Investigation of near constant loss contribution to conductivity in lithium bismo-silicate glasses

Glasses having compositions 20Li₂O · (80 − x)Bi₂O₃ · xSiO₂ (x = 55, 60, 65, 70 mol%) were investigated using impedance spectroscopy in the frequency range from 20 Hz to 1 MHz and in the temperature range from 543 to 663 K. The ac and dc conductivities, activation energy of the dc conductivity and relaxation frequency are extracted from the impedance spectra. The increase in conductivity with increase in SiO₂ content is attributed to the change in the structural units of bismuth. Both electric modulus and the conductivity formalism have been employed to study the relaxation dynamics of charge carriers in these glasses. A single ‘master curve’ for normalized plots of all the modulus isotherms observed for a given composition indicates the temperature independence of the dynamic processes for ions in these glasses. Similar values of activation energy for dc conduction and for conductivity relaxation time indicates that the ions overcome same energy barrier while conducting and relaxing. The observed conductivity spectra follows power law with exponent ‘s’ which increases regularly with frequency and approaches unity at higher frequencies. Near constant losses (NCL) characterize this linearly dependent region of conductivity spectra. A deviation from ‘super curve’ for various isotherms of conductivity spectra was also observed in high frequency region and at low temperatures, which supports the existence of different dynamic processes like NCL in addition to the ion hopping processes in the investigated glass system.     

New kinds of generalized variational-like inequality problems in topological vector spaces

In this work, we consider a generalized nonlinear variational-like inequality problem, in topological vector spaces, and, by using the KKM technique, we prove an existence theorem. Our result extends a theorem of Ahmad and Irfan [R. Ahmad, S.S. Irfan, On the generalized nonlinear variational-like inequality problems, Appl. Math. Lett. 19 (2006) 294–297].     

GPU accelerated simulations of three-dimensional flow of power-law fluids in a driven cube

Newtonian fluid flow in two- and three-dimensional cavities with a moving wall has been studied extensively in a number of previous works. However, relatively a fewer number of studies have considered the motion of non-Newtonian fluids such as shear thinning and shear thickening power law fluids. In this paper, we have simulated the three-dimensional, non-Newtonian flow of a power law fluid in a cubic cavity driven by shear from the top wall. We have used an in-house developed fractional step code, implemented on a Graphics Processor Unit. Three Reynolds numbers have been studied with power law index set to 0.5, 1.0 and 1.5. The flow patterns, viscosity distributions and velocity profiles are presented for Reynolds numbers of 100, 400 and 1000. All three Reynolds numbers are found to yield steady state flows. Tabulated values of velocity are given for the nine cases studied, including the Newtonian cases.     

On an iterative method for a class of 2 point \& 3 point nonlinear SBVPs

In this article, we propose a novel modification to Quasi-Newton method, which is now a days popularly known as variation iteration method (VIM) and use it to solve the following class of nonlinear singular differential equations which arises in chemistry $-y''(x)-\frac{\alpha}{x}y''(x)=f(x,y),~x\in(0,1),$ where $\alpha\geq1$, subject to certain two point and three point boundary conditions. We compute the relaxation parameter as a function of Bessel and the modified Bessel functions. Since rate of convergence of solutions to the iterative scheme depends on the relaxation parameter, thus we can have faster convergence. We validate our results for two point and three point boundary conditions. We allow $\partial f/\partial y$ to take both positive and negative values.     

On 3-way combinatorial identities

In this paper, we provide combinatorial meanings to two generalized basic series with the aid of associated lattice paths. These results produce two new classes of infinite 3-way combinatorial identities. Five particular cases are also discussed. These particular cases provide new combinatorial versions of Göllnitz–Gordon identities and Göllnitz identity. Seven q-identities of Slater and five q-identities of Rogers are further explored using the same combinatorial object. These results are an extension of the work of Goyal and Agarwal (Utilitas Math. 95 (2014) 141–148), Agarwal and Rana (Utilitas Math. 79 (2009) 145–155), and Agarwal (J. Number Theory 28 (1988) 299–305).     

Regioselective synthesis of phthalans via Cu(OTf)2-catalyzed 5-exo-dig intramolecular hydroalkoxylation of 2-(ethynyl)benzyl alcohols

An efficient, regioselective Cu(OTf)₂-catalyzed 5-exo-dig intramolecular hydroalkoxylation of 2-(ethynyl)benzyl alcohol, which provides a concise access to functionalized phthalan in high yields has been developed. A wide range of substrates possessing terminal, internal, and heteroaromatic alkynes can be efficiently transformed into the targeted phthalans. Substrates with primary, secondary, and tertiary benzyl alcohols also proceed well to produce the corresponding phthalans in good yields. Irrespective of the nature of the substrates, the cyclization follows highly selective 5-exo-dig regiochemistry when regioselectivity is an issue.     

Three-component reaction involving metal-free heteroannulation of N-Boc-3-amido indole, aryl aldehydes, and aromatic alkynes under microwave conditions: synthesis of highly diversified δ-carbolines

An efficient synthesis toward highly diversified δ-carbolines via one-pot multicomponent reaction using N-Boc-3-amido indoles, aryl aldehydes, and aromatic terminal alkynes under microwave conditions has been described.     

Regioselective intramolecular electrophilic substitution reactions involving π-deficient pyridine substrates: a new entry to pyridoquinazolines and benzo[h][1,6]naphthyridines

Regioselective intramolecular electrophilic substitution reactions have been described in π-deficient pyridine substrates tethered at C-2 to the aryl amine. The presence and nature of ring activating groups at C-6 led to the involvement of either N-1 or C-3 of the pyridine ring in the cyclization thereby leading to the regioselective synthesis of pyridoquinazolines and naphthyridines in excellent yields.