Induced Gravity Theory from Noether Symmetry

We discuss the functional form of the potential and the non-minimal coupling in the scalar tensor gravity (induced gravity) theories as allowed by the Noether symmetry in the spatially homogenous and isotropic spacetime background. The solution of the field equations (for k=0) are presented by using the results obtained from the Noether symmetry. It has been observed that the potential and the coupling function obtained from the Noether symmetric approach do not satisfy the continuity equation for k=± 1. Finally we present an inflationary solution that goes over to the Einstein's gravity asymptotically as t .     

Matching polynomial coefficients and the Hosoya indices of poly(p-phenylene) graphs

A general approach to determine the matching polynomial (MP) of a graph with two parts connected by an edge is presented in matrix product that is ultimately used in deducing recursion formulas for obtaining the MP coefficients of linear and cylindrical poly(p-phenylene) (PPP) graphs. The Hosoya indices of linear and cylindrical PPPs are derived in terms of that of the two immediately preceding graphs as well as in analytical forms with the use of transfer matrices. Ambient condition density and bulk modulus of linear PPPs with 2–6 phenyl rings have been found to correlate well with the logarithm of their Hosoya indices. Excellent correlations of diameters with the logarithm of Hosoya indices and strain energies with the inverse of the logarithm of Hosoya indices for cylindrical PPPr with r (= 6–16, 18, 20) phenyl rings are obtained. The linear relation between the logarithm of Hosoya indices and diameter and the inverse relation between diameter and strain energy corroborate the fact.     

Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form

Three types of graphs of linear chains, viz. linear chains with unit increment or decrement in weight on one terminal vertex, linear chains with unit increment or decrement in weight on both the terminal vertices and linear chains with unit increment in weight on one terminal vertex and decrement in that on the other terminal vertex, have been considered. The symmetry plane fragmentation and graph squaring techniques have been exploited to express the eigenspectra of such graphs of linear chains in analytical form, and have subsequently been used to express the eigenspectra of graphs of linear chains and cycles with alternant vertex weights. The derived expressions for the eigenspectra have been used to obtain the eigenspectra of linear polyacenes, methylene-substituted linear polyacenes and cylindrical polyacene strips in analytical form.     

Noether Symmetry Study in General Scalar Tensor Theory

We present the gravitational coupling function and potential function in a General Scalar Tensor Theory from Noether symmetry approach. Some exact cosmological solutions are presented in the spatially flat, homogeneous and isotropic background. The solutions are exponentially expanding without any graceful exit from inflation. Also the solutions asymptotically reduce to Einstein's theory with finite value of the coupling function supporting the earlier claim of Santiago et al. Further it is shown that in a particular case the effective Newtonian constant is determined by the effective potential of the scalar field.     

Incorporation of ovalbumin within cationic octadecylamine monolayer and a comparative study with zwitterionic DPPC and anionic stearic acid monolayer

In this communication we demonstrated the incorporation of water-soluble surface-active protein OVA within an insoluble cationic ODA monolayer and compared with zwitterionic (DPPC) and anionic (SA) monolayer. The incorporation of OVA is found to be more in ODA as compared to that of DPPC and SA. The kinetics of protein adsorption in lipid monolayer gives the idea that unfolding of OVA is less in case of DPPC than SA and ODA. The pi-A isotherm and compressibility study gives the information about the different states of the protein-lipid mixed monolayer. At higher pressure, OVA tend to squeeze out from the lipids monolayer. High-resolution field emission scanning electron microscope (FE-SEM) images confirm this observation. The surface morphology of DPPC-OVA LB film is far better than ODA-OVA and SA-OVA LB film. OVA forms large irregular aggregates on SA and ODA monolayer. Fluorescence study reveals that protein structure is perturbed more in SA and ODA system compared to that of DPPC. The overall results indicate that DPPC monolayer is better to get protein lipid mixed film than SA and ODA monolayer.     

Interaction of glucose with hemoglobin: a study in aqueous solution and at the air-water interface using the Langmuir-Blodgett technique

Here, we report the glycosylation of human adult hemoglobin (Hb) studied in aqueous solution and at the air-water interface by the Langmuir-Blodgett (LB) technique. Pressure-area (π-A) and pressure-time (π-t) measurements show that the concentration of glucose (GLC) and interaction time have an effect on Hb molecular area as well as on surface activity. Solution studies by UV-vis absorption and emission spectroscopy show that the GLC can alter the local conformation of Hb to some extent at the tryptophan and heme residues. CD spectroscopic studies in solution indicate that the α-helix content increases in the presence of GLC at the secondary structure level, which may be the cause of an increased adsorption rate of Hb. Also, secondary structure calculation using FTIR technique in the LB film follows the decrease in α-helix and increase in β-sheet structure as well as the formation of intermolecular aggregates. AFM images of Hb in the LB film indicate the transition from globular to an ellipsoid-like structure of Hb in the presence of GLC. FTIR studies of the LB film support the AFM imaging and the analysis of π-t kinetics. The molecular docking study revealed that Val 1 and Lys 132 are the most favorable docked sites along with some other sites such as Hem 147, Trp 37, Asp 94, Tyr 145, Leu 91, His 143, Glu 43 etc. The overall study may predict the processes of interactions with the increased concentration of GLC on Hb as well as on other long lived proteins.     

Symmetry-adapted linear combinations for the eigenvalues and eigenvectors of reciprocal graphs

ABSTRACT

Three classes of reciprocal graphs, viz. monocycle (G^C_n), linear chain (G^L_n) and star (G^K_n) with reciprocal pairs of eigenvalues (λ, 1/λ), are well known. Reciprocal graphs of monocycle (G^C_n) and linear chain (G^L_n) are obtained by putting a pendant vertex to each vertex of simple monocycle (C_n) and simple linear chain (L_n), respectively. A star graph of such kind is obtained by attaching a pendant vertex to the central vertex and to each of the (n ? 1) peripheral vertices of the star graph (K_{1, (n?1)}). An n-fold rotational axis of symmetry for G^C_n and (n ? 1)-fold rotational axis of symmetry for G^K_n have been exploited for obtaining their respective condensed graphs. The condensed graph for G^L_n has been generated from that of G^C_n incorporating proper boundary conditions. Condensed graphs are lower dimensional graphs and are capable of keeping all eigeninformation in condensed form. Thus the eigensolutions (i.e. the eigenvalues and the eigenvectors) in analytical forms for such graphs are obtained by solving 2 × 2 or 4 × 4 determinants that in turn result in the charge densities and bond orders of the corresponding molecules in analytical forms. Some mathematical properties of the eigenvalues of such graphs have also been explored.     

Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether Symmetry

We present the gravitational coupling function () in the vacuum scalar-tensor theory as allowed by the Noether symmetry. We also obtain some exact cosmological solutions in the spatially homogeneous and isotropic background thereby showing that the attractor mechanism is not effective enough to reduce the theory to Einstein theory. It is observed that, asymptotically, the scalar tensor theory goes over to Einstein theory with a finite value of . This work thus supports earlier works in this direction.