Adaptive quasi-likelihood estimate in generalized linear models

This paper gives a thorough theoretical treatment on the adaptive quasi-likelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.     

A study on spatially extended phase objects using speckle photography

We present an application of an improved speckle photography technique for spatially extended phase objects. A contour mapping of a thin lens displaying its phase variation is presented. A theoretical analysis is investigated followed by the experimental presentation. Reasonable interference fringes are obtained and compared with the fringes obtained for hot air. The phase information of the object is extracted using the point-by-point technique.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

AB CROSSLINKED POLYURETHANES THROUGH IONIC CROSSLINKING: INFLUENCE OF CROSSLINKING NETWORKS ON PHYSICO CHEMICAL PROPERTIES

Isocyanate-terminated prepolymers were synthesized using poly(tetramethylene oxide)glycol of molecular weight 1000 (PTMG₁₀₀₀) with tolylene-2,4-diisocyanate (TDI). The prepolymers were chain extended with N-methyldiethanolamine (N-MDEA) to form polyurethanes containing tertiary nitrogen. These polyurethanes were crosslinked with bromine terminated polyurethane, poly(urethane-imide), and poly(urethane-siloxane) through the formation of cationomers at tertiary nitrogen sites across the backbone polyurethanes.

The crosslinked cationomeric polyurethanes were characterized by Fourier Transform Infrared Spectroscopy (FTIR), Thermogravimetric Analysis (TGA), mechanical analyses, (static and dynamic), and static contact angles measurements. FTIR spectral studies confirms the formation of bromine terminated poly(urethane-imide) and poly(urethane-siloxane), as well as quaternization of the tertiary nitrogen which leads to crosslinking. A comparison of thermal stabilities of crosslinked polymers with respect to the chemical nature of bromine terminated prepolymers (BTP) indicates improved thermal stability for poly(urethane-imide) based ABCP. Stress-strain analysis shows high elongation values for poly(urethane-siloxane) and poly(urethane-imide) based ABCPs. Dynamic mechanical analysis reveals better damping for poly(urethane- siloxane) based AB crosslinked polymers.     

The extended tanh method for solving systems of nonlinear wave equations

The extended tanh method with a computerized symbolic computation is used for constructing the traveling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. The applied method will be used to solve the generalized coupled Hirota Satsuma KdV equation.     

ON SINGLE LAWS FOR VARIETIES OF QUASIGROUPS ASSOCIATED WITH EXTENDED CYCLE SYSTEMS

It has been previously shown by Lindner and Rodger that quasigroups associated with 2-perfect extended m-cycle systems can be equationally defined if and only if m ∈ {3, 5, 7}. In this paper we present a single identity for each such m which is equivalent to the identities given for these varieties.

     

A common fixed point theorem for compatible quasi contractive self mappings in metric spaces

A common fixed point theorem for weakly commuting quasi contractive self mappings with contracting orbital diameters in metric spaces [V. Berinde, A common fixed point theorem for quasi contractive type mappings, Ann. Univ. Sci. Budapest. 46 (2003) 81-90] is extended to the more general class of compatible quasi contractive self mappings. Our result does extend and generalize numerous related results in literature.