ZL-amenability and characters for the restricted direct products of finite groups

Let G   be a restricted direct product of finite groups _{Gi}i∈I${\{G_i\}}_{i\in I}$, and let Z?¹(G)${\mathrm{Z}?}^1(G)$ denote the centre of its group algebra. We show that Z?¹(G)${\mathrm{Z}?}^1(G)$ is amenable if and only if _Gi$G_i$ is abelian for all but finitely many i  , and characterize the maximal ideals of Z?¹(G)${\mathrm{Z}?}^1(G)$ which have bounded approximate identities. We also study when an algebra character of Z?¹(G)${\mathrm{Z}?}^1(G)$ belongs to _c0$c_0$ or ?^p${?}^p$ and provide a variety of examples.     

Modules in Which Every Fully Invariant Submodule is Essential in a Direct Summand

A module M is called extending if every submodule of M is essential in a direct summand. We call a module FI-extending if every fully invariant submodule is essential in a direct summand. Initially we develop basic properties in the general module setting. For example, in contrast to extending modules, a direct sum of FI-extending modules is FI-extending. Later we largely focus on the specific case when a ring is FI-extending (considered as a module over itself). Again, unlike the extending property, the FI-extending property is shown to carry over to matrix rings. Several results on ring direct decompositions of FI-extending rings are obtained, including a proper generalization of a result of C. Faith on the splitting-off of the maximal regular ideal in a continuous ring.     

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     

Stimulated raman scattering in fiber optic systems

The effect of stimulated Raman scattering (SRS) in fiber optic communications is considered. On one hand, SRS limits the launch power in a multiple-channel communication system; while on the other hand, SRS can provide optical amplification in the 1.3-μm and 1.55-μm windows. In most of the previous work these issues have been treated separately by using different assumptions. A solution is usually obtained by solving differential equations. We present a numerical method that involves the simultaneous solution of integral equations describing SRS in optical fiber. The method is general enough to be applicable for wavelength division multiplexing (WDM), optic frequency division multiplexing (OFDM), and optical amplification. However, it is efficient and simple to program and uses just a few realistic assumptions. A WDM communication system with 10 optical channels in the 1.55-μm window is studied by using this method, The data rate is above 1 Gbps. The system parameters are such that the other nonlinear effects, such as stimulated Brillouin scattering and four-wave mixing, are less significant for the system. Launch power limitations imposed by SRS are investigated for IM / DD and coherent systems. The receiver dynamic range over the wavelengths of interest is an important factor in determining the launch power limitations. An optical amplifier in the 1.3-μm window is also analyzed. The two-pump technique is investigated. With pump power levels of about 500 mw 0-dB gain can be achieved for a 30-km repeaterless link. Finally, the calculated results agree with the experiments.     

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.     

Multidimensional modified fractional calculus operators involving a general class of polynomials

In the present work, we introduce and study essentially a class of multi-dimensional modified fractional calculus operators involving a general class of polynomials in the kernel. These operators are considered in the space of functionsM _γ (R ₊ ⁿ ). Some mapping properties and fractional differential formulas are obtained. Also images of some elementary and special functions are established.     

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.