General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms

In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions g_i(i = 1,2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow‐up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature.     

On the Schröder–Bernstein property for modules

The well known Schröder–Bernstein Theorem states that any two sets with one to one maps into each other are isomorphic. The question of whether any two (subisomorphic or) direct summand subisomorphic algebraic structures are isomorphic, has long been of interest. Kaplansky asked whether direct summands subisomorphic abelian groups are always isomorphic? The question generated a great deal of interest. The study of this question for the general class of modules has been somewhat limited. We extend the study of this question for modules in this paper. We say that a module Msatisfies the Schröder–Bernstein property (S-B property) if any two direct summands of M which are subisomorphic to direct summands of each other, are isomorphic. We show that a large number of classes of modules satisfy the S-B property. These include the classes of quasi-continuous, directly finite, quasi-discrete and modules with ACC on direct summands. It is also shown that over a Noetherian ring R, every extending module satisfies the S-B property. Among applications, it is proved that the class of rings R for which every R-module satisfies the S-B property is precisely that of pure-semisimple rings. We show that over a commutative domain R, any two quasi-continuous subisomorphic R-modules are isomorphic if and only if R is a PID. We study other conditions related to the S-B property and obtain characterizations of certain classes of rings via those conditions. Examples which delimit and illustrate our results are provided.     

Micelle‐catalyzed reaction of ninhydrin with DL‐valine in the absence and presence of organic solvents

Kinetics of the DL ‐valine‐ninhydrin reaction has been studied spectrophotometrically under varying conditions of [CTAB], [ninhydrin], [DL ‐valine], pH, temperature, and %(v/v) organic solvents (solvents used: 1‐propanol, methylcellosolve, acetonitrile, and dimethyl sulfoxide). Addition of CTAB and increase in the proportion of organic solvents, both showed catalyzing effect on the reaction. The effect of simultaneous presence of CTAB and DMSO in the reaction mixture has also been seen. The rate profiles obtained for solutions containing from 10% to 70% DMSO exhibited clear maxima that shifted progressively to higher concentrations of CTAB. The experimental results are explained in terms of specific solvent effects and the formation of stoichiometric hydrate DMSO · 2H₂O and the inhibitory effect of DMSO on micelle formation. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 634–642, 2006     

Experimental and theoretical studies on the functionalization reactions of 4-benzoyl-1,5-diphenyl-1H-pyrazole-3-carboxylic acid and acid chloride with 2,3-diaminopyridine

The 1H-pyrazole-3-carboxylic acid 2 was converted in good yield (69%) into the corresponding 1H-pyrazole-3-carboxamide 5 via reaction of the acid chloride 3 with 2,3- diaminopyridine (4). A different product, the 3H-imidazo[4,5-b] pyridine derivative 6, was formed from the reaction of 3 with 4 and base in benzene for 5 hours. The structures of the synthesized compounds were determined spectroscopically. The mechanism of the reaction between 3 and 4 was examined theoretically.     

Sur quelques Théorémes globaux en geometrie finslérienne

Résumè Le travail suivant établit des théorèmes globaux relatifs aux variétes finslériennes completes dont le tenseur de courbure vérifie certaines hypothèses. Le théorème de Hopf-Rinow est d’abord démontrè, puis au moyen du calcul variationnel, on établit une géneralisation des théoremes de Myers, de Cartan et de L. W. Green.     

Conformational analysis of XA and AX dipeptides in water by electronic circular dichroism and 1H NMR spectroscopy

We measured the temperature-dependent electronic circular dichroism (ECD) spectra of AX, XA, and XG dipeptides in D2O. The spectra of all XA and AX peptides indicate a substantial population of the polyproline II (PPII) conformation, while the ECD spectra of LG, KG, PG, and AG were found to be quantitatively different from the alanine-based dipeptides. Additional UV absorption data indicate that the ECD spectra of the XG peptides stem from electronic coupling between the peptide and the C-terminal group, and that spectral differences reflect different orientations of the latter. We also measured the 1H NMR spectra of the investigated dipeptides to determine the 3JHalphaNH coupling constants for the C-terminal residue. The observed temperature dependence of the ECD spectra and the respective room-temperature 3JHalphaNH coupling constants were analyzed by a two-state model encompassing PPII and a beta-like conformation. The PPII propensity of alanine in the XA series is only slightly modulated by the N-terminal side chain, and is larger than 50%. As compared to AA, XA peptides containing L, P, S, K V, E, T, and I all cause a relative stabilization of the extended beta-strand conformation. The PPII fractions of XA peptides varied between 0.64 for AA and 0.58 for DA, whereas the PPII fractions of AX peptides were much lower. From the investigated AX peptides, only AL and AQ showed the expected PPII propensity. We found that AT, AI, and AV clearly prefer an extended beta-strand conformation. A quantitative comparison of AA, AAA, and AAAA revealed a hierarchy AAAA > AAA approximately AA for the PPII population, in agreement with predictions from MD calculations and results from Raman optical activity studies (McColl et al. J. Am. Chem. Soc. 2004, 126, 5076).     

PBL as a pedagogical approach for integrated STEM: Evidence from prospective teachers

Problem-based learning (PBL) and science, technology, engineering, and mathematics (STEM) are two acronyms widely visible in education literature today. However, few studies have explored these in connection with one another, specifically with regard to teacher preparation. This study investigated how 47 prospective elementary teachers developed PBL units and how they integrated STEM and other disciplines into those units. It also addressed the affordances and constraints of integrated STEM as perceived by the prospective elementary teachers. Data sources in this multimethod study included PBL units and interviews. Findings revealed that all of the units integrated at least two of the STEM disciplines, as well as literacy, in a variety of ways. The prospective teachers articulated perceived benefits of integrated STEM, such as: making connections across content areas, preparing students for the real world, teaching students that failure is not a bad thing, and providing future opportunities. They also addressed perceived barriers of integrated STEM, such as: having limited experience with the content, diminishing the effect of individual content areas, and needing better curriculum alignment. Overall, this study provides evidence that PBL can be a pedagogical approach to integrate STEM. Implications for teachers, teacher educators, and curriculum specialists are discussed.     

Perturbations Results for Some Classes Related to Browder Linear Relations and Applications

This paper is devoted to the investigation of the perturbation problem of right (left) Browder linear relations and lower (upper) semi-Browder linear relations under commuting compact linear relations. Further, our results are used to show the invariance of Browder’s spectrum.     

Oscillatory and Periodic Solutions of Impulsive Differential Equations with Piecewise Constant Argument

We study the existence of oscillatory and periodic solutions of a class of first order scalar impulsive delay differential equations with piecewise constant argument.     

Interactions of gamma rays with undoped and Mn-doped sodium phosphate glasses

Ultraviolet and visible spectroscopic measurements were used to investigate prepared undoped and Mn-doped sodium phosphate glasses before and after successive gamma irradiation. The effects of both glass composition and MnO₂ content on the generation of radiation-induced defects were investigated. Undoped sodium phosphate glass shows strong UV absorption, which is attributed to the presence of trace iron impurities present in the raw materials. Mn-doped glasses reveal an additional visible broad band centered at about 500 nm due to Mn³⁺, which has recently been related to the ⁵E_g →⁵T_2g transition. The radiation-induced bands are correlated with the generation of liberated electron–hole pairs during the process of gamma irradiation and the possibility of photochemical reactions especially with trace iron impurities and manganese ions. The intensity and the position of the induced bands are observed to depend on the type and composition of glass, concentration of the dopant and also on the irradiation dose. Manganese ions when present in relatively higher content have been found to show a shielding behavior towards the effects of progressive gamma irradiation causing a retardation of the growth of the induced defects. Infrared and Raman spectra of the undoped and Mn-doped glasses were measured to investigate the structural phosphate groups present and the effect of MnO₂ on the network structure. An ESR investigation was carried out to confirm the state of manganese ions in the prepared sodium phosphate glasses.