Effects of heat treatment process on thin film alloy resistance and its stability

Alloy thin film for advanced pressure sensors was manufactured by means of ion-beam sputtering SiO2 insulation film and NiCr thin film on the 17-4PH stainless steel elastic substrate. The thin film resistance was respectively heat-treated by four processes. The effects on stability of thin film alloy resistance were investigated, and paramaters of heat treatment that make thin film resistance stable were obtained. The experimental result indicates that the most stable thin film resistance can be obtained when it is heat-treated under protection of SiO2 and N2 at 673 K for 1 h, and then kept at 473 K for 24 h. Pressure sensor chips of high precision for harsh environments can be manufactured by this process.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

THE APPROXIMATION PROBLEM ON THE CLOSED CONVEX CONE AND ITS NUMERICAL SOLUTION

In this paper, we study the approximation problem on the closed convex cone, and prove that there exists a unique solution of the approximation problem, then give the algorithm to compute the unique solution.

A new extension algorithm for cubic B-splines based on minimal strain energy

Extension of a B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC2 parameter to be zero and determining the second GC2 parameter by mini- mizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C2-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given.

Reductions to Korteweg-de Vries Soliton Hierarchy

基于宽松的对的 nonlinearization， Korteweg-de Vries (KdV ) soliton 层次被分解成 Gnite 维的 Hamiltonian 系统的一个家庭， whoseLiouville integrability 借助于椭圆形的坐标被证明。由在亢奋的椭圆形的曲线的 Riemann 表面上使用 Abel-Jacobicoordinates，产生 Hamiltonian 也播种著名计算机生产厂商他 KdV soliton 层次最终被简化为线性重叠，由 theAbel-Jacobi 变量表示了。

INFINITELY MANY SOLUTIONS FOR ELLIPTIC SYSTEMS WITH STRONGLY INDEFINITE VARIATIONAL STRUCTURE

Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces.

ON A CLASS OF INHOMOGENEOUS,ENERGY-CRITICAL,FOCUSING,NONLINEAR SCHRDINGER EQUATIONS

In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrōdinger equation： iаtu=-△u-k（x）｜u｜4/N-2u,N≥3. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in tile nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, invent. Math. 166, 645-675 （2006）], where only the radial case is considered in dimensions 3. 4. 5.

Designing Bézier surfaces minimizing the L^2-norm of the Gaussian curvature

In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.

Asymptotic Behavior of Global Solutions for Double Degenerate Nonlinear Parabolic Equation

In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.

Invariant subspaces and conditional Lie-Bcklund symmetries of inhomogeneous nonlinear difusion equations

The inhomogeneous nonlinear difusion equation is studied by invariant subspace and conditional Lie-Bcklund symmetry methods.It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary diferential equations,which is equivalent to a kind of higher-order conditional Lie-Bcklund symmetries of the equations.As a consequence,a number of new solutions to the inhomogeneous nonlinear difusion equations are constructed explicitly or reduced to solving fnite-dimensional dynamical systems.

A SINGULAR BIOECONOMIC MODEL WITH DIFFUSION AND TIME DELAY

这份报纸学习一个猎物食肉动物单个 bioeconomic 系统与预定延期和散开，它被微分代数学的方程描述。为没有散开的这个系统，在那里存在三分叉现象：Transcritical 分叉，奇特导致了分叉，和 Hopf 分叉。与微分方程描述的另外的生物系统相比，奇特仅仅导致了分叉在单个系统发生并且通常与人口的扩大连接。当散开是在场的时，积极平衡点在散开率的一些批评价值失去它的稳定性，这被显示出，周期的摆动由于时间延期的增加发生。而且，数字模拟说明结果和相关生物含意的有效性被讨论。

Estimates for the Tail Probability of the Supremum of a Random Walk with Independent Increments

The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with Osubexponential integrated distributions.A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments,whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.

Visualisation techniques to support public interpretation of future climate change and land-use choices:a case study from N-E Scotland

Mitigating and adapting to climate change includes a requirement to evaluate the role of future land uses in delivering robust integrated responses that are sensitive to local landscape contexts.In practice,this emphasises the need for community engagement,planning and inclusive decision-making.Community engagement may be potentially facilitated by the use of spatially explicit quantitative scenarios of landuse change in combination with interactive visualisation.This requires a coherent framework to integrate spatial data modelling,analytical capabilities and visualisation tools in a format that will also engage diverse public audiences.These challenges were explored with a case study of virtual landscapes from N-E Scotland that was used to test preferences for scenarios of future land use.Visualisations employed texture-based rendering rather than full photo-realistic rendering to facilitate interactivity and this provided additional scope for audiences to explore multiple future scenarios compared to the present landscape.Interactive voting in a virtual landscape theatre suggested preferences for visual diversity,good stewardship and perceived naturalness that should be considered in developing planned responses to change.Further investigation of preferences was conducted using interactive 3D features located within the landscape.Study findings are reviewed against objectives for inclusive engagement in the Digital Earth agenda and used to make further recommendations on the use of scenarios and visualisation tools.In particular,technical advances in user engagement need to be developed in conjunction with emerging good practice that addresses ethical,behavioural and inclusion issues so that the content is presented in as transparent and unbiased format as possible.

Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations

In this paper,the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions.It is shown that if the two-component nonlinear vector differential operator F=(F 1,F 2) with orders {k 1,k 2 } (k 1 ≥ k 2) preserves the invariant subspace W 1 n 1 × W 2 n 2 (n 1 ≥ n 2),then n 1 n 2 ≤ k 2,n 1 ≤ 2(k 1 + k 2) + 1,where W q n q is the space generated by solutions of a linear ordinary differential equation of order n q (q=1,2).Several examples including the (1+1)-dimensional diffusion system and Ito 's type,Drinfel'd-Sokolov-Wilson's type and Whitham-Broer-Kaup's type equations are presented to illustrate the result.Furthermore,the estimate of dimension for m-component nonlinear systems is also given.

Long Time L^1-behavior for the Incompressible Magneto-hydrodynamic Equations in a Half-space

The large time Ll-behavior of the strong solution （including the first and second order spacial derivatives） to the incompressible magneto-hydrodynamic （MHD） equations is given in a half-space. The main tool employed in this article is a new weighted estimate for the Stokes flow in L1（Rn＋）, such a study is of independent interest.

Existence of Solutions for the Critical Elliptic System with Inverse Square Potentials

Let Ω∈← 0 be an open bounded domain in RN （N 〉 3） and 2＊（s） = 2（N-8） =2（N-s）N-22. We consider the following elliptic system of two equations in where A, μ 〉 0 and α, β 〉 1 satisfy α ＋ β = 2＊（s）. Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions.