The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

The optical properties of monocrystalline, intrinsic silicon are interest for technological applications as well fundamental studies atom-surface interactions. For an enhanced understanding, it is great to explore analytic models which able fit the experimentally determined dielectric function $\epsilon(T_\Delta, \omega)$, over a wide range frequencies and temperature parameter $T_\Delta = (T-T...

We illustrate a general technique for evaluating photonic band structures in periodic d -dimensional microstructures in which the dielectric constant epsilon (omega) exhibits rapid variations with frequency omega . This technique involves the evaluation of generalized electromagnetic dispersion surfaces omega ( k--> ,epsilon) in a (d+1) -dimensional space consisting of the physical d -dimension...

Restricted star colouring is a variant of introduced to design heuristic algorithms estimate sparse Hessian matrices. For $k\in\mathbb{N}$, $k$-restricted ($k$-rs colouring) graph $G$ function $f:V(G)\to{0,1,\dots,k-1}$ such that (i)$f(x)\neq f(y)$ for every edge $xy$ G, and (ii) there no bicoloured 3-vertex path ($P_3$) in with the higher colour on its middle vertex. We show $k\geq 3$, it NP-c...

Abstract We investigate some key analytic properties of Fourier coefficients and Hecke eigenvalues attached to scalar-valued Siegel cusp forms $F$ degree 2, weight $k,$ level $N$. First, assuming that is a eigenform not Saito–Kurokawa type, we prove an improved bound in the $k$-aspect for smallest prime at which its eigenvalue negative. Secondly, show there are infinitely many sign changes amon...

(K(x),Na(1-x))NbO(3) (KNN) thin films were deposited on (001)SrRuO(3)/(001)Pt/(001)MgO substrates by RF-magnetron sputtering, and their piezoelectric properties were investigated. The x-ray diffraction measurements indicated that the KNN thin films were epitaxially grown with the c-axis orientation in the perovskite tetragonal system. The lattice constant of the c-axis increased with increasing...

The solvent dielectric constant is considered an important factor in determining the redox potential of the heme-containing protein cytochrome c in solution. In this study, we investigate the electrochemical response of cytochrome c in aqueous/organic solvent mixtures (100% aqueous buffer, 30% acetonitrile, 40% dimethyl sulfoxide, and 50% methanol), reporting the redox potential (E degrees'), e...

The detailing of the intermolecular interactions in dense solid oxygen is essential for an understanding of the rich polymorphism and remarkable properties of this element at high pressure. Synchrotron inelastic x-ray scattering measurements of oxygen K-edge excitations to 38 GPa reveal changes in electronic structure and bonding on compression of the molecular solid. The measurements show that...

The population relaxation of the OD stretching vibration of HOD diluted in H(2)O is studied by time-resolved infrared pump-probe spectroscopy for temperatures between 278 and 663 K in the density range 0.281 OD stretching transition at low temperatures show a delay between excited state decay and formation of the therm...

Zinc isotope separations were studied by displacement chromatography using the chelating properties of malate, citrate and lactate exchange resin and EDTA as ligands. After each chromatographic operation, the heavier zinc isotopes were found to preferentially fractionated into the carboxylate complex solution phase. The separation coefficients (epsilon) for zinc isotope separation had the large...