN from first-principles calculations

Structural, thermodynamic and electronic properties of zinc-blende AIN under pressure are investigated by first- principles calculations based on the plane-wave basis set. Through the analysis of enthalpy variation of AIN in the zinc-blende （ZB） and the rock-salt （RS） structures with pressure, we find the phase transition of A1N from ZB to RS structure occurs at 6.7GPa. By using the quasi-harmonic Debye model, we obtain the heat capacity Cv, Debye temperature θD, Gruneisen parameter γ and thermal expansion coefficient α. The electronic properties including fundamental energy gaps and hydrostatic deformation potentials are investigated and the dependence of energy gaps on pressure is analysed.

Urban Stormwater Modeling with Local Inertial Approximation Form of Shallow Water Equations: A Comparative Study

This study focused on the performance and limitations of the local inertial approximation form model(LIM)of the shallow water equations(SWEs)when applied in urban flood modeling.A numerical scheme of the LIM equations was created using finite volume method with a first-order spatiotemporal Roe Riemann solver.A simplified urban stormwater model(SUSM)considering surface and underground dual drainage system was constructed based on LIM and the US Environmental Protection Agency Storm Water Management Model.Moreover,a complete urban stormwater model(USM)based on the SWEs with the same solution algorithm was used as the evaluation benchmark.Numerical results of the SUSM and USM in a highly urbanized area under four rainfall return periods were analyzed and compared.The results reveal that the performance of the SUSM is highly consistent with that of the USM but with an improvement in computational efficiency of approximately 140%.In terms of the accuracy of the model,the SUSM slightly underestimates the water depth and velocity and is less accurate when dealing with supercritical flow in urban stormwater flood modeling.Overall,the SUSM can produce comparable results to USM with higher computational efficiency,which provides a simplified and alternative method for urban flood modeling.

Compton profiles of NiO and TiO_2 obtained from first principles GWA spectral function

In this work,we first use momentum density studies to understand strongly correlated electron behavior,which is typically seen in transition metal oxides.We observe that correlated electron behavior as seen in bulk NiO is due to the Fermi break located in the middle of overlapping spectral functions obtained from a GW（G is Green’s function and W is the screened Coulomb interaction） approximation（GWA） calculation while in the case of TiO2 we can see that the origin of the constant momentum distribution in lower momenta is due to a pile up of spectra before the Fermi energy.These observations are then used to compare our calculated Compton profiles with previous experimental studies of Fukamachi and Limandri.Our calculations for NiO are observed to follow the same trend as the experimental profile but it is seen to have a wide difference in the case of TiO2 before the Fermi break.The ground state momentum densities differ significantly from the quasiparticle momentum density,thus stressing the importance of the quasiparticle wave function as the input for the study of charge density and the electron localization function.Finally we perform a calculation of the quasiparticle renormalization function,giving a quantitative description of the discontinuity of the GWA momentum density.

Structural and thermodynamic properties of AlB2 compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter （HGH） scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB2 compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters α/αo and c/co on pressure P, the normalized primitive cell volume V/Vo on pressure P, the variation of the thermal expansion α with pressure P and temperature T, as well as the Debye temperature OD and the heat capacity Cv on pressure P and temperature T.

Time-Dependent Density-Functional Calculations for Optical Spectra of Na2 and Na4 Clusters

With the frame of the time-dependent local density approximation, an efficient description of the optical response of clusters has been used to study the photo-absorption cross section of Na2 and Na4 clusters. It is shown that our calculated results are in good agreement with the experiment. In addition, our calculated spectrum for the Na4 cluster is in better agreement with experiment than the GW absorption spectrum.

基于两部模型的组合惩罚似然估计方法研究及其应用

在统计学中,多借助零膨胀模型研究零膨胀数据潜在的模型结构及变量选择问题。然而,在多数情况下,响应变量的非零部分为定量数据,简单的零膨胀模型无法刻画这类数据的模型结构,对应的参数估计方法也不再适用。鉴于此,学者提出处理零膨胀半连续数据的两部模型。本文将组合惩罚似然估计方法引入两部模型,研究其变量选择问题。提出一种新的处理高维统计分析问题的惩罚似然估计方法:NCPM (New Combined Punishment Method),并将该方法应用于太原市降水量数据,分析其影响因素。模拟及实例分析结果均表明本文的方法行之有效,较传统的惩罚似然估计方法具有更高的预测精度。