ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS

We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A（A）, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.     

A compact local one‐dimensional scheme for solving a 3D N‐carrier system with Neumann boundary conditions

We consider a mathematical model for thermal analysis in a 3D N‐carrier system with Neumann boundary conditions, which extends the concept of the well‐known parabolic two‐step model for micro heat transfer. To solve numerically the complex system, we first reduce 3D equations in the model to a succession of 1D equations by using the local one‐dimensional (LOD) method. The obtained 1D equations are then solved using a fourth‐order compact finite difference scheme for the interior points and a second‐order combined compact finite difference scheme for the points next to the boundary, so that the Neumann boundary condition can be applied directly without discretizing. By using matrix analysis, the compact LOD scheme is shown to be unconditionally stable. The accuracy of the solution is tested using two numerical examples. Results show that the solutions obtained by the compact LOD finite difference scheme are more accurate than those obtained by a Crank‐Nicholson LOD scheme, and the convergence rate with respect to spatial variables is about 2.6. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

THE EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF SECOND ORDER DIFFERENTIAL EQUATIONS

In this paper, a fixed point theorem in C1[0,1] space is established using the properties of the fixed point index. This theorem is applied to prove the existence of positive solution to the boundary value problems of second order differential equations.     

The dynamics of an impulsive delay predator–prey model with stage structure and Beddington-type functional response

In this paper, an impulsive delay predator–prey model with stage structure and Beddington-type functional response is established. By using the discrete dynamical system determined by the stroboscopic map, we obtain the existence and global attractivity of the predator-extinction periodic solution. By use of the theory on delay and impulsive differential equation, we study the permanence of the system. Finally, an example is given to show the effectiveness of the main results.     

The dynamics of an impulsive one-prey multi-predators system with delay and Holling-type II functional response

Considering the effects of changing environments, delays, impulses and functional response, a one-prey multi-predators system is established in this paper. Using comparison theorem and some analysis techniques, sufficient conditions ensuring the global attractivity of the prey-extinction positive periodic solution and the permanence of the system are obtained. Finally, examples and numerical simulations are given to show the effectiveness of the main results.     

Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder

Analytical study for electromagnetothermoelastic behaviors of a hollow cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads are presented. For the case that the electric, magnetic, thermal and mechanical properties of the material obey an identical power law in the radial direction, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow cylinder are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β and applying suitable electric, thermal and mechanical loads can optimize the FGPM hollow cylindrical structures. This will be of particular importance in modern engineering design.     

Nonsmooth version of Fountain theorem and its application to a Dirichlet-type differential inclusion problem

In this paper we establish a nonsmooth version of Fountain theorem by adopting the framework of nonsmooth analysis theory, which is a generalization of Theorem 3.6 of Willem (1996) [2]. Then we present an application of this theorem to a Dirichlet-type differential inclusion problem.     

Compositional analysis of a polymer-induced liquid-precursor (PILP) amorphous CaCO3 phase

Amorphous calcium carbonate (ACC) has been of keen interest in the biomimetics field because of recent evidence which suggests it plays an important role in biomineralization. In this report, an in vitro model system is used to examine the composition of an amorphous phase generated by polyanionic process-directing agents, such as the sodium salt of polyaspartic acid (Pasp), which is considered a simple mimic to the proteins associated with calcific biominerals. This additive leads to the formation of a highly hydrated, amorphous mineral precursor to calcium carbonate (CaCO₃), referred to as a polymer-induced liquid-precursor (PILP) phase. The precursor phase was collected by centrifugation, and the quantity of precursor phase and the water content were determined. It was found that Pasp promotes and stabilizes the amorphous precursor, which has a composition that steadily changes with time as the polymer and water are excluded. Elemental analysis was used to investigate the role of the polymer in influencing the calcium/carbonate ratio, the water content, and the amount of precursor phase. Raman and ATR-FTIR spectroscopy were used to compare the compositions of the precursor phases generated with different polymeric concentrations. The role of Pasp in generating and stabilizing the ACC precursor phase is discussed.     

正、负离子表面活性剂混合体系溶致液晶生成的相行为

研究了烷基(C8,C12,C14)三甲基溴化铵、烷基(C12,C14)溴化吡啶与烷基(C8,C12)硫酸钠混合体系溶致液晶形成的条件与结构的变化.在高浓度的水溶液中,随着正、负离子表面活性剂摩尔比接近于1,液晶结构由六角相过渡为层状相.表面活性剂非极性链长改变,对相行为影响显著,短碳链的正、负离子表面活性剂混合体系,在等摩尔比时,体系为层状液晶或立方液晶为主,夹杂少许沉淀.随碳链增长,两类表面活性剂间的静电吸引效果表现为生成沉淀的摩尔比例范围变宽,沉淀量增多,共存的液晶相减少,甚至消失.若只改变正离子的极性头基,季胺盐比吡啶盐与烷基硫酸盐的作用要强,形成不溶物的混合摩尔比例范围更宽.     

Preparation and properties of GaFeO<Subscript>3</Subscript> thin films grown at various oxygen pressures by pulsed laser deposition

We report the results of an analytical investigation on the bronze alloys of the Porta del Paradiso by Lorenzo Ghiberti using a portable X-ray fluorescence instrument. The study was carried out on five panels of the bronze artwork. It provided information on the artist’s selection of the sculptural alloys and on some manufacturing details of interest for understanding the development of the art foundry during the early Renaissance. PACS 81.05.Bx; 81.70.Jb; 82.80.Ej