Viscoelastic Timoshenko Beams with Occasionally Constant Relaxation Functions

For a prescribed desirable arbitrary decay suitable viscoelastic materials are determined through their relaxation functions. It is shown that if we wish to have a decay of order ??(t) then the kernels should be of the same order. That is their product with this function should be summable.     

The decay rate for a fractional differential equation

We consider the fractional differential equation

     

Poly(p‐phenylene methylene)‐based block copolymers by mechanistic transformation

The synthesis of poly(p‐phenylene methylene) (PPM)‐based block copolymers such as poly(p‐phenylene methylene)‐b‐poly(ε‐caprolactone) and poly(p‐phenylene methylene)‐b‐polytetrahydrofuran by mechanistic transformation was described. First, precursor PPM was synthesized by acid‐catalyzed polymerization of tribenzylborate at 16 °C. Then, this polymer was used as macroinitiators in either ring‐opening polymerization of ε‐caprolactone or cationic ring‐opening polymerization of tetrahydrofuran to yield respective block copolymers. The structures of the prepolymer and block copolymers were characterized by GPC and ¹H NMR investigations. The composition of block copolymers as determined by ¹H NMR and TGA analysis was found to be in very good agreement. The thermal behavior and surface morphology of the copolymers were also investigated, respectively, by differential scanning calorimetry and atomic force microscopy measurements, and the contribution of the major soft segment has been observed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Highly sensitive spectrophotometric methods for the determination, validation and thermogravimetric analysis of antiulcer drugs, nizatidine and ranitidine in pure and pharmaceutical preparations

Two sensitive, simple and rapid UV and second order derivative spectrophotometric methods were developed for the determination of nizatidine and ranitidine hydrochloride in pure form and pharmaceutical preparations. For the first method, UV spectrophotometic method, nizatidine was determined at 325 nm and ranitidine at 325.5 nm with detection limits of 0.07 and 0.04 μg/mL, respectively. For the second method, the distances between two extremum values (peak-to-peak amplitudes), 328/356.5 nm for nizatidine and 326/357 nm for ranitidine were measured in the second order derivative-spectra. The detection limits were found to be 0.02 μg/mL for nizatidine and 0.016 μg/mL for ranitidine, respectively. The thermal analysis of the two drugs was studied by Thermogravimetric Analysis-Differential Scanning Calorimetry (TGA-DSC) techniques. Enthalpy changes were obtained 121.9 and 124.15 J/g for nizatidine and ranitidine, respectively. The proposed method was successfully applied to the analysis of pharmaceutical preparations. The results were in good agreement with those obtained using the reference method; no significant difference were found in the accuracy and precision as revealed by the accepted values of t- and F-tests.     

Spectrofluorimetric Determination and Validation of Biotin in Pure and Dosage Form via Derivatization with 4-Fluoro-7-nitrobenzofurazan

A simple and highly sensitive spectrofluorimetric method was developed for the determination of biotin in pure and dosage form. The method is based on the derivatization of biotin with 4‐fluoro‐7‐nitrobenzofurazan in borate buffer of pH 9.0 to yield a yellow, fluorescent product. The various chemical conditions that affected the reaction were studied. The method was validated for specificity, linearity, precision, accuracy, recovery and robustness. At optimized experimental conditions, a linear relationship between the fluorescence intensity of the concentration of biotin is observed in the range 45–450 ng/mL. Limit of detection and quantification were 0.038 and 0.114 ng/mL, respectively. The percentage mean recovery was 99.96. The proposed procedure was successfully applied to the determination of biotin in its dosage form with mean recovery of 101.23±1.22 for biotin tablets. The results obtained were in good agreement with those obtained by the reference method.     

Length 3 complexes of abelian sheaves and Picard 2-stacks

We define a tricategory T[−2,0] of length 3 complexes of abelian sheaves, whose hom-bigroupoids consist of weak morphisms of such complexes. We also define a 3-category 2Pic(S) of Picard 2-stacks, whose hom-2-groupoids consist of additive 2-functors. We prove that these categories are triequivalent as tricategories. As a consequence we obtain a generalization of Deligne's analogous result about Picard stacks in SGA4, Exposé XVIII (Deligne (1973) [11]).     

A New Class of Kernels Leading to an Arbitrary Decay in Viscoelasticity

A new assumption on the relaxation in a viscoelastic problem ensuring uniform stability in an arbitrary rate is established. This assumption replaces a usual condition and allows for a much wider class of kernels. As consequences several earlier results are extended and improved.     

On a non-dissipative Kirchhoff viscoelastic problem

In this paper we consider a Kirchhoff type viscoelastic problem, and prove uniform stability of the system. We do not rely on the dissipativity of the system or the boundedness of the energy as in the previous treatments. There appears a quadratic term which we cannot estimate by the initial energy as our system is not clearly dissipative in advance.     

Viscous dissipation effect on heat transfer characteristics of rectangular microchannels under slip flow regime and H1 boundary conditions

Viscous dissipation effect on heat transfer characteristics of a rectangular microchannel is studied. Flow is governed by the Navier–Stokes equations with the slip flow and temperature jump boundary conditions. Integral transform technique is applied to derive the temperature distribution and Nusselt number. The velocity distribution is taken from literature. The solution method is verified for the case where viscous dissipation is neglected. It is found that, the viscous dissipation is negligible for gas flows in microchannels, since the contribution of this effect on Nu number is about 1%. However, this effect should be taken into account for much more viscous flows, such as liquid flows. Neglecting this effect for a flat microchannel with an aspect ratio of 0.1 for Br=0.04 underestimates the Nu number about 5%.