Determination of optimal feedback terminal controllers for general boundary conditions using generating functions

Given a nonlinear system and a performance index to be minimized, we present a general approach to expressing the finite time optimal feedback control law applicable to different types of boundary conditions. Starting from the necessary conditions for optimality represented by a Hamiltonian system, we solve the Hamilton-Jacobi equation for a generating function for a specific canonical transformation. This enables us to obtain the optimal feedback control for fundamentally different sets of boundary conditions only using a series of algebraic manipulations and partial differentiations. Furthermore, the proposed approach reveals an insight that the optimal cost functions for a given dynamical system can be decomposed into a single generating function that is only a function of the dynamics plus a term representing the boundary conditions. This result is formalized as a theorem. The whole procedure provides an advantage over methods rooted in dynamic programming, which require one to solve the Hamilton-Jacobi-Bellman equation repetitively for each type of boundary condition. The cost of this favorable versatility is doubling the dimension of the partial differential equation to be solved.     

Synthesis and applications of heterobifunctional poly(ethylene oxide) oligomers

Poly(ethylene oxide) (PEO) oligomers are employed extensively in pharmaceutical and biomedical arenas mainly due to their excellent physical and biological properties, including solubility in water and organic solvents, lack of toxicity, and absence of immunogenicity. PEO can be chemically modified and reacted with, or adsorbed onto, other molecules and surfaces. Sophisticated applications for PEO have increased the demand for PEO oligomers with tailored functionalities, and heterobifunctional PEOs are often needed. This review discusses the synthesis and applications of heterobifunctional PEO oligomers possessing amine, carboxylate, thiol, and maleimide functional groups.     

A strategy for the electro-organic synthesis of new hydrocaffeic acid derivatives

Electrochemical treatment processes can significantly contribute to the protection of the environment through the minimization of waste and toxic materials in effluents. From a pharmaceutical point of view and due to the existing resemblance between the electrochemical and biological reactions, it can be assumed that the oxidation mechanisms on the electrode and in the body share similar principles. In this paper, the application of electrochemical studies in the design of an environmentally friendly method was delineated for the new hydrocaffeic acid (HCA, 3,4-dihydroxy hydrocinnamic acid) derivatives synthesis at carbon electrodes in an undivided cell. In this cell, the EC mechanism reaction was involved, comprising two steps alternatively; (1) electrochemical oxidation and (2) chemical reaction. In particular, the electro-organic reactions of HCA, an important biological molecule, were studied in a water–acetonitrile (90:10 v/v) mixture in the presence of benzenesulfinic acid (3) and p-toluenesulfinic acid (4). The research included the use of a variety of experimental techniques, such as cyclic voltammetry, controlled-potential electrolysis and product spectroscopic identification.     

Plasma power can make better powders

It may be a truism to say that round powders pack better, but spheroidisation of powder particles is one of the successful commercial applications of induction plasma technology and can play a key role in substantial improvement of powder quality and fluidity…     

Parametric circles and spheres

Formulations for parametric circles and spheres in terms of rational Gaussian (RaG) curves and surfaces are introduced. With the proposed formulations, a full circle is generated by interpolating a closed RaG curve to the vertices of an equilateral triangle, and a full sphere is generated by interpolating a closed RaG surface to the vertices of an octahedron with equilateral triangular faces. Generation of circles and spheres in this manner is very intuitive and easy to remember as the weights are all 1 and the nodes are all unique and uniformly spaced.     

海洋钻井液有机物添加剂生物降解性评价

随着海洋石油的勘探开发，钻井液有机添加剂不可避免地进入海洋．因此在海洋勘探开发过程中应选择环保性能好，即生物降解性能好的有机物添加剂。用累计耗氧量法测定了海洋钻井液有机添加剂的生物降解性，研究评价了有机添加剂的生物降解规律和机理，探讨了有机物生物降解性同其化学结构的内在联系，为海洋勘探开发过程中选择环保性能好的有机物添加剂提供理论依据。总结实验结果发现：淀粉类(如DFD-140和FI-E1等)最容易生物降解；其次是纤维素类(如MV-CMC等)和烯类单体聚合物(如PAM和PHP)；而沥青类、两性离子类则难以生物降解，有的甚至对生物降解起抑制作用。