具有p-Laplace算子的一类高阶奇异边值问题解的存在性

本文研究下面问题的正解其中Φp(s)=|s|p-2s,p>1．f在点x(i)=0,i=0,．．．,n-2可能是奇异的．证明建立在Leray-Schauder拓扑度和Vitali收敛定理的基础上．     

A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.     

Evaluation of dissociation constants of ammonium ion in aqueous lithium perchlorate and lithium chloride-sodium chloride mixed solutions

The Pitzer approach has been applied to the evaluation of dissociation constants of ammonium ion in lithium perchlorate and lithium chloride-sodium chloride mixed solutions at 25°C. The calculated values showed good agreement with the observed values, provided all the higher-order interaction terms ('s and 's) concerned were introduced. The unknown (NH₄LiClO₄) value was determined from the isopiestic measurements of NH₄ClO₄–LiClO₄ mixed solutions. Parameters in the Pitzer formalism for ammonia-ion interactions involved in LiCl and NaCl media were determined by use of the activity coefficients of ammonia measured in LiCl–NaCl mixed solutions by a transpiration method.     

High resolution instrumentation system for fibre-Bragg grating aerospace sensors

A passive technique for high-resolution detection of the wavelength of peak reflection from fibre Bragg grating (FBG) sensors is presented. The approach, based on a de-convolution of the FBG spectrum and the spectrometer resolution, essentially overcomes the low spectral resolution (≈0.1 nm) associated with commercial spectrometers employing CCD detection. The performance of two algorithms, the Centroid Detection algorithm (CDA) and the least squares method (LSQ), are compared. The LSQ algorithm offers resolution enhancement of at least two orders of magnitude and is shown to be independent of the FBG intensity and bandwidth over a broad range.     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.     

Q变形非简谐振子广义奇偶相干态的高阶压缩特性

给出了Q变形的非简谐振子广义奇偶相干态的完备性证明,并且研究了它们的高阶压缩特性.结果表明,它们可组成一个完备的Hilbert空间,且均可呈现奇数阶压缩效应.     

Effects of phonon-phonon coupling on low-lying states in neutron-rich Sn isotopes

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.     

Family of instantons of the Kraichnan model with a frozen velocity field

We find the family of instantons of the Kraichnan model with a frozen velocity field. Using these instantons, we investigate the asymptotic behavior of higher orders of the perturbation theory series constructed for the response function. We demonstrate that although the number of diagrams increases factorially with the degree of the perturbation series term, the perturbation series itself has a finite and sometimes even infinite convergence radius. We thus disprove the commonly accepted view that the type of series convergence can be determined by estimating the number of diagrams in higher orders of the perturbation theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 2, pp. 200–213, February, 2009.     

Analytical approaches to the delta-Eddington model of the radiative transfer through vertically inhomogeneous optical depths

Analytical approaches have been developed for one-dimensional monochromatic delta-Eddington radiative transfer equation through a vertically inhomogeneous medium. They are based on the solution of the Riccati equation that arises from the decoupling of the two-stream radiances, and seek to approximate the exponent functions in the solution as opposed to finding the solution as a whole. Depending on the case, Green–Liouville approximation or other techniques presented in this paper are utilized for finding these exponents. Though developed for atmospheric radiative transfer problems applicable to the global climate change modelling, and for non-invasive medical applications on tissue–light interactions, the techniques considered here are quiet general in nature. Hence, they can also be useful in other boundary value problems of the diffusion type that involve linear second order ordinary differential equations with variable coefficients.