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 GC^2-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 GC^2 parameter to be zero and determining the second GC^2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C-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

Based on the nonlinearization of Lax pairs, the Korteweg-de Vries （KdV） soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Hamiltonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by the Abel-Jacobi variables.

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 diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.

A SINGULAR BIOECONOMIC MODEL WITH DIFFUSION AND TIME DELAY

This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena： Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.

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.

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.

Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations

In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （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.