Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem. We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential ill-posedness, the stability estimate obtained is optimal. AMS 2000 Mathematics Subject Classification. Primary 35R30, Secondary 35B60, 33C90     

The Kμ-Transformation on McBride's Spaces of Generalized Functions

In this paper we define the K_μ- transformation on certain spaces of generalized functions introduced by A.C. McBride by employing the kernel method. we also establish relations between the generalized K_μ- transformation and certain fractional integral operators.     

A new identity for Parseval frames

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

     

Random Flights in Higher Spaces

We consider in this paper random flights in ℝ ^d performed by a particle changing direction of motion at Poisson times. Directions are uniformly distributed on hyperspheres S ₁ ^d . We obtain the conditional characteristic function of the position of the particle after n changes of direction. From this characteristic function we extract the conditional distributions in terms of (n+1)−fold integrals of products of Bessel functions. These integrals can be worked out in simple terms for spaces of dimension d=2 and d=4. In these two cases also the unconditional distribution is determined in explicit form. Some distributions connected with random flights in ℝ³ are discussed and in some special cases are analyzed in full detail. We point out that a strict connection between these types of motions with infinite directions and the equation of damped waves holds only for d=2. Related motions with random velocity in spaces of lower dimension are analyzed and their distributions derived.     

Electron acceleration using two crossed Bessel beams in vacuum

The direct acceleration of electrons by using two crossed linearly polarized Bessel beams with equal frequency and amplitude in vacuum is studied and compared with the case of single linearly polarized Bessel beam. It is found that two zeroth- and first-order Bessel beams with π-rad phase difference have a nonvanishing longitudinal electric field on the z-axis, which can be maximized under certain conditions and used to accelerate electrons. Two crossed zeroth- and first-order Bessel beams have a larger maximum longitudinal electric field on the z-axis than that of a single first-order Bessel beam, and are suited for laser electron acceleration.     

Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions: II. The Heterogeneous Case

We consider the problem of discriminating between two independent multivariate normal populations, N_p(μ₁, Σ₁) and N_p(μ₂, Σ₂), having distinct mean vectors μ₁ and μ₂ and distinct covariance matrices Σ₁ and Σ₂. The parameters μ₁, μ₂, Σ₁, and Σ₂ are unknown and are estimated by means of independent random training samples from each population. We derive a stochastic representation for the exact distribution of the “plug-in” quadratic discriminant function for classifying a new observation between the two populations. The stochastic representation involves only the classical standard normal, chi-square, and F distributions and is easily implemented for simulation purposes. Using Monte Carlo simulation of the stochastic representation we provide applications to the estimation of misclassification probabilities for the well-known iris data studied by Fisher (Ann. Eugen.7 (1936), 179–188); a data set on corporate financial ratios provided by Johnson and Wichern (Applied Multivariate Statistical Analysis, 4th ed., Prentice–Hall, Englewood Cliffs, NJ, 1998); and a data set analyzed by Reaven and Miller (Diabetologia16 (1979), 17–24) in a classification of diabetic status.     

复合多层介质在可变温度和集中荷载作用下的位移和应力

研究了多层介质中的热弹性位移和应力.多层介质具有不同厚度,各层又具有不同的弹性性质,最上层表面上作用热荷载和集中荷载.假设各层分别是均匀、各向同性弹性材料,各层相关的位移分量是轴对称的,对称轴为各层表面的垂线.因此,各层应力函数满足无体力的单一方程.利用积分变换法求解了该方程,对由任意多个层数构造的多层介质,给出了其相应层数基础热弹性位移和应力的解析表达式.并对3层介质和4层介质时的数值结果进行了比较.     

环上半线性椭圆型方程正解的存在性和唯一性

本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件.     

Functional inequalities involving special functions II

This paper is motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen. We prove a chain of inequalities for hypergeometric functions, generalized and normalized Bessel functions, Kummer functions and for some general power series. Some particular cases and refinements are given.