Bivaraiate Generalized Baskakov Kantorovich Operators

This paper is in continuation of our work in \cite{PNM}, wherein we introduced generalized Baskakov Kantorovich operators $K_n^a(f;x)$ and established some approximation properties e.g. local approximation, weighted approximation, simultaneous approximation and $A-$statistical convergence. Also, we discussed the rate of convergence for functions having a derivative coinciding a.e. with a function of bounded variation. The purpose of this paper is to study the bivariate extension of the operators $K_n^a(f;x)$ and discuss results on the degree of approximation, Voronovskaja type theorems and their first order derivatives in polynomial weighted spaces.Comment: 1

Generalized Baskakov Kantorovich Operators

In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally, we obtain the rate of convergence for functions having a derivative coinciding almost everywhere with a function of bounded variation for these operator

Approximation by complex Szasz-Durrmeyer-Chlodowsky operators in compact disks

In the present article, we deal with the overconvergence of the Sz?asz-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic functions in compact disks. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. In such a way, we put in evidence the overconvergence phenomenon for the Sz?asz-Durrmeyer-Chlodowsky operators, namely the extensions of approximation properties with exact quantitative estimates and orders of these convergencies to sets in the complex plane that contain the interval [0,\infty)

Circular orbit spacecraft control at the L4 point using Lyapunov functions

The objective of this work is to demonstrate the utility of Lyapunov functions in control synthesis for the purpose of maintaining and stabilizing a spacecraft in a circular orbit around the L4 point in the circular restricted three body problem (CRTBP). Incorporating the requirements of a fixed radius orbit and a desired angular momentum, a Lyapunov function is constructed and the requisite analysis is performed to obtain a controller. Asymptotic stability is proved in a defined region around the L4 point using LaSalle's principle.Comment: Accepted for presentation at European Control Conference 201

Better approximation of functions by genuine Bernstein-Durrmeyer type operators

The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence

Constraining the symmetry energy content of nuclear matter from nuclear masses: a covariance analysis

Elements of nuclear symmetry energy evaluated from different energy density functionals parametrized by fitting selective bulk properties of few representative nuclei are seen to vary widely. Those obtained from experimental data on nuclear masses across the periodic table, however, show that they are better constrained. A possible direction in reconciling this paradox may be gleaned from comparison of results obtained from use of the binding energies in the fitting protocol within a microscopic model with two sets of nuclei, one a representative standard set and another where very highly asymmetric nuclei are additionally included. A covariance analysis reveals that the additional fitting protocol reduces the uncertainties in the nuclear symmetry energy coefficient, its slope parameter as well as the neutron-skin thickness in $^{208}$Pb nucleus by $\sim 50\%$. The central values of these entities are also seen to be slightly reduced.Comment: 6 pages, 2 figures, Accepted in Physical Review

Hierarchical Cellular Structures in High-Capacity Cellular Communication Systems

In the prevailing cellular environment, it is important to provide the resources for the fluctuating traffic demand exactly in the place and at the time where and when they are needed. In this paper, we explored the ability of hierarchical cellular structures with inter layer reuse to increase the capacity of mobile communication network by applying total frequency hopping (T-FH) and adaptive frequency allocation (AFA) as a strategy to reuse the macro and micro cell resources without frequency planning in indoor pico cells [11]. The practical aspects for designing macro- micro cellular overlays in the existing big urban areas are also explained [4]. Femto cells are inducted in macro / micro / pico cells hierarchical structure to achieve the required QoS cost effectively.Comment: 7 pages, 8 figures, International Journa

Lower Limits on the Strengths of Gamma Ray Lines from WIMP Dark Matter Annihilation

We study the spectra of gamma ray signals that arise from dark matter annihilation in the universe. We focus on the large class of theories where the photon spectrum includes both continuum spectrum of gamma rays that arise from annihilation into Standard Model states at tree level, as well as monochromatic gamma rays arising from annihilation directly into two photons at the one loop level. In this class of theories we obtain lower bounds on the ratio of the strength of the gamma ray line relative to the gamma ray continuum as a function of the dark matter mass and spin. These limits are obtained from the unitarity relation between the tree level amplitude of the primary annihilation channel and the imaginary part of the loop level amplitude for annihilation directly into photons, with the primary decay products running in the loop. These results are exact in the limit that dark matter annihilation is exclusively to a single Standard Model species, occurs through the lowest partial wave and respects CP. Away from this limit the bounds are approximate. Our conclusions agree with the known results in the literature in the case of the Minimal Supersymmetric Standard Model (MSSM). We use the Fermi-LAT observations to translate these limits into upper bounds on the dark matter annihilation cross section into any specific Standard Model state.Comment: 11 pages, 3 figures, 1 table ;v2: 14 pages, 6 figures, 2 tables, added discussion of effects of the continuum spectrum in the neighborhood of the line, matches version in PR

Reassessing nuclear matter incompressibility and its density dependence

Experimental giant monopole resonance energies are now known to constrain nuclear incompressibility of symmetric nuclear matter $K$ and its density slope $M$ at a particular value of sub-saturation density, the crossing density $\rho_c$. Consistent with these constraints, we propose a reasonable way to construct a plausible equation of state of symmetric nuclear matter in a broad density region around the saturation density $\rho_0$. Help of two additional empirical inputs, the value of $\rho_0$ and that of the energy per nucleon $e(\rho_0)$ are needed. The value of $K(\rho_0)$ comes out to be $211.9\pm 24.5$ MeV.Comment: 5 page including 4 figures. Phys. Rev. C (in press

Determining the density content of symmetry energy and neutron skin: an empirical approach

The density dependence of nuclear symmetry energy remains poorly constrained. Starting from precise empirical values of the nuclear volume and surface symmetry energy coefficients and the nuclear saturation density, we show how in the ambit of microscopic calculations with different energy density functionals, the value of the symmetry energy slope parameter $L$ alongwith that for neutron skin can be put in tighter bounds. The value of $L$ is found to be $L$= 64$\pm$5 MeV. For $^{208}$Pb, the neutron skin thickness comes out to be 0.188 $\pm$0.014 fm. Knowing $L$, the method can be applied to predict neutron skins of other nuclei.Comment: 5 pages, Phys. Rev. Lett. (accpeted