Nested regular polygon solutions for planar 2N-body problems

In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

2-median location improvement problems under weighted l_1 norm and l_∞ norm on trees

This paper focuses on the 2-median location improvement problem on tree networks and the problem is to modify the weights of edges at the minimum cost such that the overall sum of the weighted distance of the vertices to the respective closest one of two prescribed vertices in the modified network is upper bounded by a given value.l1 norm and l∞norm are used to measure the total modification cost. These two problems have a strong practical application background and important theoretical research value. It is shown that such problems can be transformed into a series of sum-type and bottleneck-type continuous knapsack problems respectively.Based on the property of the optimal solution two O n2 algorithms for solving the two problems are proposed where n is the number of vertices on the tree.

Diagonal form fast multipole boundary element method for 2D acoustic problems based on Burton-Miller boundary integral equation formulation and its applications

This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.

Sodium glucose cotransporter-2 inhibitors: Are we targeting old devil with new problems?

Dear editor,The advent of modern molecular mechanism’s approach to disease treatment is highly advancing to mitigate/normalize the symptoms of disease i.e.hyperglycemia by targeting at least eight different pathophysiological approaches popularly known as omnious octet[1].Importantly,type 2 diabetes is a

Quantum algorithm for a set of quantum 2SAT problems

We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability(Q2SAT)problem,which is a generalization of 2-satisfiability(2SAT)problem.For a Q2SAT problem,we construct the Hamiltonian which is similar to that of a Heisenberg chain.All the solutions of the given Q2SAT problem span the subspace of the degenerate ground states.The Hamiltonian is adiabatically evolved so that the system stays in the degenerate subspace.Our numerical results suggest that the time complexity of our algorithm is O(n^(3.9))for yielding non-trivial solutions for problems with the number of clauses m=dn(n-1)/2(d■0.1).We discuss the advantages of our algorithm over the known quantum and classical algorithms.

NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS

This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.

Problems Related to Divers Health and Comfort in Hyperbaric He-O_2 Environment

The Diver Gas Recovery System(DGRS)is an important accessory equipment of the 300m Saturation Dive System. The system facilitates the recycling of the breathing gases for divers,therefore,it has great economic benefits. In April 1995, a 300 m unmanned test and a 100 m manned test on the HY2031 DGRSwere carried out successively.Ten months later,another manned test on the HY2032 DGRS

SOLVING THE VELOCITY PARAMETER OF THE 2-D WAVE INVERSE PROBLEMS WITH THE INTEGRATION-CHARACTERISTIC METHOD

For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.

Second Boundary Value Problems for 2n-th Order Nonlinear Differential Equations

Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.

中高职“3+2”衔接教育及存在的问题、原因与对策

通过对湖北省及全国部分地区中高职“3+2”衔接技能人才分段培养的调研,梳理人才培养过程中存在的问题及主要原因。一是高职阶段学生学习动力不足,学生管理难度大;原因有中职段管理不严,学习无压力,及教学设计存在问题;二是课程设置存在脱节与重叠现象;问题原因是标准未严格执行,并且中高职校缺乏沟通;三是存在衔接口径不匹配现象;原因在于缺乏专业设置标准及监督。针对问题提出了相应的对策建议。一是要建立统一的专业衔接标准、专业教学标准,加强标准执行情况的检查力度;二是要改革“3+2”转段考核的方式,加强中职学生平时成绩的要求与管理;三是加强中高职的沟通与交流;四是延伸中高职衔接为中高本衔接。

Perturbation finite element solution for chemo-elastic boundary value problems under chemical equilibrium

Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids.In this work,a perturbation finite element(FE)formulation is developed to analyze chemo-elastic boundary value problems(BVPs)under chemical equilibrium.The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration.The compositional expansion coefficient is used as the perturbation parameter.After the perturbation expansion,a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps.The presence of a numerical solution enables modeling 3D chemo-elastic solids,such as battery electrodes or ionic gels,of any geometric shape with defects of different shapes.The proposed method is tested in several numerical examples such as plates with circular or elliptical holes,and cracks.The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect.Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips,and the intensity of these peaks increases as the far field solute concentration decreases.

A 2-PERIODIC TRIGONOMETRIC INTERPOLATION PROBLEM

2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

Application for Superconvergence of Finite Element Approximations for the Elliptic Problem by Global and Local L²-Projection Methods

Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.

Numerical Computation of Figure-eight Solution for 3-body Problems

The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3-body in plane R2. The algorithm adopted here is the steepest descent method, which is simple but very valid for our problem.

ON A PROBLEM OF(O,2)-INTERPOLATION

The object in this paper is to consider the problem of existence,uniqueness,explicil representation of(0, 2)-interpolation on the zeros of(1-x^2)P~_(n-1)(x)/x when n is odd,where P_(n-1)denotes Legendre polynomial of degree n-1,and the problem of convergence of interpolatory polynomials.

A SISO mixed H2／l1 optimal control problem and its solution

Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation

This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.