A Lagrangian search method for the <Emphasis Type="Italic">P</Emphasis>-median problem

In this paper, we propose a novel algorithm for solving the classical P-median problem. The essential aim is to identify the optimal extended Lagrangian multipliers corresponding to the optimal solution of the underlying problem. For this, we first explore the structure of the data matrix in P-median problem to recast it as another equivalent global optimization problem over the space of the extended Lagrangian multipliers. Then we present a stochastic search algorithm to find the extended Lagrangian multipliers corresponding to the optimal solution of the original P-median problem. Numerical experiments illustrate that the proposed algorithm can effectively find a global optimal or very good suboptimal solution to the underlying P-median problem, especially for the computationally challenging subclass of P-median problems with a large gap between the optimal solution of the original problem and that of its Lagrangian relaxation.     

Model correction for the formation of amorphous silicon by ion implantation

The critical dose at which an implanted amorphous layer in silicon is formed cannot be explained by a previous energy independent model. An energy dependent correction to this model can explain our ESR data as well as other data. The correction is most important for light ions.     

Nanocomposite structures of polypyrrole derivatives and poly (acrylonitrile‐co‐itaconic acid) produced by in situ polymerization as carbon nanofiber precursor

This study aimed to produce nanoparticles of poly (acrylonitrile‐co‐itaconic acid) (P (AN‐co‐IA)) containing conjugated polymers of pyrrole, N‐Methylpyrrole, 2,5‐dimethylpyrrole, and 1‐(Triisopropylsilyl)pyrrole which were synthesized by emulsion polymerization. Nanocomposite structures of P (AN‐co‐IA)/polypyrrole and polymer of pyrrole derivatives were produced via in situ polymerization, and the nanoparticle formation were followed by morphologic and ultraviolet‐visible (UV‐Vis) spectroscopic methods. Characterizations were made by Fourier transform infrared‐attenuated total reflectance (FTIR‐ATR) and Raman spectroscopy. Atomic force microscopy (AFM) was used for investigating the surface characteristics of the nanoparticles. Characterization results revealed that nanoparticles containing conjugated polymers had rougher surface than P (AN‐co‐IA) nanoparticles. It was also observed that the nanoparticles were well‐distributed although having some agglomerates. Moreover, depending on the type of monomer of conjugated polymer, the shape and size of the produced nanoparticles differed by conjunction with their polymerization rate. These findings can be used as a startup information for production of carbon nanofibers (CNFs) with desired properties after oxidation and carbonization, and as a high‐performance and cost‐effective flame and heat‐resistant material (oxidized copolymers of polyacrylonitrile nanofiber).     

Changes in the Inter- and Intra- Fibrillar Structure of Lyocell (TENCEL®) Fibers after KOH Treatment

Lyocell fibers were treated with KOH up to 8 M which was demonstrated to distribute homogeneously at the outer zones of fiber cross section compared to NaOH which accesses more deeply but less homogenously. Both NaOH and KOH solutions can be used to lower significantly the fibrillation of lyocell fibers. However, due to intrafibrillar swelling together with deep penetration ability of alkali seen for NaOH treatments results in great fiber tensile strength loss which is not observed for KOH treatments due to its inability to penetrate the fiber completely. The porous structure of fibers was studied by inverse size exclusion chromatography (ISEC) to identify mean pore diameter, total pore area and accessible pore volume (APV). Mean pore diameter of fibers decreased after KOH treatments which did not change after NaOH treatments. Wide angle X-ray diffraction analyses (WAXD) were applied to identify the crystallinity index and crystallite size. In general, fiber properties such as water retention value, carboxyl content using methylene blue sorption method, depth of color measured after dyeing with C.I. Direct Red 81 and weight loss were distinctly different in the ranges up to 2 M, 2-5 M and 5 to 8 M KOH. KOH treatment suggests new possibilities for the pretreatment of lyocell fibers to lower fibrillation while slightly lowering elongation at break without a distinct loss in tensile strength and with less decrease in carboxyl content and weight loss without changing dyeing properties of fibers compared to NaOH treatment.     

Atomgewichte

Ohne Zusammenfassung     

A particular solution of Heun equation for Hulthen and Woods‐Saxon potentials

In this article a particular solution of Heun equation is derived by making use of the Nikiforov‐Uvarov (NU) method which provides exact solutions for general hypergeometric equation and eigenvalues together with eigenfunctions of the Heun equation for this particular solution are obtained. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrödinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods‐Saxon potentials).

     

A general class of evolutionary equations

Using observable quantities and state variable of a dynamical process, a general evolutionary equation is defined which unifies classical ordinary differential equations, partial differential equations, and hereditary systems of retarded and neutral type. Specific illustrations are given using transmission lines nearest-neighbor coupled at the boundary and the theory of heat transfer in solids. Some spectral theory for linearization of the equations is also discussed. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 268–288, February, 2007.     

Synthesis of a simplified bryostatin C-ring analogue that binds to the CRD2 of human PKC-alpha and construction of a novel BC-analogue by an unusual Julia olefination process

[structure: see text] The synthesis of two truncated bryostatin analogues 2 and 3 is described. High-field NMR measurements on the C-ring analogue 3 in C(2)H(3)CN containing 25% (2)H(2)O have shown that it binds to the CRD2 of human PKC-alpha at virtually the same position as phorbol-13-acetate (PA) and bryostatin 1 (1). NMR titration studies have also revealed that 3 binds to the CRD2 with a potency similar in magnitude to PA but much less potently than 1.