BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u＂ = ｜u｜^p

In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.     

On existence and stability in the theory of swelling porous elastic soils

The aim of this paper is to introduce a new functional in thestudy of swelling porous elastic soils saturated by a fluid.This new functional is a useful tool; it allows us to provethe existence of solutions in the case of a compressible fluid.We also prove the stability of solutions and the exponentialdecay in the case of an incompressible fluid. We study as wellthe continuous dependence with respect to the initial time.     

Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as

(a) uniqueness of invariant measure for the signal,

(b) uniqueness of invariant measure for the pair (signal, filter),

(c) a finite memory property of the filter,

(d) a property of finite time dependence between the signal and observation σ fields and

(e) asymptotic stability of the filter.

Previous works on the asymptotic stability of the filter for a variety of filtering models then identify a rich class of filtering problems for which the above equivalent properties hold.     

Solid phase extraction for analysis of biogenic carbonates by electrothermal vaporization inductively coupled plasma mass spectrometry (ETV-ICP-MS): an investigation of rare earth element signatures in otolith microchemistry

Uptake of trace elements into fish otoliths is governed by several factors such as life histories and environment in addition to stock and species differences. In an attempt to elucidate the elemental signatures of rare earth elements (REEs) in otoliths, a solid phase extraction (SPE) protocol was used in combination with electrothermal vaporization (ETV) as a sample introduction procedure for the determinations by inductively coupled plasma quadrupole mass spectrometry (ICP-MS). Effects of various parameters, such as carrier gas flow rate, atomization temperature and chemical modification, were examined for optimization of the conditions by ETV-ICP-MS. Atomization was achieved at 2800 °C. Lower temperatures (i.e. 2600 °C) resulted in severe memory problems due to incomplete atomization. Palladium was used as a chemical modifier. It was found that an increase in Pd concentration up to 0.5 μg in the injection volume (70 μl) led up to four-fold enhancement in the integrated signals. This phenomenon is attributed to the carrier effect of Pd rather than the stabilization since no significant losses were observed for high temperature drying around 700 °C even in the absence of Pd. Preconcentration was performed on-line at pH 5 by using a mini-column of Toyopearl AF-Chelate 650M chelating resin, which also eliminated the calcium matrix of otolith solutions. After preconcentration of 6.4 ml of solution, the concentrate was collected in 0.65 ml of 0.5% (v/v) HNO₃ in autosampler cups, and then analyzed by ETV-ICP-MS. The method was validated with the analysis of a fish otolith certified reference material (CRM) of emperor snapper, and then applied to samples. Results obtained from otoliths of fish captured in the same habitat indicated that otolith rare earth element concentrations are more dependent on environmental conditions of the habitat than on species differences.     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

Convergence of Computational Methods and Stability of Self-Balanced Stresses under Shrinkage of Spherical Inclusions of a Damageable Material

Some iterative methods for calculating self-balanced stresses under shrinkage of a ball inclusion enclosed in a spherical matrix of a physically nonlinear damageable material. The stability of this system was studied using methods of catastrophe theory. It has been established that the beginning of divergence of the proposed iterative processes coincides with the moment of transition of the system to an unstable position of equilibrium.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

蓝光相变光盘的多层膜结构设计

为了使光盘获得优良的记录／读出性能并能够长期稳定地使用，必须优化设计相变光盘的多层膜结构。采用自行设计的模拟分析相变光盘读出过程设计软件，从光学角度出发模拟计算了蓝光(405nm)相变光盘的膜层结构，研究了多层膜系的反射率和反射率对比度等光学参量与各层膜厚度和槽深的关系。研究得出的最佳多层膜结构为：下介电层／记录层／上介电层／反射层的厚度对于台记录为100nm／10nm／25nm，／60nm，而对于槽记录则为140nm／15nm／30nm，／60nm，槽深为50nm。模拟计算结果对于将来高密度蓝光相变光盘的制备具有一定的指导意义。     

时间分辨红外发射光谱法对自由基反应的研究

在过去的 15年中 ,傅立叶变换红外发射光谱法广泛应用于研究气相自由基反应 .Sloan首先研究了O(1D)的反应 ,随后Leone和Hancock研究了O(3 P)的反应 .此后 ,孔繁敖和朱起鹤等研究了小自由基 ,包括CH、CH2 、CH3 、C2 H3 、C2 H5、C2 H、C3 H3 和C3 H5与O2 、NO、N2 O、NO2 等分子的反应。在红外光谱中观察到各个反应的初生产物和初步反应通道 ,和从头算的理论研究结合起来 ,这些反应的机理已基本弄清 .