Max-min of polynomials and exponential diophantine equations

In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z.     

A molecular dynamics simulation of a homogeneous organic-inorganic hybrid silica membrane

A new molecular dynamics simulation method was successfully applied to construct a homogeneous organic-inorganic hybrid silica membrane using the hybrid-pcff (h-pcff) potential function. Analysis suggested that the hybrid BTESE silica membrane provided a looser network and larger cavity size for the enhancement of gas permeability and selectivity.     

Anisotropic oxygen plasma etching of colloidal particles in electrospun fibers

Oxygen plasma etching of electrospun polymer fibers containing spherical colloids is presented as a new approach towards anisotropic colloidal nanoparticles. The detailed morphology of the resulting nanoparticles can be precisely controlled in a continuous way. The same approach is also amenable to prepare inorganic nanoparticles with double-sided patches.     

Fabrication of single crystal CuGaS2 nanorods by X-ray irradiation

CuGaS(2) nanorods were synthesized by irradiating the precursor solution with intense X-rays. The products are single crystal nanorods with preferential [220] growth and a uniform size distribution. We also report on the photoresponse of drop-cast films of these nanorods.     

Strain-stiffening response in transient networks formed by reverse wormlike micelles

Strain-stiffening, that is, an increase in material stiffness at large deformations, is a property of many biological materials. Currently, model systems for the study of this phenomenon are elastic networks (gels) of semiflexible filamentous biopolymers such as actin, keratin, or fibrin. Here, we demonstrate strain-stiffening in a class of viscoelastic solutions, comprising reverse wormlike micelles. These structures are formed by the coassembly of the physiological surfactants, lecithin and bile salt, in an organic solvent, cyclohexane. In contrast to the biopolymer gels, the networks here are transient and are formed by the physical entanglement of relatively flexible worms. Our results suggest that neither a permanent network nor a high filament rigidity is required for strain-stiffening. We suggest a different origin, based on a temporary strain-induced increase in the volume fraction of entangled worms. Our system can also serve as a convenient synthetic model for future studies into this phenomenon.     

Transesterification of Soybean Oil Catalyzed by Calcium Hydroxide which Obtained from Hydrolysis Reaction of Calcium Carbide

Calcium carbide residue (CCR) was investigated in transesterification reaction of triglycerides to determine its viability as a solid catalyst for biodiesel synthesis. Literature survey showed that CCR has never been studied as a solid catalyst in the transesterification of triglyceride. The scope of the study includes the effects of CCR calcination temperature, calcination time, the alcohol/oil molar ratio, the catalyst amount (wt % of oil) and the reaction time. The relationship between chemical composition and catalytic activity of waste cement was also investigated. These CCR catalysts, thermally activated at 600 °C, can give rise to fatty acid methyl esters (FAME) purity higher than 99.5%, after 3 h of reaction, when oil/methanol molar ratio of 1/12 and 1 wt % of the catalyst were employed. Application of CCR as catalyst for biodiesel production in this study may not only provide a cost‐effective and environment friendly way of recycling CCR waste but also reduce hopefully the cost of biodiesel production.     

Synthesis of bisquinoline–pyrrole oligoamide as G-quadruplex binding ligand

A one-pot procedure using ammonium formate under palladium catalysis for the reductive dechlorination and reduction of nitro group of 4-chloro-8-nitro–quinoline derivatives has be successfully carried out. This has lead to the synthesis of bisquinoline–pyrrole oligoamide 1, which show significant G-quadruplex selectivity in preference to duplex DNA. The cooperativity between the bisquinoline and pyrrole oligoamide moieties for good binding affinity to G-quadruplex was proven by synthesizing 2 and 3 lacking a quinoline ring and pyrrole amide, respectively, and both show much reduce affinity to G-quadruplex. Altogether, the results demostrate that the appropriate combination of two chromophores to form the hybride can attenuate binding affinity and selectivity towards G-quadruplex, an important criteria for the rational drug design.     

Simulation of harmonic oscillators on the lattice

This work deals with the simulation of a two-dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second-order linear differential equations, which can be recast into matrix form. The explicit solutions which govern the dynamics of this system can be expressed in terms of matrix trigonometric functions. For the derivation we employ the Lagrangian formalism to determine the correct solutions, which extremize the underlying action of the system. In the numerical evaluation we develop diverse state-of-the-art algorithms which efficiently tackle equations with matrix sine and cosine functions. For this purpose, we introduce two special series related to trigonometric functions. They provide approximate solutions of the system through a suitable combination. For the final computation an algorithm based on Taylor expansion with forward and backward error analysis for computing those series had to be devised. We also implement several MATLAB programs which simulate and visualize the two-dimensional lattice and check its energy conservation.