Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.     

Pseudo-atoms, atoms and a Jordan type decomposition in effect algebras

The aim of this paper is to introduce and investigate the concept of pseudo-atoms of a real-valued function m defined on an effect algebra L; a few examples of pseudo-atoms and atoms are given in the context of null-additive, null-null-additive and pseudo-null-additive functions and also, some fundamental results for pseudo-atoms under the assumption of null-null-additivity are established. The notions of total variation |m|, positive variation m⁺ and negative variation m⁻ of a real-valued function m on L are studied elaborately and it is proved for a modular measure m (which is of bounded total variation) defined on a D-lattice L that, m is pseudo-atomic (or atomic) if and only if its total variation |m| is pseudo-atomic (or atomic). Finally, a Jordan type decomposition theorem for an extended real-valued function m of bounded total variation defined on an effect algebra L is proved and some properties on decomposed parts of m such as continuity from below, pseudo-atomicity (or atomicity) and being measure, are discussed. A characterization for the function m to be of bounded total variation is established here and used in proving above-mentioned Jordan type decomposition theorem.     

The Asymptotic Variance of the Continuous-Time Kernel Estimator with Applications to Bandwidth Selection

We derive simple expressions for the asymptotic variance of the kernel-density estimator of a stationary continuous-time process in one and d dimensions and relate convergence rates to sample path smoothness. Important applications include methods for selecting optimal smoothing parameters and construction of confidence bands for testing hypotheses about the density. In a simulation study the results are applied to bandwidth selection for discrete-time processes that can be modelled as continuous-time processes sampled at a high rate.     

Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes

We consider the problem of estimating the covariance of two diffusion-type processes when they are observed only at discrete times in a nonsynchronous manner. In our previous work in 2003, we proposed a new estimator which is free of any ‘synchronization’ processing of the original data and showed that it is consistent for the true covariance of the processes as the observation interval shrinks to zero; Hayashi and Yoshida (Bernoulli, 11, 359–379, 2005). This paper is its sequel. Specifically, it establishes asymptotic normality of the estimator in a general nonsynchronous sampling scheme.     

Dynamic properties of a body with discontinual mass variation

In this paper the procedure for the dynamic analysis of body separation is introduced. Based on the general laws of classical dynamics, the method for obtaining the velocity and the angular velocity of the remainder body during separation is developed. Due to the discontinual mass variation, the jump-like change of the velocity and the angular velocity of the body is evident. Various types of motion of the separated body are considered. Depending on the type of motion of the separated body the dynamic properties of the remainder body are obtained. As a special case the in-plane motion of the body before and after separation is considered. The theoretical considerations are applied for the separation analysis of a rotor (a shaft-disc system). The transient motion of the body after separation is investigated. To prove the correctness of the procedure suggested in the paper, the case when the mass and the moment of inertia of the separated body are infinitesimal is analyzed. The obtained differential equations are the same as those previously obtained.     

General Regular Variation of n-th Order and the 2nd Order Edgeworth Expansion of the Extreme Value Distribution （Ⅰ）

In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.     

The play operator on the rectifiable curves in a Hilbert space

The vector play operator is the solution operator of a class of evolution variational inequalities arising in continuum mechanics. For regular data, the existence of solutions is easily obtained from general results on maximal monotone operators. If the datum is a continuous function of bounded variation, then the existence of a weak solution is usually proved by means of a time discretization procedure. In this paper we give a short proof of the existence of the play operator on rectifiable curves making use of basic facts of measure theory. We also drop the separability assumptions usually made by other authors. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of thiophilic chromatography to deplete serum immunoglobulins in sample preparation for bidimensional electrophoresis

Serum is a typical sample for non-invasive studies in clinical research. Its proteome characterization is challenging, since requires extensive protein depletion. Methods used nowadays for removal of high-abundance proteins are expensive or show quite often a low loading capacity, which has strong repercussions on the number of samples and replicates per analysis.In order to deplete immunoglobulins (Igs) and albumin (HSA) from 1 mL serum samples, we have developed a protocol based on a combination of thiophilic chromatography, not previously used in clinical proteomics, and a HSA-specific resin. Ig/HSA-depleted samples, immunoglobulinome and albuminone were analyzed by 2-DE. Thiophilic chromatography, coupled with HSA-depletion, allows a good 2-DE resolution as well as the visualization of new spots. Moreover, it yields enough protein to evaluate technical variability and facilitate subsequent protein identification. To validate the protocol, we carried out a preliminary comparative study between triplicate Igs/HSA-depleted serum samples from healthy control individuals and recently diagnosed/untreated rheumatoid arthritis (RA) patients. RA patients showed several acute phase proteins, as well as additional serum proteins, differentially and significantly regulated.Therefore, thiophilic chromatography can be used as an efficient and economical method in 2-DE to deplete immunoglobulins from large human serum samples before a more extensive fractioning.     

基于强度传输方程的相位检索

为了从直接测量的强度图像中计算出相位信息,研究了基于强度传输方程的相位检索技术.设计了一个实用的相位检索系统,包含经典傅里叶相位检索和基于整体变分的相位检索算法.通过测量聚焦平面和前后散焦平面光波场的空间强度,求解二阶微分方程得到相位.与迭代相位检索技术相比克服了其迭代不确定性、收敛速度慢等缺点.实验表明,利用强度传输...     

Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

We study a family of generalized slope limiters in two dimensions for Runge–Kutta discontinuous Galerkin (RKDG) solutions of advection-diffusion systems. We analyze the numerical behavior of these limiters applied to a pair of model problems, comparing the error of the approximate solutions, and discuss each limiter’s advantages and disadvantages. We then introduce a series of coupled p-enrichment schemes that may be used as standalone dynamic p-enrichment strategies, or may be augmented via any in the family of variable-in-p slope limiters presented.