On maximal area integral problem for analytic functions in the starlike family

For an analytic function $f$ defined on the unit disk $|z|<1$, let $\Delta(r,f)$ denote the area of the image of the subdisk $|z|<r$ under $f$, where $0<r\le 1$. In 1990, Yamashita conjectured that $\Delta(r,z/f)\le \pi r^2$ for convex functions $f$ and it was finally settled in 2013 by Obradovi\'{c} and et. al.. In this paper, we consider a class of analytic functions in the unit disk satisfying the subordination relation $zf'(z)/f(z)\prec (1+(1-2\beta)\alpha z)/(1-\alpha z)$ for $0\le \beta<1$ and $0<\alpha\le 1$. We prove Yamashita's conjecture problem for functions in this class, which solves a partial solution to an open problem posed by Ponnusamy and Wirths.Comment: 12 pages, 8 figures, 2 tables, submitted to a journa

On a generalization of close-to-convex functions

A motivation comes from {\em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference operator acting on analytic functions in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:\,|z|<1\}$. We use the terminology {\em $q$-close-to-convex functions} for the $q$-analog of close-to-convex functions. The $q$-theory has wide applications in special functions and quantum physics which makes the study interesting and pertinent in this field. In this paper, we obtain some interesting results concerning conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in the $q$-close-to-convex family. As a result we find certain dilogarithm functions that are contained in this family. Secondly, we also study the famous Bieberbach conjecture problem on coefficients of analytic $q$-close-to-convex functions. This produces several power series of analytic functions convergent to basic hypergeometric functions.Comment: 14 pages, to appear in a journal (this version of the paper may not be the final version

CPMD/GULP QM/MM Interface for Modeling Periodic Solids: Implementation and its Application in the Study of Y-Zeolite Supported Rhn_n Clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane-wave density functional theory based CPMD code and the empirical force-field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born-Oppenheimer and Car-Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel in order to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in {\alpha}-cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh$_n$ ; $n$=2 to 6) formed from Rh(C$_2$H$_4$)$_2$ complex adsorbed within a cavity of Y-zeolite in a reducible atmosphere of H$_2$ gas.Comment: 15 pages; 10 pages; Accepted in Journal of Computational Chemistry (2016

An Optimized Ion Trap Geometry to Measure Quadrupole Shifts of 171^{171}Yb+^+ Clocks

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the $^{171}$Yb-ion. This trap will produce nearly ideal harmonic potential where the quadrupole shifts due to the anharmonic components can be reduced by four orders of magnitude. This will be useful to reduce the uncertainties in the clock frequency measurements of the $6s~{^2}S_{1/2} \rightarrow 4f^{13} 6s^2 ~{^2}F_{7/2}$ and $6s~{^2}S_{1/2} \rightarrow 5d ~{^2}D_{3/2}$ transitions, from which we can deduce precise values of the quadrupole moments ($\Theta$s) of the $4f^{13} 6s^2 ~{^2}F_{7/2}$ and $5d ~{^2}D_{3/2}$ states. Moreover, it may be able to affirm validity of the measured $\Theta$ value of the $4f^{13} 6s^2 ~{^2}F_{7/2}$ state where three independent theoretical studies defer almost by one order in magnitude from the measurement. We also perform calculations of $\Theta$s using the relativistic coupled-cluster (RCC) method. We use these $\Theta$ values to estimate quadrupole shift that can be measured in our proposed ion trap experiment.Comment: 1 table, 5 figure

Non-abelian representations of the slim dense near hexagons on 81 and 243 points

We prove that the near hexagon $Q(5,2) \times \mathbb{L}_3$ has a non-abelian representation in the extra-special 2-group $2^{1+12}_+$ and that the near hexagon $Q(5,2) \otimes Q(5,2)$ has a non-abelian representation in the extra-special 2-group $2^{1+18}_-$. The description of the non-abelian representation of $Q(5,2) \otimes Q(5,2)$ makes use of a new combinatorial construction of this near hexagon

Neutron star matter with strange interactions in a relativistic quark model

The effect of strange interactions in neutron star matter and the role of the strange meson-hyperon couplings are studied in a relativistic quark model where the confining interaction for quarks inside a baryon is represented by a phenomenological average potential in an equally mixed scalar-vector harmonic form. The hadron-hadron interaction in nuclear matter is then realized by introducing additional quark couplings to $\sigma$, $\omega$, $\rho$, $\sigma^*$ and $\phi$ mesons through mean-field approximations. The meson-baryon couplings are fixed through the SU(6) spin-flavor symmetry and the SU(3) flavor symmetry to determine the hadronic equation of state (EoS). We find that the SU(3) coupling set gives the potential depth between $\Lambda$s around $-5$ MeV and favours a stiffer EoS.The radius for the canonical neutron star lies within a range of $12.7$ to $13.1$ km.Comment: 9 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1609.02708, arXiv:1702.0231

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Structure related optical properties of electron beam evaporated ZrO2:10%SiO2 thin films

ZrO2:10%SiO2 thinfilms have been deposited on fused silica substrate by reactive electron beam co-evaporation technique at different oxygen partial pressure. The structural analysis shows tetragonal phase with residual tensile stress in the films. The intensity of the tetragonal t(110) phase are found increasing with increasing oxygen pressure. The optical band gap is found increasing from 5.06 eV to 5.28 eV because of increasing crystalinity of monoclinic phase, while the film grain size remains almost constant with increase of oxygen pressure, concludes that the crystallite or grain size has no effect on the optical properties of the films. The dispersion of the refractive index is discussed in terms of single oscillator Wimple-DiDomenico model. The dispersion energy parameter better known as structural order parameter are found increasing with the intensity of t(110) phase. It is observed that films having higher value of order parameter show lower surface roughness which concludes that the local microstructure ordering can predominantly influence the grain morphology which in turn can lead to better surface for higher value of order parameter.Comment: 10 pages, 10 figures and one tabl

Nuclear symmetry energy in a modified quark meson coupling model

We study nuclear symmetry energy and the thermodynamic instabilities of asymmetric nuclear matter in a self-consistent manner by using a modified quark-meson coupling model where the confining interaction for quarks inside a nucleon is represented by a phenomenologically averaged potential in an equally mixed scalar-vector harmonic form. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to $\sigma$, $\omega$, and $\rho$ mesons through mean-field approximations. We find an analytic expression for the symmetry energy ${\cal E}_{sym}$ as a function of its slope $L$. Our result establishes a linear correlation between $L$ and ${\cal E}_{sym}$. We also analyze the constraint on neutron star radii in $(pn)$ matter with $\beta$ equilibrium

Characterization of Micro-Roughness Parameters and Optical Properties of Obliquely Deposited HfO2 Thin Films

Oblique angle deposited oxide thin films have opened up new dimensions in fabricating optical interference devices with tailored refractive index profile along thickness by tuning its microstructure by varying angle of deposition. Microstructure of thin films strongly affects surface morphology as well as optical properties. Since surface morphology plays an important role for the qualification of thin film devices for optical or other applications, it is important to investigate morphological properties. In present work, HfO2 thin films have been deposited at several oblique angles. Morphological statistical parameters of such thin films viz., correlation length, intrinsic roughness, fractal spectral strength, etc., have been determined through suitable modelling of extended power spectral density function. Intrinsic roughness and fractal spectral strength show an interesting behaviour with deposition angle and the same has been discussed in the light of atomic shadowing, re-emission and diffusion of ad-atoms. Further refractive index and thickness of such thin films have been estimated from transmission spectra. Refractive index and grain size depict an opposite trend with deposition angle and their variation has been explained by varying column slanting angle and film porosity with deposition angle.Comment: 23 pages including figure