Controllability of Nonsmooth Discrete Systems with Delay

This paper is concerned with a study of local controllability to discrete inclusions with delay. The sufficient conditions for relative and complete local controllability are obtained on the base of using Mordukhovich's nonsmooth constructions.     

多功能柱净化-高效液相色谱法检测谷物中的玉米赤霉烯酮

建立了玉米和小麦中玉米赤霉烯酮（ZEN）的多功能柱净化-高效液相色谱检测方法。样品经乙腈-水混合溶剂（V（乙腈）：V（水）=84：16）提取,通过多功能净化柱（MFC）进行一次性净化,以Symmetry^R C18柱为分离柱,甲醇-水（V（甲醇）：V（水）=68：32）为流动相进行高效液相色谱分离和检测。玉米赤霉烯酮的质量浓度在0．01～4．0μg／mL范围内呈良好线性,相关系数为0．9996。检出限为0．04μg／g,在0、04—5．0mg／kg添加范围内的回收率为87．5％～98．6％,相对标准偏差为1．5％～8．3％。     

Normal coderivative for multifunctions and implicit function theorems

In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280].     

Decomposability in the space of HKP‐integrable functions

In this paper we introduce the notion of decomposability in the space of Henstock‐Kurzweil‐Pettis integrable (for short HKP‐integrable) functions. We show representations theorems for decomposable sets of HKP‐integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.     

Bi-functional optimization of actively cooled, pressurized hollow sandwich cylinders with prismatic cores

All metallic, hollow sandwich cylinders having ultralight two-dimensional (2D) prismatic cores are optimally designed for maximum thermo-mechanical performance at minimum mass. The heated cylinder is subjected to uniform internal pressure and actively cooled by forced air convection. The use of two different core topologies is exploited: square- and triangular-celled cores. The minimum mass design model is so defined that three failure modes are prevented: facesheet yielding, core member yielding, and core member buckling. The intersection-of-asymptotes method, in conjunction with the fin analogy model, is employed to build the optimization model for maximum heat transfer rate. A non-dimensional parameter is introduced to couple the two objectives—structural and thermal—in a single cost function. It is found that the geometry corresponding to maximum heat transfer rate is not unique, and square-celled core sandwich cylinders outperform those having triangular cells. The eight-layered sandwich cylinders with square cells have the best overall performance in comparison with other core topologies. Whilst a sandwich cylinder with shorter length is preferred for enhanced thermo-mechanical performance, the influence of the outer radius of the cylinder is rather weak.     

聚苯胺微／纳米结构及其应用

导电聚合物微／纳米结构保留了轻质、类金属电导率和可逆化学和电化学特性,又具有纳米材料的高比表面积、尺寸和量子效应,它在电子器件、储能器件、传感器件等领域具有广泛的技术应用前景。其中,由于聚苯胺的制备方法简单、原料易得和独特的质子酸掺杂和脱掺杂机制,使聚苯胺微／纳米结构的可控制备及其应用研究已成为当前导电聚合物研究的热点...     

Upper-semi-continuity and cone-concavity of multi-valued vector functions in a duality theory for vector optimization

Following a few words on multifunctions in the mathematical literature, a very brief recall on dual spaces, some preliminary notations and definitions in the introduction, we give some results on those functions in the second paragraph. In the third paragraph, a duality theory in cone-optimization involving multifunctions is developed with the concept of the strong instead of the weak cone-optimality criterium. The results so obtained account for existing ones on univocal vector-function optimization and they hold in spaces of arbitrary dimension.The author is grateful to the refuree's helpful suggestions.     

Applications of the method of partial inverses to convex programming: Decomposition

A primal–dual decomposition method is presented to solve the separable convex programming problem. Convergence to a solution and Lagrange multiplier vector occurs from an arbitrary starting point. The method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction. In the nonseparable case, it specializes to a known method, the proximal method of multipliers. Conditions are provided which guarantee linear convergence.This research was sponsored, in part, by the Air Force Office of Scientific Research under grant 80-0195.     

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].     

Uniform Fe3O4–PANi/PS composite spheres with conductive and magnetic properties and their hollow spheres

Core–shell multifunctional composite spheres consisting of Fe₃O₄–polyaniline (PANi) shell and polystyrene (PS) core were fabricated using core–shell-structured sulfonated PS spheres (with uniform diameter of 250 nm) as templates. PANi was doped in situ by sulfonic acid resulting the composite spheres are well conductive. Dissolved with solvent, PS cores were removed from the core–shell composite spheres and hollow Fe₃O₄–PANi spheres were obtained. Removing the PANi and PS components by calcinations produced hollow Fe₃O₄ spheres. The cavity size of the hollow spheres was uniformly approximate to 190 nm and the shell thickness was 30 nm. The cavity size and the shell thickness can be synchronously controlled by varying the sulfonation time of the PS templates. The shell thickness in size range was of 20–86 nm when the sulfonation time was changed from 1 to 4 h. These resulting spheres could be arranged in order by self-assembly of the templates. Both the Fe₃O₄–PANi/PS composite spheres and the hollow Fe₃O₄ spheres exhibit a super-paramagnetic behavior. Scanning electron microscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, and X-ray powder scattering were used to characterize these as-prepared spheres. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.