Some fixed point theorems in convex metric spaces

The concept of a convex metric space was introduced by Takahashi [10]. He observed that it is possible to generalize fixed point theorems in Banach spaces. Subsequently, Machado [8], Itoh [5], Naimpally, Singh and Whitfield [9] and Beg and Azam [2], among others have studied fixed point theorems in convex metric spaces. This paper is a continuation of these investigations.     

Sorption and immobilization of cellulase on silicate clay minerals

The interaction of organic molecules with mineral surfaces is a subject of interest in a variety of disciplines. Enzymes are able to be sorbed and immobilized by clay minerals and humic colloids in soil environment. The present study was done to elucidate some aspects of sorption and immobilization of cellulase on soil components by analysis of the sorption, and immobilization of cellulase on Avicel, a soil sample, illite, kaolinite, montmorillonite, and palygorskite. Palygorskite displayed the highest sorption capacity. Sorbents coated with hydroxyaluminum displayed significantly higher capacity than uncoated sorbents. The positive effects of Al(OH)(x) coating on sorption capacities of the different sorbents were not equal. The effect decreased in the order soil > palygorskite > kaolinite > Avicel > montmorillonite > illite. The amount of sorbed cellulase desorbed from external surfaces of soil was quite low (about 16%), especially in coated samples (about 6%). X-ray diffraction analysis of K-montmorillonite and Ca-montmorillonite showed that Al(OH)(x) was intercalated between the montmorillonite layers. Immobilization of cellulase on the sorbents did not result in expansion of their crystal structures. Therefore, it may be concluded that the amount of cellulase immobilized on internal surfaces of the sorbents was negligible.     

The Synthesis of Polyfunctional Aromatic Ring Systems. Structural Analogues of Phloroglucides,Aranciamycin, Cryptosporin and Terramycin

The synthesis of the title compounds is described. Some of the compounds prepared were found to be active against a number of pathogenic microorganisms in vitro.     

Computational studies on cyclic [n]paraphenyleneacetylenes using homodesmotic reactions

Cyclic [n]paraphenyleneacetylenes ([n]CPPAs) are potentially useful compounds for molecular electronics. In this article, a homodesmotic reaction scheme coupled with density functional theory has been used to estimate theoretically strain energies and heats of formation of [n]CPPAs. Calculations have been done for a series of [n]CPPAs, containing up to ten phenylacetylene units. Strain energies of [n]CPPAs decrease, while heats of formation increase steadily with the increase in the number of phenylacetylene units using homodesmotic reaction schemes. B3LYP and mPW1PW91 functionals have been used with the Pople basis set 6-31G* to analyze the trends. The results are sensitive to the scheme of homodesmotic reaction chosen, thereby necessitating careful chemical consideration before spending considerable computational resources for higher [n]CPPAs not considered here. Computational estimates for the ring diameter of [n]CPPAs and absolute entropy have also been obtained here. The HOMO-LUMO gaps of the belt shaped [n]CPPAs show an odd–even difference. In addition, the HOMOs of the [3]CPPA, [5]CPPA, [7]CPPA and [9]CPPA are doubly degenerate.     

An analytical and numerical study of peristaltic transport of a Johnson-Segalman fluid in an endoscope

In the present study, we discuss the peristaltic flow of a Johnson-Segalman fluid in an endoscope. Perturbation, homotopy, and numerical solutions are found for the non-linear differential equation. The comparative study is also made to check the validity of the solutions. The expressions for pressure rise frictional forces, pressure gradient, and stream lines are presented to interpret the behavior of various physical quantities of the Johnson-Segalman fluid.     

Relativistic symmetries in the Hulth6n scalar-vector-tensor interactions

In the presence of spin and pseudospin （p-spin） symmetries, the approximate analytical bound states of the Dirac equation for scalar-vector-tensor Hulth6n potentials are obtained with any arbitrary spin-orbit coupling number using the Pekeris approximation. The Hulth6n tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov-Uvarov （NU） method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given.     

Global existence and nonexistence results for a class of semilinear hyperbolic systems

In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the L_p → L_q type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd.     

Template‐Free Synthesis of Highly b‐Oriented MFI‐Type Zeolite Thin Films by Seeded Secondary Growth

Highly b‐oriented, closely packed, MFI zeolite films are prepared on seeded stainless‐steel plates using organic template‐free, secondary growth solutions, containing aluminum sulfate as a crystallization agent. The number of a‐oriented twin crystals is significantly reduced, and even eliminated, simply by restricting the pH value of the secondary growth solution to the narrow range of 11.1–11.3. Values of pH can be adjusted through the controlled addition of (NH₄)₂SO₄ or H₂SO₄ to secondary growth solutions of the composition (1 SiO₂:0.57 NaOH:137.5 H₂O:0.0050 (Al₂(SO₄)₃?18 H₂O)) or by simply decreasing the molar composition of NaOH with no extra additives.     

Local density of states of one-dimensional Mott insulators and charge-density wave states with a boundary

We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.     

Viscous Cosmology and Thermodynamics of Apparent Horizon

It is shown that the differential form of Friedmann equations of Friedman--Robertson--Walker (FRW) universe can be recast as a similar form of the first law T_hdS_h = dE + WdV of thermodynamics at the apparent horizon of FRW universe filled with the viscous fluid. It is also shown that by employing the general expression of temperature associated with the apparent horizon of an FRW universe and assumed that the temperature T_m of the energy inside the apparent horizon is proportional to the horizon temperature T_m= bT_h, we are able to show that the generalized second law of thermodynamics holds in the Einstein gravity provided T_h-T_m/r^~_A ≤(ρ+P^~).