Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds

In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

The enhanced volume source boundary point method for the calculation of acoustic radiation problem

The Volume Source Boundary Point Method (VSBPM) is greatly improved so that it will speed up the VSBPM's solution of the acoustic radiation problem caused by the vibrating body. The fundamental solution provided by Helmholtz equation is enforced in a weighted residual sense over a tetrahedron located on the normal line of the boundary node to replace the coefficient matrices of the system equation. Through the enhanced volume source boundary point analysis of various examples and the sound field of a vibrating rectangular box in a semi-anechoic chamber, it has revealed that the calculating speed of the EVSBPM is more than 10 times faster than that of the VSBPM while it works on the aspects of its calculating precision and stability, adaptation to geometric shape of vibrating body as well as its ability to overcome the non-uniqueness problem.

Position optimization of particular solution sources for distributed source boundary point method by volume velocity-matching

Choosing particular solution source and its position have great influence on accu- racy of sound field prediction in distributed source boundary point method. An optimization method for determining the position of particular solution sources is proposed to get high accu- racy prediction result. In this method, tripole is chosen as the particular solution. The upper limit frequency of calculation is predicted by setting 1% volume velocity relative error limit using vibration velocity of structure surface. Then, the optimal position of particular solution sources, in which the relative error of volume velocity is minimum, is determined within the range of upper limit frequency by searching algorithm using volume velocity matching. The transfer matrix between pressure and surface volume velocity is constructed in the optimal position. After that, the sound radiation of structure is calculated by the matrix. The results of numerical simulation show that the calculation error is significantly reduced by the proposed method. When there are vibration velocity measurement errors, the calculation errors can be controlled within 5% by the method.

EXISTENCE THEOREMS FOR A SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH IMPULSES

In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0＋ u（t） = f （t, u（t）, c D σ 0＋ u（t））, t ∈ [0, T ], u（0） = αu（η）, u（T ） = βu（η）, where 1 〈 δ 〈 2, 0 〈 σ 〈 1, α, β∈ R, η∈ （0, T ）, αη（1 -β） ＋ （1-α）（T βη） = 0 and c D δ 0＋ , c D σ 0＋ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results.

POSITIVE SOLUTIONS TO AN m-POINT BOUNDARY VALUE PROBLEM

The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.

Effects of Grain Boundary Characteristics on Its Capability to Trap Point Defects in Tungsten

Acoustic one-way manipulations have recently attracted significant attention due to the deep implications in many diverse fields such as biomedical imaging and treatment.However,the previous mechanisms of asymmetric manipulation of airborne sound need to use elaborate heavyweight structures and only work in certain frequency ranges.We propose a mechanism for designing an ultra-lightweight and optically transparent structure with asymmetric transmission property for normally incident plane waves.Instead of fabricating solids into complicated artificial structures with limited bandwidth and heavy weight,we simply use xenon to fill a spatial region of asymmetric shape which allows the incident plane wave to pass along one direction while reflecting the reversed wave regardless of frequency.We demonstrate both analytically and numerically its effectiveness of producing highly-asymmetric transmission within an ultra-broad band.Our design offers new possibility for the design of one-way devices and may have far-reaching impact on various scenarios such as noise control.

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.

Existence of solutions for fourth-order boundary value problem with parameter

This paper is a sequel to a previous paper （Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69（2）, 1364-1375 （2008）） in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.

Sequence Boundary:Its Significance in Stratigraphic Subdivision,Correlation and Classification

Sequence boundary is studied in detail in reference to the Permian Guadalupian Lopingian boundary, based on high resolution correlation of conodont zones. A conceptual synchronous stratigraphic boundary, corresponding to the age of the sequence boundary dated in the conformable portion of the sequence boundary, is defined as the sequence chronostratigraphic boundary (SCB). The sequence boundary is proved to be dual in nature in regards to tin-synchrony and diachroneity of stratigraphic boundaries. The merits of the sequence boundary in stratigraphic subdivision, correlation and classification are elucidated in comparison with the lithostratigraphic boundary, the biostratigraphic boundary and the traditional approach of the global stratotype section and point (GSSP ). By integrating the virtues of the sequence boundary and the GSSP, it is proposed that the GSSP should be established in the conformable portion of the related sequence boundary. The boundary established in light of this approach is defined as the best natural boundary. The analysis of the sequence boundary leads to the conclusion that sequence stratigraphy is a regional and transitional stratigraphic system between local lithostratigraphy and global chronostratigraphy. Therefore, a new tripartite stratigraphic classification scheme is tentatively proposed.

POSITIVE SOLUTIONS FOR SOME 1-DIMENSIONAL BOUNDARY VALUE PROBLEMS OF LAPLACE-TYPE

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.

Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.

RECONSTRUCTION STABILITY OF NEARFIELD ACOUSTIC HOLOGRAPHY

The distributed source boundary point method （DSBPM） is used as the spatial transform algorithm for realizing nearfield acoustic holography （NAH）, the sensitivity of the reconstructed solution to the measurement errors is analyzed, and the regularization method is proposed to stabilize the reconstruction process, control the influence of the measurement errors and get a better approximate solution. An oscillating sphere is investigated as a numerical example, the influence of the measurement errors on the reconstruction solution is demonstrated, and the feasibility and validity of the regularization method are validated. Key words： Acoustic holography Boundary point method Inverse problem Regularization

Quadrilaterals, extremal quasiconformal extensions and Hamilton sequences

The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.

Algorithm of Slub Yarn Parameter Measurement Based on Capacitive Sensors

A new algorithm of measurement slub yarn parameter was put forward to improve precision and efficient. The basic principal of measurement slub yarn by parallel-plate capacitor was introduced,and slub yarns were tested with a measurement system developed by ourselves. Time sequence for slub length and slub space can be got. And distributions of slub length,slub space and slub scaling factor can also be obtained. The agreement can be attained compared with those original settings. Some error was analyzed also. Consequently this system is effective,and can be adopted in practice.

Microstructural features of Mg-8%Sn alloy and its correlation with mechanical properties

The aim of this investigation is to establish a structure-property correlation of Mg-8%Sn alloys aged at different time interval.The alloy under the present investigation was aged at elevated(200℃)temperature for various holding period.Differently aged alloys show retention of intermetallic phases after ageing,but in different area fraction of the same with ageing time.Mechanical properties evaluation and corresponding microstructural characterizations were performed to correlate their strength and ductility properties with their microstructural features(i.e.,grain size,grain connectivity and the area fraction of intermetallic phases).

Radiation efects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition

The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and convective boundary condition are also taken into account.The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis.The resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity transformations.Numerical solutions have been obtained for the velocity,temperature and nanoparticle fraction profles.The influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.

STRESS RATE INTEGRAL EQUATIONS OF ELASTOPLASTICITY

The stress rate integral equations of elastoplasticity are deduced based on Ref. [1] by consistent methods. The point at which the stresses and/or displacements are calculated can be in the body or on the boundary, and in the plastic region or elastic one. The existence of the principal value integral in the plastic region is demonstrated strictly, and the theoretical basis is presented for the paticular solution method by unit initial stress fields. In the present method, programming is easy and general, and the numerical results are excellent.