Strongly nonlinear variational inequalities and generalized pseudocontractions

The solvability of a class of generalized strongly nonlinear variational inequality problems on nonempty closed convex sets in Hilbert spaces is presented.     

Fluctuations in apparent mass at the bottom of granular columns due to different arrangements

We report the fluctuations in apparent mass at the bottom of granular columns due to various configurations. It is found that the fluctuations decrease with the increase in the ratio of diameters of silo to grain. For the arrangement of different grain layers in a column, the higher fluctuations appear when the larger grains are stacked at the bottom layer while reversing the order of grain-layers leads to smaller fluctuations. We attribute this behavior to the randomness in the direction of frictional forces between the grains and the confining wall. Moreover, due to polydisperse media, the development of inhomogeneous force transmission in grains may cause this to happen.     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

Reduction of quantum phase fluctuations in intermediate states

Recently we have shown that the reduction of the Carruthers-Nieto symmetric quantum phase fluctuation parameter (U) with respect to its coherent state value corresponds to an antibunched state, but the converse is not true. Consequently reduction of U is a stronger criterion of nonclassicality than the lowest order antibunching. Here we have studied the possibilities of reduction of U in intermediate states by using the Barnett-Pegg formalism. We have shown that the reduction of phase fluctuation parameter U can be seen in different intermediate states, such as binomial state, generalized binomial state, hypergeometric state, negative binomial state, and photon added coherent state. It is also shown that the depth of nonclassicality can be controlled by various parameters related to intermediate states. Further, we have provided specific examples of antibunched states, for which U is greater than its Poissonian state value.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

Improvement in electrical and magnetic properties of mixed Mg-Al-Mn ferrite system synthesized by citrate precursor technique

In the present work, mixed magnesium-manganese ferrites of composition Mg_0.9Mn_0.1Al_0.3Co_zFe_1.7−zO₄ where z=0.3, 0.5 and 0.7 have been synthesized by the citrate precursor technique. X-ray diffraction patterns of the samples confirmed the formation of single-phase spinel structure. The ferrites have been investigated for their electric and magnetic properties such as dc resistivity, Curie temperature, saturation magnetization, initial permeability and relative loss factor (RLF). Fairly constant value of initial permeability over a wide frequency range (0.1-20 MHz) and low values of the relative loss factor of the order of 10⁻⁴-10⁻⁵, in the frequency range 0.1-30 MHz, are the cardinal achievements of the present investigation. In addition to this, initial permeability was found to increase with an increase in temperature while RLF was observed to be low at these temperatures. The dc resistivity and Curie temperature were found to increase with an increase in cobalt content. The mechanisms contributing to these results are discussed in detail in this paper.     

A characterization of domains in <Emphasis Type="Bold">C</Emphasis><Superscript>2</Superscript> with noncompact automorphism group

Let D be a bounded domain in C ² with a non-compact group of holomorphic automorphisms. Model domains for D are obtained under the hypotheses that at least one orbit accumulates at a boundary point near which the boundary is smooth, real analytic and of finite type. The author was supported by DST (India) Grant No.: SR/S4/MS-283/05 and in part by a grant from UGC under DSA-SAP, Phase IV.     

On a finite difference scheme for Burgers’ equation

In this paper we study properties of numerical solutions of Burger’s equation. Burgers’ equation is reduced to the heat equation on which we apply the Douglas finite difference scheme. The method is shown to be unconditionally stable, fourth order accurate in space and second order accurate in time. Two test problems are used to validate the algorithm. Numerical solutions for various values of viscosity are calculated and it is concluded that the proposed method performs well.     

Graphene oxide‐catalyzed CSp3–H activation of methylarenes in aqueous medium: A unified metal‐free access to amides and benzimidazoles

Graphene oxide (GO)‐catalyzed selective synthesis of amides via C_Sp3–H activation of methylarenes and consequent C–N bond formation with anilines under aqueous medium has been described. Oxygen functionality allied with GO surface played a dual role both as acid catalyst and oxidizing agent to some extent. However, GO has a copious effect on the reaction, shown by a high TOF value with TBHP as co‐oxidant. The decisive role of carboxylic acid functional groups on GO nanosheets in this metal‐free strategy has been confirmed and was monitored by various analytic techniques viz. Fourier transform‐infrared, UV–Vis, Raman and XPS. A plausible mechanism was proposed by control experiments and by the isolation of the intermediate. Over‐oxidation of methylarenes was not detected, and high recyclability of the carbocatalyst with its heterogeneous behavior facilitated the isolation and purification of the desired products. We have further explored the utility of this process for the chemoselective synthesis of benzimidazoles.     

Identification of metabolites in coriander seeds (Coriandrum Sativum L.) aided by ultrahigh resolution total correlation NMR spectroscopy

NMR is a fast method for obtaining a holistic snapshot of the metabolome and also offers quantitative information without separating the compounds present in a complex mixture. Identification of the metabolites present in a plant extract sample is a crucial step for all plant metabolomics studies. In the present work, we used various two dimensional (2D) NMR methods such as J-resolved NMR, total correlation spectroscopy (TOCSY), and heteronuclear single quantum coherence sensitivity enhanced NMR spectroscopy for the identification of 36 common metabolites present in Coriandrum sativum L. seed extract. The identified metabolites belong to the following classes: organic acids, amino acids, and carbohydrates. ¹H NMR spectra of such complex mixtures in general display tremendous signal overlap due to the presence of a large number of metabolites with closely resonating multiplet signals. This signal overlapping leads to ambiguity in an assignment, and hence, identification of metabolites becomes tedious or impossible in many cases. Therefore, the utility of pure-shift proton spectrum along the indirect (F₁) dimension of the F₁-PSYCHE-TOCSY spectrum is demonstrated for overcoming ambiguity in assignment of metabolites in crowded spectral regions from Coriandrum sativum L. seed extract sample. Because pure-shift NMR methods yield ultrahigh resolution spectrum (i.e., a singlet peak per chemical site) along one or more dimensions, such spectra provide better identification of metabolites compared with regular 2D TOCSY where signal overlap and peak distortions lead to ambiguity in the assignment. Nine metabolites were unambiguously assigned by pure-shift F₁-PSYCHE-TOCSY spectrum, which was unresolved in regular TOCSY spectrum.