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.     

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.     

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.     

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.     

Applications of Fruit Polyphenols and Their Functionalized Nanoparticles Against Foodborne Bacteria: A Mini Review

The ingestion of contaminated water and food is known to cause food illness. Moreover, on assessing the patients suffering from foodborne disease has revealed the role of microbes in such diseases. Concerning which different methods have been developed for protecting food from microbes, the treatment of food with chemicals has been reported to exhibit an unwanted organoleptic effect while also affecting the nutritional value of food. Owing to these challenges, the demand for natural food preservatives has substantially increased. Therefore, the interest of researchers and food industries has shifted towards fruit polyphenols as potent inhibitors of foodborne bacteria. Recently, numerous fruit polyphenols have been acclaimed for their ability to avert toxin production and biofilm formation. Furthermore, various studies have recommended using fruit polyphenols solely or in combination with chemical disinfectants and food preservatives. Currently, different nanoparticles have been synthesized using fruit polyphenols to curb the growth of pathogenic microbes. Hence, this review intends to summarize the current knowledge about fruit polyphenols as antibacterial agents against foodborne pathogens. Additionally, the application of different fruit extracts in synthesizing functionalized nanoparticles has also been discussed.     

Enhancement of the properties and mesophases stability after the electron beam irradiation on a racemic anti-ferroelectric liquid crystalline mixture

The display parameters and the stability of the various mesophases of a newly synthesised racemic mixture of anti-ferroelectric liquid crystals (AFLCs) have been boosted with the help of the electron beam irradiation. The mixture has phase sequence of isotropic–smectic C–smectic C_A crystal. The effective macroscopic polarisation and transition temperatures of the various mesophases of the irradiated mixture have increased as compared with the pure mixture. The macroscopic polarisation of the mixture has increased from 21 to 27 nC/cm² due to the irradiation. From various studies, we have observed that the temperature range of the smectic C_A phase has increased by 20.6°C with marginal decrease in the temperature range of the smectic C phase.     

Synthesis of angular triquinanes from 1-Alkynylbicyclo[3.2. 0]hept-2-en-7-ones. A tandem alkoxy-cope ring Expansion/Transannular ring closure reaction

Addition of ethenyllithium reagents to the carbonyl group of dialkyl squarate-derived 1-alkynylbicyclo[3.2.0]hept-2-ene-7-ones (15), followed by a TBAF workup, results in a low-temperature anion-accelerated alkoxy-Cope rearrangement which proceeds by way of a strained cyclic allene intermediates (e.g.,17). This leads to the formation of angularly fused triquinanes (e.g., 20) in which each of the rings is functionally differentiated. Bicyclo[6.3. 0]undecadienones (e.g., 36) are the major products when the reactions are quenched with aqueous bicarbonate rather than TBAF. Under analogous conditions 2-alkylidene-1-alkynylbicyclo[3.2. 0]heptan-7-ones also give bicyclo[6.3.0]undecadienones by a mechanism that was established to involve a 1,5-hydrgen shift in a strained allene intermediate. The synthetic scope and mechanism of these and related transformations are discussed.