SCALAR CURVATURE TYPE PROBLEM ON THE THREE DIMENSIONAL BOUNDED DOMAIN

In this paper we prove an existence result for the nonlinear elliptic problem：-△u = Ku5,u 〉 0 in Ω,u = 0 on Ω,where Ω is a smooth bounded domain of R3 and K is a positive function in Ω.Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument.

Influence of Psychiatric Problems on Clinical Outcomes during the First 12 Months after Primary Total Knee Arthroplasty

Background: Total knee arthroplasty (TKA) is a useful treatment option for advanced knee osteoarthritis. Excellent clinical outcomes after TKA have been widely recognized, but the influence of psychiatric problems on them has not been focused on until quite recently. This study aimed to assess the influence of psychiatric problems on clinical outcomes after TKA in Japanese patients using two assessment scales developed in Japan because the Japanese cultural lifestyle is specifically characterized by bending to the floor and standing up. Methods: Clinical outcomes and psychiatric problems were evaluated using the Japanese Knee Osteoarthritis Measure (JKOM) and Brief Scale for Psychiatric Problems in Orthopaedic Patients (BS-POP), respectively. A total of 115 TKA patients were evaluated preoperatively and at 3, 6, and 12 months after TKA. The patients were classified into four groups (groups A-D) based on the BS-POP score. The JKOM scores were then compared between the two groups (groups A and D) with the worst and least psychiatric problems. The JKOM improvement rate between pre- and postoperative status in both groups A and D was also calculated. Results: The total JKOM score was significantly poorer in group A than in group D preoperatively and at 3, 6, and 12 months after TKA. The improvement rate showed no significant difference between groups A and D. Conclusion: Psychiatric problems influence both the poorer post- and preoperative clinical outcomes. However, a similar improvement rate in both groups A and D has indicated that TKA can be an effective treatment even for patients with psychiatric problems.

THE FOKAS-LENELLS EQUATION ON THE FINITE INTERVAL

Using the Fokas unified method, we consider the initial boundary value problem for the Fokas-Lenells equation on the finite interval. We present that the Neumann boundary data can be explicitly expressed by Dirichlet boundary conditions prescribed, and extend the idea of the linearizable boundary conditions for equations on the half line to Pokas-Lenells equation on the finite interval.

FREE BOUNDARY VALUE PROBLEM OF ONE DIMENSIONAL TWO-PHASE LIQUID-GAS MODEL

In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions whenβ∈ （0, 1）, which have improved the result of Evje and Karlsen, and we obtain the regularity of the solutions by energy method.

Resource Planning and Allocation Problem Under Uncertain Environment

This paper generalizes the classic resource allocation problem to the resource planning and allocation problem, in which the resource itself is a decision variable and the cost of each activity is uncertain when the resource is determined. The authors formulate this problem as a two-stage stochastic programming. The authors first propose an efficient algorithm for the case with finite states. Then, a sudgradient method is proposed for the general case and it is shown that the simple algorithm for the unique state case can be used to compute the subgradient of the objective function. Numerical experiments are conducted to show the effectiveness of the model.

Cuckoo search with varied scaling factor

Cuckoo search （CS）, inspired by the obligate brood parasitic behavior of some cuckoo species, iteratively uses L6vy flights random walk （LFRW） and biased/selective random walk （BSRW） to search for new solutions. In this study, we seek a simple strategy to set the scaling factor in LFRW, which can vary the scaling factor to achieve better performance. However, choosing the best scaling factor for each problem is intractable. Thus, we propose a varied scal- ing factor （VSF） strategy that samples a value from the range [0,1] uniformly at random for each iteration. In addition, we integrate the VSF strategy into several advanced CS vari- ants. Extensive experiments are conducted on three groups of benchmark functions including 18 common test functions, 25 functions proposed in CEC 2005, and 28 functions intro- duced in CEC 2013. Experimental results demonstrate the ef- fectiveness of the VSF strategy.

A CASCADIC MULTIGRID ALGORITHM FOR COMPUTING THE FIEDLER VECTOR OF GRAPH LAPLACIANS

In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalne. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.

STABLE SOLUTION OF TIME DOMAIN INTEGRAL EQUATION METHODS USING QUADRATIC B-SPLINE TEMPORAL BASIS FUNCTIONS

This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.

The Generalized Order Tensor Complementarity Problems

The main propose of this paper is devoted to study the solvability of the generalized order tensor complementarity problem.We define two problems:the generalized order tensor complementarity problem and the vertical tensor comple-mentarity problem and show that the former is equivalent to the latter.Using the degree theory,we present a comprehensive analysis of existence,uniqueness and stability of the solution set of a given generalized order tensor complementarity problem.

Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials

The localized method of fundamental solutions(LMFS)is a relatively new meshless boundary collocation method.In the LMFS,the global MFS approxima-tion which is expensive to evaluate is replaced by local MFS formulation defined in a set of overlapping subdomains.The LMFS algorithm therefore converts differential equations into sparse rather than dense matrices which are much cheaper to calcu-late.This paper makes thefirst attempt to apply the LMFS,in conjunction with a domain-decomposition technique,for the numerical solution of steady-state heat con-duction problems in two-dimensional(2D)anisotropic layered materials.Here,the layered material is decomposed into several subdomains along the layer-layer inter-faces,and in each of the subdomains,the solution is approximated by using the LMFS expansion.On the subdomain interface,compatibility of temperatures and heatfluxes are imposed.Preliminary numerical experiments illustrate that the proposed domain-decomposition LMFS algorithm is accurate,stable and computationally efficient for the numerical solution of large-scale multi-layered materials.

Solving the Perspective-Three-Point Problem Using Comprehensive Grobner Systems

A complete solution classification of the perspective-three-point(P3P) problem is given by using the Gr?bner basis method. The structure of the solution space of the polynomial system deduced by the P3P problem can be obtained by computing a comprehensive Gr?bner system. Combining with properties of the generalized discriminant sequences, the authors give the explicit conditions to determine the number of distinct real positive solutions of the P3P problem. Several examples are provided to illustrate the effectiveness of the proposed conditions.

Painlevé-Kuratowski Convergences of the Solution Sets for Perturbed Vector Equilibrium Problems without Monotonicity

In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the Painlev^-Kuratowski Convergence of the weak efficient solution sets and efficient solution sets for the perturbed vector equilibrium problems with a sequence of mappings converging in real linear metric spaces. These results extend and improve some known results in the literature.

Efficient ID-based proxy multi-signature scheme secure in random oracle

Proxy signature schemes enable an entity to del- egate its signing rights to any other party, called proxy signer. As a variant of proxy signature primitive, proxy multi- signature allows a group of original signers to delegate their signing capabilities to a single proxy signer in such a way that the proxy signer can sign a message on behalf of the group of original signers. We propose a concrete ID-based proxy multi-signature scheme from bilinear pairings. The proposed scheme is existential unforgeable against adaptively chosen message and given ID-attack in random oracle model under the computational Diltie-Hellman （CDH） assumption. The fascinating property of new scheme is that the size of a proxy multi-signature is independent of the number of original sign- ers. Furthermore the proposed scheme is simple and com- putationally more efficient than other ID-based proxy multi- signature schemes.

THE APPLICATION OF RANDOM MATRICES IN MATHEMATICAL PHYSICS

In this paper, we introduce the application of random matrices in mathe- matical physics including Riemann-Hilbert problem, nuclear physics, big data, image processing, compressed sensing and so on. We start with the Riemann- Hilbert problem and state the relation between the probability distribution of nontrivial zeros and the eigenvalues of the random matrices. Through the random matrices theory, we derive the distribution of Neutron width and prob- ability density between energy levels. In addition, the application of random matrices in quantum chromo dynamics and two dimensional Einstein gravity equations is also present in this paper.