A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics

The main object of this paper is to present a general mathematical theory applicable to the study of a large class of linear variational inequalities arising in electronics. Our approach uses recession tools so as to define a new class of problems that we call “semi-complementarity problems”. Then we show that the study of semi-complementarity problems can be used to prove new qualitative results applicable to the study of linear variational inequalities of the second kind.     

A study on melt grafting of maleic anhydride onto low‐density polyethylene and its blend with polyamide 6

Graft copolymerization of low‐density polyethylene (LDPE) with a maleic anhydride (MAH) was performed using intermeshing corotating twin‐screw extruder in the presence of benzoyl peroxide (BPO). The LDPE/polyamide 6 (PA6) and LDPE‐g‐MAH/PA6 blends were prepared in a corotating twin‐screw extruder. The melt viscosity of the grafted LDPE was measured by a capillary rheometer. The grafted copolymer was characterized by Fourier transform infrared spectroscopy (FTIR) and scanning electron microcopy (SEM). The influence of the variation in temperature, BPO and MAH concentration, and temperature on the grafting degree and on the melt viscosity was studied. The grafting degree increased appreciably up to about 0.45 phr and then decreased continuously with an increasing BPO concentration. According to the FTIR analysis, it was found that the amount of grafted MAH on the LDPE chains was ～5.1%. Thermal analysis showed that melting temperature of the graft copolymers decreases with increasing grafting degree. In addition to this, loss modulus (E″) of the copolymers first increased little with increasing grafting and then obviously decreased with increasing grafting degree. Furthermore, the results revealed that the tensile strength of the blends increased linearly with increasing PA6 content. The results of SEM and mechanical test showed that the blends have good interfacial adhesion and good stability of the phase structure, which is reflected in the mechanical properties. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 267–275, 2010     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

Squeezed flow and heat transfer over a porous surface for viscous fluid

Flow and heat transfer over a permeable sensor surface placed in a squeezing channel is analyzed. A constant transpiration through the sensor surface is assumed. Locally non-similar momentum and energy equations are solved by three different methods, against the transpiration parameter τ, for different values of the squeezing parameter b, and Prandtl number Pr. From the investigation, it is found that when the channel being squeezed, the skin-friction reduces but the heat transfer coefficient increases. Increase in the value of the squeezing parameter onsets reverse flow at the sensor surface when fluid is being injected and the affect is enhanced with the increase of injection through the surface. It is further observed that increase of suction of fluid through the sensor thins the thermal and the momentum boundary layer regions, whereas injection of fluid leads to thickening of both the thermal and the momentum boundary layer regions. Heat transfer from the surface of the sensor increases with the increase of the value of Pr for the entire range of surface mass-flux parameter τ. M. A. Hossain is on leave of absence from University of Dhaka.     

Ultrafast experiments on intermolecular electron transfer in the benzene - bromine atom charge transfer complex

Ultrafast pump - probe measurements have been made on the benzene - bromine atom charge transfer (CT) complex in CCl₄ and cyclohexane solutions. Ultrafast optical excitation of the CT band of the complex yields an ion pair, which is comprised of a benzene cation and a bromide anion. The rate of charge recombination between the bromide and the benzene cation in the ion pair has been observed to be much faster than the rate of diffusion apart. The charge recombination rate is accelerated at high benzene concentrations as a result of the formation of a benzene dimer cation - bromide ion pair which undergoes much faster charge recombination than the benzene cation - bromide ion pair.     

Analytic method for solving coupled nonlinear Schroedinger equations with oscillating terms describing polarized soliton oscillations

Using a variational method, a new model of the nonlinear propagation of optical solitons generated from semiconductor lasers through lossy elliptically low birefringent fiber, is presented within the framework of a system of coupled nonlinear Schroedinger (CNLS) equations with oscillating terms. This analytic model demonstrates polarized soliton oscillations in a lossy elliptically low birefringent optical fiber.     

On the structure ofn-point sets

Letn be an integer greater than one. Our main result, called the “Structure Theorem” is that a set that containsn−1 disjoint continua that are cut by a single line cannot be ann-point set, that is, a set that meets every line in preciselyn points. This theorem unifies and significantly improves upon a number of known theorems. The second part of the paper is devoted to several theorems that address the question when a set that meets every line in at mostn points can be extended to ann-point set. These theorems also highlight the sharpness of the Structure Theorem.