About contingent epiderivatives

In this paper we analyze some questions concerning the contingent epiderivative. When the ordering cone is not necessarily pointed we introduce the notion of family of contingent epiderivatives. We also investigate the relationship between the contingent derivative and the generalized epiderivative. Furthermore, we give existence theorems with respect to Daniell cones. As a particular case, we study set-valued maps that take values in Rn.     

High-pressure and high-temperature generation using diamond/sic composite anvils prepared with hot isostatic pressing

Using a hot isostatic pressing (HIP) technique, we synthesized diamond/SiC composites from diamond and Si powders. At an HIP condition of 1450 °C and 100 MPa, a pressure much lower than that of the diamond stability field, diamond powders react with molten Si to form well-sintered diamond/SiC composites. Cubes of the composites with 15 mm edge length were thereby fabricated, and an application to the second stage anvils in a Kawai-type high-pressure apparatus was attempted. A hybrid anvils system using four cubes of the composites and four of the conventional WC was introduced and heating experiments up to 1600 °C became possible. Because the diamond/SiC composites are transparent to X-rays, the present system is applicable not only to diffraction studies but also to radiographic studies that need a larger window for an X-ray image.     

The first,the biggest,and other such considerations

We investigate the relation between the underlying dynamics of randomly evolv ing systems and the extrema statistics for such systems. Independent processes, Fokker-Planck processes and Lévy processes are considered.     

高温高压下文石和方解石的拉曼光谱研究

利用金刚石压腔结合拉曼光谱分析技术,研究了文石在18～388 ℃,71～2 014 MPa,以及方解石在19～351 ℃,96～1 823 MPa条件下的拉曼光谱特征,并得到文石和方解石的拉曼位移与温度、 压力三者之间的关系式。研究结果表明,文石和方解石的拉曼位移随温度压力的变化规律相似,都随压力升高向高频移动,除文石的704 cm-1外均随温度升高向低频移动。二者的晶格振动ν_i/T值均大于[CO₃]基团内振动的值,说明CaO₆八面体的热膨胀性大于[CO₃]基团的热膨胀性。二者的对称伸缩振动ν/T及ν/P值不同,由于该振动拉曼位移和C—O键的键长有关,方解石的C—O键的热膨胀性比文石小而可压缩性比文石大。另外升温升压过程中文石和方解石可以相互转化,伴随该过程发生的[CO₃]基团旋转变形等动力学因素也可以造成二者ν_i/T和ν_i/P值差异。     

Effect of microencapsulation using soy protein isolate and gum arabic as wall material on red raspberry anthocyanin stability,characterization, and simulated gastrointestinal conditions

This study involves microencapsulation of anthocyanin extract (AC) from red raspberry using a freeze drying technique involving ultrasonication of soy protein isolate (SPI), gum arabic (AG), and their combination. Analyses included microcapsule properties, encapsulation efficiency, antioxidant capacity using the DPPH assay, Fourier-transform infrared spectroscopy (FTIR), color, thermal stability, stability during storage, morphology, and simulated gastrointestinal conditions. Encapsulation efficiency (EE) ranged from 93.05% to 98.87% for all microcapsules. The morphology of microcapsules by scanning electron microscopy (SEM) indicated a broken glass shape, with mean size of microcapsules ranging from 21.07 ± 2.71 μm to 48.19 ± 2.33 μm using Mastersizer analyzer. A good relationship obtained between zeta potential (ZP) and FTIR spectrum indicated that there is a chemical cross linking interaction between wall material and core material. All microcapsules enhanced the thermal stability of AC in the temperature range 80–114 °C. Furthermore, AC retention (up to 48%) during storage at 37 °C for 60 days revealed that treatment H combination of SPI and AG was best. In addition, SPI and AG combination presented good release behavior under simulated gastrointestinal conditions compared with unencapsulated anthocyanin.     

A note on the compactness of the index set in convex optimization. Application to metric regularity

We consider the linear quadratic optimal control problem in the infinite time horizon case for a class of discrete-time systems controlled by a continuous inputs. We show that, under certain hypothesis, the Hilbert uniqueness method can be used to determine the optimal control.     

On expansions of functions of two variables in mixed Fourier-Jacobi series and their application for estimation of errors of cubature formulas

Some problems of expansion of functions of two variables in mixed Fourier-Jacobi series are discussed. In particular, estimates of the convergence rate of these series on classes of functions of two variables characterized by generalized moduli of continuity are given. Applications of these results and estimation of residues of some Chebyshev-type mixed cubature formulas are discussed.     

Representation of the Lagrange Multipliers for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two

Necessary conditions are derived for optimal control problems subject to index-2 differential-algebraic equations, pure state constraints, and mixed control-state constraints. Differential-algebraic equations are composite systems of differential equations and algebraic equations, which arise frequently in practical applications. The structure of the optimal control problem under consideration is exploited and special emphasis is laid on the representation of the Lagrange multipliers resulting from the necessary conditions for infinite optimization problems.The author thanks the referees for careful reading and helpful suggestions and comments.     

Smooth and Nonsmooth Lipschitz Controls for a Class of Vector Differential Equations

This paper is devoted to the study of a class of control problems associated to a nonlinear second-order vector differential equation with pointwise state constraints. The control is realized via a function of the state. We extend the results of Akkouchi, Bounabat, and Goebel to vector differential equations and furthermore consider the more general case. Under proper conditions, we prove the existence of optimal controls in the class of Lipschitz functions and obtain an optimality condition which looks somehow like the Pontryagin maximum principle for a smooth optimal control function. For a nonsmooth optimal control function, we derive a suboptimality condition by means of the Ekeland variational principle.Communicated by M. J. BalasThis work was supported by 985 Project of Jilin University. The author thanks Professor Yong Li for valuable suggestions. He also thanks Professor M. J. Balas and the anonymous referees for their comments.     

On the Krein and Friedrichs extensions of a positive Jacobi operator

We show that for a positive linear operator acting in ℓ² and defined from

a_nx_n+1+b_nx_n+a_n-1x_n-1