Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods.     

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.     

LIMIT CYCLES FOR A CLASS OF NONPOLYNOMIAL PLANAR VECTOR FIELDS(II)

In this paper, the problem of limit cycles for a class of nonpolynomial planar vector felds is investigated. First, based on Liapunov method theory, we obtain some sufcient conditions for determining the origin as the critical point of such nonpolynomial planar vector felds to be the focus or center. Then, using Dulac criterion, we establish some sufcient conditions for the nonexistence of limit cycles of this nonpolynomial planar vector felds. And then, according to Hopf bifurcation theory, we analyze some sufcient conditions for bifurcating limit cycles from the origin. Finally, by transforming the nonpolynomial planar vector felds into the generalized Li′enard planar vector felds, we discuss the existence, uniqueness and stability of limit cycles for the former and latter planar vector felds. Some examples are also given to illustrate the efectiveness of our theoretical results.     

Reflected SPDEs Driven by Fractional Noises

In this paper,we study the stochastic partial differential equation with two reflecting smooth walls h^1 and h^2,driven by a fractional noise,which is fractional in time and white in space.The large deviation principle for the law of the solution to this equation,will be established through developing a classical method.Furthermore,we obtain the H?lder continuity of the solution.     

Maximum Likelihood Estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.     

立体几何中的活跃分子——直角四面体

三条侧棱两两相互垂直的四面体是一种特殊的四面体,我们称之为直角四面体,它具有以下性质:(1)任何一条侧棱垂直另两个侧棱构成的平面;(2)三个侧面两两垂直;(3)顶点在底面上的射影是底面三角形的垂心等,立体几何中很重要的概念和定理.都能从这个直角四正面体中衍生,因此深入研究直角四面体,对于把握空间图形中直线和平面的关系,尤为重要.下面利用直角四面体的性质简解两道商考题.……     

Time variant multi-objective linear fractional interval-valued transportation problem

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.     

Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.     

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Peridynamics via finite element analysis

Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.     

The Cauchy problem for ut=Δu+|∇u|

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained.     

含有批处理机的三机流水作业加工总长问题在某些情形下的强NP困难性

本文研究含有批处理机的三台机器流水作业加工总长问题在某些情形下的计算复杂性。在批处理机上同时加工的工件组成一个工件批，一个工件批的所有工件同时开始、同时结束。当批处理机的容量有限时，我们证明了下列情形为强NP困难的：第一台机器是批处理机、其余两台机器是单机；第二台机器是单机、其余两台机器是批处理机；第三台机器是批处理机、其余两台机器是单机。     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Dynamical Spin Susceptibility in the t–J Model in the Superconducting Phase

Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

基于VAR风险指标的投资组合模糊优化

在二目标有价证券选择基础上 ,引入目前流行的风险指标 VAR,以收益率与风险损失为目标 ,将模糊概念运用于有价证券组合选择 ,按投资者给定的期望目标及容差 ,讨论了 S型隶属函数模型 .通过 VAR的给定 ,将投资者所能承受的最大损失锁定 ,更好地反映出投资者对目标值的取值意图 .依据深圳股票市场9只股票收益率数据 ,采用进化规划进行优化计算 ,并验证模型的有效性 .     

Strategic defense and attack for series and parallel reliability systems

A system of independent components is defended by a strategic defender and attacked by a strategic attacker. The reliability of each component depends on how strongly it is defended and attacked, and on the intensity of the contest. In a series system, the attacker benefits from a substitution effect since attacker benefits flow from attacking any of the components, while the defender needs to defend all components. Even for a series system, when the attacker is sufficiently disadvantaged with high attack inefficiencies, and the intensity of the contest is sufficiently high, the defender earns maximum utility and the attacker earns zero utility. The results for the defender (attacker) in a parallel system are equivalent to the results for the attacker (defender) in a series system. Hence, the defender benefits from the substitution effect in parallel systems. With budget constraints the ratio of the investments for each component, and the contest success function for each component, are the same as without budget constraints when replacing the system values for the defender and attacker with their respective budget constraints.     

Evolution of non-spreading Airy wavepackets in time dependent linear potentials

We report on the use of the algebraic methods to obtain the explicit form of the solution of the Schrödinger equation with a linear potential. We consider the case of the explicitly time dependent Hamiltonian and formulate the general conditions that allow for the solutions to be found that are expressed in terms of Airy functions, yielding non spreading wave packets. The relevant physical meaning of these solutions is analyzed and the examples of their applications are given. The role, played by the Airy transform and its relevance to the problems, involving linear potentials is discussed. Eventually, we present a thorough discussion on the analogy between the Airy and the Gauss-Weierstrass transform, often employed in the solutions of the heat type equations.