A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

RESEARCH ON THE COMPANION SOLUTION FOR A THIN PLATE IN THE MESHLESS LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method(GFEM), boundary element method(BEM) and element free Galerkin method(EFGM), and is a truly meshless method possessing wide prospects in engineering applications. The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem.

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.

Improved non-singular local boundary integral equation method

When the source nodes are on the global boundary in the implementation of local boundary integral equation method （LBIEM）, singularities in the local boundary integrals need to be treated specially. In the current paper, local integral equations are adopted for the nodes inside the domain and moving least square approximation （MLSA） for the nodes on the global boundary, thus singularities will not occur in the new al- gorithm. At the same time, approximation errors of boundary integrals are reduced significantly. As applications and numerical tests, Laplace equation and Helmholtz equation problems are considered and excellent numerical results are obtained. Furthermore, when solving the Helmholtz problems, the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions. Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.

On Local Integrated Cosine Functions

Suppose X is a Banach space, and A is a closed operator. We give some equivalent conditions between A generating a local integrated cosine functions and the existence of solutions of abstract Cauchy problems.

ON THE LOCALIZATION AND CONVERGENCE OF MULTIPLE FOURIER INTEGRAL BY BOCHNER-RIESZ MEANS

In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).

INTEGRATION OF A ZONAL FUNCTION RELATED TO THE LOCAL HARMONIC ANALYSIS ON SPHERES

In studying Local harmonic analysis on the sphere S',R.S.Strichartz introduced certain zonab functionsid(x,y))which satisfy the equation

A MESHLESS METHOD OF A THIN PLATE

A meshless approach to analysis of arbitrary Kirechhoff plates bythe local boundary integral equation (LBIF) method is presented. Themethod combines the advantageous features of all the three meth- ods:the Galerkin finite element method (GFEM), the boundary elementmethod (BEM) and the element- free Galerkin method (EFGM). It is atruly meshless method, which means that the discretization is inde-pendent of geometric subdivision into elements or cells, but is onlyboundary integration, however over a local boundary cen- tered) overa domain in question.

Real-Variable Theory of Local Variable Hardy Spaces

In this paper, we give a complete real-variable theory of local variable Hardy spaces.First, we present various real-variable characterization in terms of several local maximal functions.Next, the new atomic and the finite atomic decomposition for the local variable Hardy spaces are established. As an application, we also introduce the local variable Campanato space which is showed to be the dual space of the local variable Hardy spaces. Analogous to the homogeneous case, some equivalent definitions of the dual of local variable Hardy spaces are also considered. Finally, we show the boundedness of inhomogeneous Calderon–Zygmund singular integrals and local fractional integrals on local variable Hardy spaces and their duals.

On the Ratio Inequalities for Locally Square Integrable Martingales

In this paper, we establish some ratio inequalities for locally square inte-grable martingales, and give some extensions of the related results for continuous local martingales.

Integrated communication and localization in millimeter-wave systems

As the fifth-generation(5G)mobile communication system is being commercialized,extensive studies on the evolution of 5G and sixth-generation(6G)mobile communication systems have been conducted.Future mobile communication systems are evidently evolving toward a more intelligent and software-reconfigurable functionality paradigm that can provide ubiquitous communication,as well as sense,control,and optimize wireless environments.Thus,integrating communication and localization using the highly directional transmission characteristics of millimeter waves(mmWaves)is a promising route.This approach not only expands the localization capabilities of a communication system but also provides new concepts and opportunities to enhance communication.In this paper,we explain the integrated communication and localization in mmWave systems,in which these processes share the same set of hardware architecture and algorithms.We also provide an overview of the key enabling technologies and the basic knowledge on localization.Then,we provide two promising directions for studies on localization with an extremely large antenna array and model-based(or model-driven)neural networks.We also discuss a comprehensive guidance for location-assisted mmWave communications in terms of channel estimation,channel state information feedback,beam tracking,synchronization,interference control,resource allocation,and user selection.Finally,we outline the future trends on the mutual assistance and enhancement of communication and localization in integrated systems.

Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces

In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the authors first obtain the two-weight weak-type estimate for the locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(b') ,and then obtain the two-weight weak-type estimate for the local fractional integrals.In addition,the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of(u,v)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.

On a Version of Rosenthal’s Inequality for Locally Square Integrable Martingales

In this paper, we study the constants in a version of Rosenthal’s inequality for locally square integrable martingales. We prove that the order of growth rates of the constants is the same as in the case of discrete time martingales.

Laws of the Iterated Logarithm for Locally Square Integrable Martingales

Three types of laws of the iterated logarithm （LIL） for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a number of FLIL are obtained, and Chung LIL is extended.

Reliable iris localization using integral projection function and 2D-shape properties

Iris recognition technology recognizes a human based on his/her iris pattern. However, the accuracy of the iris recognition technology depends on accurate iris localization. Localizing a pupil region in the presence of other low-intensity regions, such as hairs, eyebrows, and eyelashes, is a challenging task. This study proposes an iris localization technique that includes a localizing pupillary boundary in a sub-image by using an integral projection function and two-dimensional shape properties （e.g., area, geometry, and circularity）. The limbic boundary is localized using gradients and an error distance transform, and the boundary is regularized with active contours. Experimental results obtained from public databases show the superiority of the Drooosed techniaue over contemporary methods.

The vertical distribution characteristics of integral turbulence statistics in the atmospheric boundary layer over an urban area in Beijing

Turbulence data(2008–2012) from a 325 m meteorological tower in Beijing, which consisted of three layers(47,140, and 280 m), was used to analyze the vertical distribution characteristics of turbulent transfer over Beijing city according to similarity theory. The conclusions were as follows.(1) Normalized standard deviations of wind speeds/ui * were plotted as a function only of a local stability parameter. The values under near-neutral conditions were 2.15, 1.61, and 1.19 at 47 m, 2.39, 1.75,and 1.21 at 140 m, and 2.51, 1.77, and 1.30 at 280 m, showing a clear increase with height. The normalized standard deviation of wind components fitted the 1/3 law under unstable stratification conditions and decreased with height under both stable and unstable conditions.(2) The normalized standard deviation of temperature fitted the.1/3 law in the free convection limit, but was quite scattered with different characteristics under near-neutral conditions. The normalized standard deviations of humidity and the CO2 concentration fitted the.1/3 law under unstable conditions, and remained constant under near-neutral and stable stratification. The normalized standard deviation of scalars, i.e., temperature, humidity, and CO2 concentration, all increased with height.(3) Compared with momentum, and the water vapor and CO2 concentrations, the turbulence correlation coefficient for heat was smaller under near-neutral conditions, but larger under both stable and unstable conditions. A dissimilarity between heat, and the water vapor and CO2 concentrations was observed in urban areas. The relative correlation coefficients between heat and each of momentum, humidity, and CO2 concentration(|rwT/ruw|, |rwT/rwc| and |rwT/ruq|) in the lower layers were always larger than in higher layers, except for the relative correlation coefficient between heat and humidity in an unstable stratification. Therefore, the ratio between heat and each of momentum, humidity, and CO2 concentration decreased with height.

Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin(MLPG)method with radial basis function(RBF)kernels generated trial spaces.Local weak-form testings are done with stepfunctions.It is proved that subject to sufficiently many appropriate testings,solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed.Moreover,an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation.Numerical results(in double precision)give good agreement with the provided theory.

A LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENTS

By using the Ito's calculus, a law of the iterated logarithm is established for the processes with independent increments (PⅡ). Let X = {Xt, t ≥ 0} be a PII with Ext=0,V(t)=Ext2<∞and limt∞V(t)=∞ If one of the following conditions is satisfied,(2) Suppose the Levy's measure of X may be written as v(dt,ds) = Ft(dx) dV(t) and there is a σ-finite measure G such tnat ,

Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

In this paper,we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equalorder element pair P_(1)−P_(1)which do not satisfy the inf-sup condition.The two-scale method consist of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh.Convergence of the optimal order in the H1-norm for velocity and the L^(2)-norm for pressure are obtained.The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relation h=O(H^(2)).Numerical experiments completely confirm theoretic results.Therefore,this method presented in this paper is of practical importance in scientific computation.