Weighted integral inequalities for conjugate A-harmonic tensors

We first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in L^s(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings.     

Various methods of reconstruction of a cavity in an orthotropic layer

Direct and inverse problems of oscillations of an anisotropic layer with a cylindrical cavity of an arbitrary cross-sectional shape under the action of a load applied to the layer surface are considered. An asymptotic approach to solving these problems with cavities of small relative sizes is proposed. Numerical results of solving direct and inverse problems are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 181–189, May–June, 2009.     

A nonconvex dissipative system and its applications (II)

This paper presents exact solutions in terms of implicit functions and hyperbolic functions to a nonconvex dissipative system, controlled by a Duffing–van der Pol nonlinear equation with a fifth-order nonlinearity. Applications to the complex Ginzburg–Landau equation are illustrated and several classes of uniformly translating solutions are obtained accordingly. Part of the work was announced at the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering, Virginia Tech. University, Blacksburg, Virginia, August 15–17, 2005. This work is supported by NSF Grant CCF–0514768.     

Inverse coefficient problem for a wave equation in a bounded domain

The nonlinear inverse problem for a wave equation is investigated in a three-dimensional bounded domain subject to the Dirichlet boundary condition. Given a family of solutions to the equation defined on a closed surface within the original domain, it is required to reconstruct the coefficient determining the velocity of sound in the medium. The solutions used for this purpose correspond to the acoustic medium perturbations localized in the neighborhood of a certain closed surface. The inverse problem is reduced to a linear integral equation of the first kind, and the uniqueness of the solution to this equation is established. Numerical results are presented.     

Center and isochronous center problems for quasi analytic systems

This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved. This research is partially supported by the National Natural Science Foundation of China (10671179 and 10771196) and the Natural Science Foundation of Yunnan Province (2005A0092M)     

Axially symmetric cavitation flow at small cavitation numbers

A method for computing the drag coefficient of a body in an axially symmetric, steady-state cavitation flow is presented. A ‘vortex ring’ distribution along the wetted body surface and along the cavity interface is assumed. Since the location of the cavitation interface is unknown a priori, an iterative procedure is used, where, for the first stage, an arbitrary cavitation interface is assumed. The flow field is then solved, and by an iterative process the location of the cavitation interface is corrected. Even though the flow field is governed by the linear Laplace equation, strong non-linearity resulting from the kinematic boundary conditions appears along the cavitation interface. An improved numerical scheme for solving the dual Fredholm integral equations is obtained by formulating high-order approximations to the singular integrals in order to reduce the matrix dimensions. Good agreement is found between the numerical results of the present work, experimental results and other solutions.     

Subset selection for the least probable multinomial cell

Summary An inverse sampling procedureR is proposed for selecting a randomsize subset which contains the least probable cell (i.e., the cell with the smallest cell probabilities) from a multinomial distribution withk cells. Type 2-Dirichlet integrals are used (i) to express the probability of a correct selection in terms of integrals with parameters only in the limits of integration, (ii) to prove that the least favorable configuration underR is the so-called slippage configuration withk equal cell probabilities, and (iii) to express exactly the expectation of the total number of observations required and the expectation of the subset size under the procedureR.     

Determination of the H2-H2 potential from absolute integral cross section measurements

Absolute integral cross sections have been measured for n-H₂-n-H₂ at primary particle velocities between 1270 and 9650 m/sec with a 77 °K target. The number density of target particles was determined with an accuracy of 1% by the method of dynamic expansion. The velocity dependence of the integral cross section was also measured for the isotopic systems n-D₂-n-H₂ and n-D₂-n-D₂ at primary beam velocities between 280 and 1170 m/sec with a 15 °K target. All available integral cross section data are compared with literature potentials. A new potential is proposed, which exhibits one bound state for H₂-H₂.Dedicated to Professor H. Hartmann on his 60^th birthday.     

Boundary element formulation for geometrically nonlinear elastostatics

The basic integral relationships for geometrically nonlinear problems are presented. Using the boundary element method they allow for the solution of a new range of problems in geometrically nonlinear elastostatics.