Quasi-Conformally Flat Submanifolds with Parallel Mean Curvature Vector

Introduction Let ()nppNc = (N, h) denote an (n p)-dimensional indefinite space form, that is, a connected space form ()nppNc endowed with a pseudo-Riemannian metric h, given by 11(,)pniijjipjhvwvwvw= ==-邋, ,xvwTN"? When 0c>, ()nppNc is denoted by ()nppSc . A smooth immersion:nppMNy of an n- dimensional connected manifold M is said to be a space-like submanifold if the induced metric via y is a Riemannian metric on M. Let M be an n-dimensional complete space-like submanifold with par…     

Constructing parametric triangular patches with boundary conditions

The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are defined on different parameter spaces. Therefore, it is necessary to define interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between different parameter spaces. In this paper we present a new method to define boundary conditions. Boundary conditions defined by the new method have the same parameter space if the three given surface patches can be converted into the same form through affine transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G^1 continuity. The resulting parametric triangular patch preserves precision of the applied classic method.     

An Optimal Content Caching Framework for Utility Maximization

For desirable quality of service, content providers aim at covering content requests by large network caches. Content caching has been considered as a fundamental module in network architecture. There exist few studies on the optimization of content caching. Most existing works focus on the design of content measurement,and the cached content is replaced by a new one based on the given metric. Therefore, the performance for service provision with multiple levels is decreased. This paper investigates the problem of finding optimal timer for each content. According to the given timer, the caching policies determine whether to cache a content and which existing content should be replaced, when a content miss occurs. Aiming to maximize the aggregate utility with capacity constraint, this problem is formalized as an integer optimization problem. A linear programming based approximation algorithm is proposed, and the approximation ratio is proved. Furthermore, the problem of content caching with relaxed constraints is given. A Lagrange multiplier based approximation algorithm with polynomial time complexity is proposed. Experimental results show that the proposed algorithms have better performance.     

THE GENERALIZED RIEMANN-HILBERT PROBLEM WITH CARLEMAN''''S SHIFT AND HIGHER-ORDER DERIVATIVES FOR GENERALIZED CAUCHY-RIEMANN EQUATIONS

This paper deals with the Noether theory of the generalized Riemann-Hilbert problem with Carleman'sshift and higher-order derivatives for generalized Cauchy-Riemann equations.Let D be a (m + 1) -connected domain with the boundary0,1,……,N) are simple closed curves, z = 0 D.In this paper, the following problem A for generalized Cauchy-Rirmann equtions is donsideredFind the sectionally regular solution of the equationson the domain D, and the boundary values of which satisfy the condition;     

超球上双全纯映照的凸形界限(英文)

1.IntroductionR.Nevanlinna proved the following result in 1920:Let S be the family offunctions which are analytic and univalent in the unit disc,satisfying f(0)=0,f′(0)=1,then there is an r_0(?)(0,1),such that any function in S maps the disc(?)r_0,there is a function in S whichmaps (?)相似文献   

Composition operators between p-Bloch space and q-Bloch space in the unit ball

Let B_n be the unit ball of C~n and φ= (φ_1,…,φ_n) a holomorphic self-map of B_n. The main purpose of this paper is todiscuss the boundedness and compactness of composition operator C_φ between p-Bloch space β~p(B_n) and q-Bloch space β~p(B_n), where p≥0 and q≥0.     

Weighted composition operators between generally weighted Bloch spaces of polydisk

Let φ be a holomorphic self-map of the open unit polydisk U nin C nand ψ a holomorphic function on U n,p,q0. ∨In this paper,we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and φ,sufficient conditions for the weighted composition operator Wψ,φ induced by ψ and φ to be bounded and compact between the generally weighted Bloch spaces are investigated.     

Exact n-width on the class of analytic functions in the space of continuous functions

Let ω(·) be a given concave modulus of continuity and ω(g,·) be the modulus of continuity of a function g∈C, where C is the space of 2π-periodic, continuous functions on R with norm ‖f‖C∶=maxt∈R|f(t)|, r,ω∞,β(r=0,1,2,…) denotes those 2π-periodic, real-valued functions f on R that are analytic in the strip Sβ∶=｛z∈C：|Imz|＜β｝, β＞0, and satisfy the restriction condition: ω(f(r),·)≤ω(·). In this paper, the exact n-width of the class of functions r,ω∞,β in the space C is determined.     

Grain size distribution and topology in 3D grain growth simulation with large-scale Monte Carlo method

Three-dimensional normal grain growth was appropriately simulated using a Potts model Monte Carlo algorithm. The quasi-stationary grain size distribution obtained from simulation agreed well with the experimental result of pure iron. The Weibull function with a parameter β=2.77 and the Yu-Liu function with a parameter v =2.71 fit the quasi-stationary grain size distribution well. The grain volume distribution is a function that decreased exponentially with increasing grain volume. The distribution of boundary area of grains has a peak at S/〈S〉=0.5, where S is the boundary area of a grain and 〈S〉 is the mean boundary area of all grains in the system. The lognormal function fits the face number distribution well and the peak of the face number distribution is f=10. The mean radius of f-faced grains is not proportional to the face number, but appears to be related by a curve convex upward. In the 2D cross-section, both the perimeter law and the Aboav-Weaire law are observed to hold.     

Exact n-width on the class of analytic functions in the space of continuous functions

Let ω ( · ) be a given concave modulus of continuity and ω (g, · ) be the modulus of continuity of a function g ∈ C,where C is the space of 2π-periodic, continuous functions on (R) with norm ‖ f ‖ C := max | f( t ) |,(h) ∞,β r,ω( r= 0,1,2,… ) denotes those 2π-periodic, real-valued functions f on R that are analytic in the strip Sβ:= { z ∈ C: |Imz | ＜ β|, β ＞ 0, and satisfy the restriction condition: ω(f(r), ·)≤ω(·). In this paper, the exact n-width of the class of functions(h) ∞,β r,ωin the space C is determined.     

On the largest linear span of binary sequences with period p 2 from interleaved construction

Let S be a family of binary sequences constructed from interleaved construction. The linear spans of binary sequences in S are studied in this paper. In order to achieve the largest linear span, a criterion is presented for the base sequences with periodp, where p is a prime and 2 is a primitive root modulop2. It is shown that any sequence in S has the largest linear span under the criterion. Moreover, such base sequences can be chosen easily.     

Artificial Boundary Method for Calculating Ship Wave Resistance

The calculation of wave resistance for a ship moving at constant speed near a free surface is considered. This wave resistance is calculated with a linearized steady potential model. To deal with the unboundedness of the physical domain in the potential flow problem, we introduce one vertical side as an artificial upstream boundary and two vertical sides as the artificial downstream boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the potential flow problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. The solution of the variational problem by the finite element method gives the numerical approximation of the potential flow around the ship, which was used to calculate the wave resistance. The numerical examples show the accuracy and efficiency of the proposed numerical scheme.     

DIFFERENCE-BOUNDARY INTEGRO DIFFERENTIAL EQUATION METHOD FOR TWO DIMENSIONAL PARABOLIC EQUATION

Let Ω be a bounded domain in R~2 with smooth boundary and Ω' be the complementary set of Ω∪ .We consider the Neumann's problem of parabolic equation as follow;Let τ be time step, t_k=k_τ and u~k(x)=u(x,t,). We discrete u/ t of (1) by use of difference and getwhereQ~K=1/t(u~K-u~(k-1)-t u~k/ t+f(u~k)-f(u~(k-1)).(2) is a family of Neumann's boundary value problems of Helmholtz equation. Let E(x,y) be the funda-mental solution to Helmholtz equation, i. e.     

Reality over Web： Pervasive Computing Meets the Web

Reality over Web （ROW） is a novel concept, where a window on the web corresponds to a window onto a real space. Once the correspondence is established, users should be able to interact or manipulate the objects or people in the real space through the web window. In this paper, we introduce the RoW concept and highlight the principles that govern its design and implementation. A system architecture for realizing the RoW concept is described along with a proof-of-concept prototype that implements portions of the RoW concept. One essential part of an RoW implementation is accurate Iocationing of objects and people in a video frame. The Iocationing problem becomes particularly challenging because we want to reuse existing infrastructure as much as possible. We developed a high-frequency sound-based Iocationing scheme and implemented it on the prototype. The results from initial experiments performed on the Iocationing scheme are reported here.     

Hyperbolic heat conduction restricted by continuous boundary interface

Finite difference method (FDM) combined with MacCormack' s predictor-corrector scheme is used to solve the problem of hyperbolic heat conduction in a finite medium. One of its boundary surfaces is heated by a rectangular pulsed energy source while the other surface is tightly contacted with another medium where the continuous boundary condition is satisfied. Some non-Fourier heat conduction behaviors have been analyzed theoretically.``     

Earthquake Disaster Simulation for an Urban Area, with GIS, CAD,FEA, and VR Integration

For a disaster whose scale includes an urban area, it is difficult to be studied with physical experiments. Numerical simulation is found a very efficient tool for such problem. This paper aims at developing an integrated urban earthquake simulation system (UESS) that uses GIS as the model source, CAD as the model generating tools, FEA as damage prediction, and virtual reality (VR) as the post-process platform. An automatic procedure was developed to buildup the 3D structural model of buildings in an urban area, as well as to simulate their earthquake performances, from the digital map of GIS. And the simulation results were presented in an integrated interface with a GIS view-port for position finding, a CAD view-port for 3D structural damage identification, and a VR view-port for 3D dynamic structural vibration display. An urban example with more than 7000 buildings was select to demonstrate the feasibility of proposed system.     

A general method for numerical Green''''s function in arbitrarily layered soils

A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layersoils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying thepertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vectormatrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is ap-plicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.     

CONDITIONS FOR THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF NONLINEAR SINGULAR INTEGRAL EQUATION

I. In recent years, I have done some researches on H_(R. K)(W) space, and solved one type of non-linear sin-gular integration equations with displacement:where the conditions for the existence and uniqueness of the solution can be found there is also a method in-volving successive approximation by which the solution can be estimated. The research on this type of equa-tion provides a theoritical foundation for the solution of the non-linear Riemann boundary value problem.Ha, R_(R. K)(W) defined as follows;     

Formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic sextic fields

Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, Zhang Xianke from 1948 to 1988.     

Parameterization for fitting triangular mesh

In recent years, with the development of 3D data acquisition equipments, the study on reverse engineering has become more and more important. However, the existing methods for parameterization can hardly ensure that the parametric domain is rectangular, and the parametric curve grid is regular. In order to overcome these limitations, we present a novel method for parameterization of triangular meshes in this paper. The basic idea is twofold: first, because the isotherms in the steady temperature do not intersect with each other, and are distributed uniformly, no singularity (fold-over) exists in the parameterization; second, a 3D harmonic equation is solved by the finite element method to obtain the steady temperature field on a 2D triangular mesh surface with four boundaries. Therefore, our proposed method avoids the embarrassment that it is impossible to solve the 2D quasi-harmonic equation on the 2D triangular mesh without the parametric values at mesh vertices. Furthermore, the isotherms on the temperature field are taken as a set of iso-parametric curves on the triangular mesh surface. The other set of iso-parametric curves can be obtained by connecting the points with the same chord-length on the isotherms sequentially. The obtained parametric curve grid is regular, and distributed uniformly, and can map the triangular mesh surface to the unit square domain with boundaries of mesh surface to boundaries of parametric domain, which ensures that the triangular mesh surface or point cloud can be fitted with the NURBS surface.