Vol. 6 & Issue 2 ; Section C : Physical Sciences
Date : Feb.2016 to April 2016
A Theoretical Study of the Faraday Effect in a Semiconductor Cylindrical Quantum Wire and Evaluation of Faraday Rotation Angle (FR) as a Function of Photon Energy for a Given Radius of Wire 
Mrs. Raina Nasreen , Shyam Nandan Prasad and L.K. Mishra 

Abstract
Using the theoretical formulation of G G Jarailova and T G Ismailov (J Korean Phys. Soc.) and JiangLan Liu and K Chang (J Appl Phys Lett), we have theoretically studied the Faraday effect in a semiconductor cylindrical Quantum wire. We have evaluated Faraday rotation (FR) angle θF (abs. U) as a function of photon energy (eV) for various radius of wire R and different magnetic field B. Our theoretically evaluated results indicate that Faraday angle increases with decreasing radius of the wire and with increasing magnetic field. Our theoretically evaluated results are in good agreement with the other theoretical workers. Such types of studies will be quite beneficial in the field of nanoelectronics, magnetooptical recording and information display.

Variable Luminosity of Secondary Gamma Rays During the close Approach of The Mars to the Earth 
Nidhi Jain, Shubhra Tiwari, Sushil Kumar Gandhi, S. N. A. Jaaffrey 

Abstract
In order to investigate the variable luminosity for the cosmic shower of the Secondary Gamma Rays (SGRs), we employed scintillation detector on ground. The temporal variability is associated with the interaction of the extraterrestrial flux of the Galactic Cosmic Radiation (GCR) and Solar Energetic Particles (SEPs), with the rather denser gaseous components in the lower atmosphere of the Earth. We measured the additional perturbation in the SGRs due to Mars during its closest approach to Earth in the month of August 2003, which happened after the lapse of 58380 years. Although small in magnitude, but we were able to detect significant variability for SGRs luminosity in the range of 1.54.5 keV/sec for the prominent peaks which were present almost in every observed spectrum taken over the entire onemonth observations. Exponential model is fitted to examine the SGRs variability caused by the recession of Mars from its close approach. The obtained value of t= 3.5795 0.2968 is found close to the theoretical value of 3.8 within the limit of experimental error.

Spectral Study of EXO2030+375 Using RXTE Data 
Sushil Kumar Gandhi, Shubhra Tiwari, Nidhi Jain, & S.N.A. Jaaffrey 

Abstract
We report the spectral properties of the Xray pulsar EXO2030+375. The observations were made using Rossi Xray timing explorer space satellite. The spectral analysis is carried out for the flux of xray energy range 330 keV. The Xray continuum spetra of proportional counter array could be represented by a two component model, a power law with an exponential cutoff at higher energies and a blackbody. An iron line at about 6.46.6 keV was also included.High mass Xray binaries (HMXBs) were among the very first bright Xray sources detected and optically identified in the 1970s, comprising of a orbiting compact object around a massive OB class star. The compact object should be either a neutron star (NS) or black hole and is a strong Xray emitter from the gravitational energy of accretion of matter of the OB companion. The HMXBs, conventionally, can be further divided into two subgroups: those in which be star is primary (Be/Xray binary) and those in which the primary star is a supergiant (SG/Xray binary)1,2 .

A Theoretical Study of Faraday effect in a semiconductor hollow cylinder with finite thickness and evaluation of Faraday (FR) angle as a function of incident light energy for different values of thickness of quantum cylinder 
Mrs. Raina Nasreen, Shyam Nandan Prasad and L. K. Mishra 

Abstract
Using the theoretical formalism of G G Jabrailova and T G Ismailov (Optoelectronics and Advanced Materials (2010)) and D Dragoman (J Opt Soc Am (2005)), we have theoretically studied the interband FR in a semiconductor hollow quantum cylinder with parabolic confinement potential. Numerical results were obtained with GaAs/AlGaAs hollow cylinder. The selection rules for interband transitions in the fields of right and left circularly polarized light were obtained and the analytical formula for the FR angle has been derived. We evaluated the FR angle as a function of incident light energy for different values of the thickness of the hollow cylinder in the presence of magnetic field. We observed that FR angle oscillates between maxima and minima and the amplitude of the maxima and the distance between them increases with decreasing thicness of the wall. We have also shown the dependence of the overlap integral on quantum numer n and the dependence of the transition energy corresponding to the right and left circularly polarized light on the magnetic field. Our theoretically obtained results are in good agreement with the other theoretical workers.

Vibrational Assignments and Molecular Structure of 2Trifluromethy] Benzonitrile by HartreeFock and Density Functional Theory Calculations 
F. Liakath Ali Khan, G.Saravanan, A. Md. Sabeelullah Roomy 

Abstract
In this work, we will report a combined experimental and theoretical study on molecular structure, vibrational spectra and UV spectral analysis of 2[Trifluromethyl] benzonitrile (2[TFM]BN ). The FTIR solid phase (4000400 cm^{1}), and FTRaman spectra (350050 cm^{1}) of 2[TFM] BN was recorded. The molecular geometry, harmonic vibrational frequencies and bonding features of 2[TFM]BN in the ground state have been calculated by using ab initio HF/ 6311++G(d,p) and density functional methods (B3LYP) with 6311G(d,p)/ 6311++ G(d,p) as basis sets. The complete assignments were performed on basis of the TED of vibrational modes, calculated with SQM method. Stability of the molecule arising from hyper conjugative interactions, charge delocalization has been analyzed using NBO analysis. The UV spectrum was measured in ethanol solution. The energy and oscillator strength calculated by TDDFT method are in agreement with the experimental findings. The calculated HOMO and LUMO energies confirm that charge transfer occurs within the molecule. Calculation results were applied to simulate IR and Raman spectra of the title compound which show good agreement with observed spectra. MEP and Mulliken charges are also calculated.

Unbiased Linear Approximate MLEs for the Location and Scale Parameters of the HalfLogistic Distribution Under TypeII Right Censoring 
A. Vasudeva Rao and G. Ranga Babu 

Abstract
Since the ML method does not yield an explicit estimator for the scale parameter of halflogistic distribution even in complete samples, this paper provide a simple method of deriving a linear estimator, based on a TypeII right censored sample, by making linear approximations to the intractable terms of the likelihood equation of scale parameter. A Monte Carlo simulation study is made to investigate the performance of this new linear approximate MLE (LAMLE) in relation to MLE and Balakrishnan and Wong’s^{7} AMLE. Based on the LAMLE of scale parameter and the MLE of location parameter, we construct ‘unbiased’ LAMLEs for location and scale parameters of halflogistic distribution from TypeII right censored samples. When compared these estimators with the corresponding BLUEs based on exact variances, surprisingly, we found that these estimators are just as efficient as the BLUEs. Finally, we present some numerical examples to compare various estimators developed here.

Effect of Temperature and Light intensity on Growth of Pleurotus florida 
S. A. Shinde, A. B. Pandey and S. S. Patil 

Abstract
Study was conducted to study the effect of temperature and light intensity on the growth, yield of mushroom fruiting bodies of P. florida. Minimum spawn run period (14 to 19 days) and minimum period for formation of pin head (1721 days),fruiting bodies (20 – 25 days) was recorded at 25 0C. Maximum period for spawn run ( 26 to 32 days), pin head formation (31 – 35 days) and fruiting body formation (34 48 days) were reported at 15 ^{0}C. From study it was found that, with increase in temperature from 15 to 25^{0}C, the yield of mushroom fruiting bodies increased progressively and spawn run period decreased. With increase in period of light exposure from 5 to 14 hours/day and its intensity from 200 – 600 lx, the yield of mushroom was found to be increased. Maximum yield of mushroom fruiting bodies was found (780 gm/kg dry straw) when light exposure of 14 hours at 600 lx light intensity and minimum yield (230 gm/kg dry straw) was recorded to 5 hours of light exposure at 200 lx light intensity.

Study Some Factors Effecting Phase Shift In the Rotation Sensor 
Shatha.M.ALHilly, Afaf. F. Sultan 

Abstract
The effect of the angular velocity on the interference pattern of Mach Zehnder interferometer by using Sagnac effect had been investigated in this study.Different angular velocities (1.5°/sec, 3°/sec,4.5°/sec, and 6°/sec), different diameters of turns (0.22m, 0.4m, 0.6m, and o.75m) and different length of optical fibers (2.8m, 12.8m) were used to study the effect of phase shift. It has been found that any increase in each of the angular velocity, length of optical fiber and diameter of turn leads to an increase in the phase shift. Finally in comparing the experimental with theoretical results, it is found that, there is a good agreement between them.

Study of Excess Thermodynamic Parameters of Binary Liquid Mixtures of Methyl Benzoate with 1Nonanol at Different Temperatures 
G. Sridevi 

Abstract
The densities, viscosities and ultrasonic velocities of the binary liquid mixtures of Methyl Benzoate with 1Nonanol have been measured at temperatures 303.15K, 308.15K, 313.15K and 318.15K over the entire range of mole fraction of Methyl Benzoate. From the experimental data various thermo acoustical parameters namely adiabatic compressibility (β), free length (L_{f}), free volume (V_{f}), internal pressure (π_{i}),enthalpy (H) and Gibb’s free energy of activation have been evaluated. Excess values of the above parameters have also been calculated. The results are explained on the basis of molecular interactions present in these mixtures

Undirected ZeroDivisor Graphs of Commutative Ring 
Sapna Shrimali and Varta Teotia 

Abstract
For a commutative ring R, the zerodivisor graph of commutative ring is undirected graph and we are mentioned about ‘n’ module zerodivisor graph which are undirected where ‘n’ is nonprime and n. Zero divisor Graph is connected, where n≥6 is any finite number.

Chaos in Dynamical BoseEinstein Condensate 
Priyanka Verma , A. B. Bhattacherjee and Man Mohan 

Abstract
We examine the chaos in a 1D BoseEinstein condensate (BEC) in a periodically driven Optical Lattice (OL) potential. We numerically solve the GrossPitaevskii Equation (GPE) where the dynamical potential considered has time dependent phase detuning between the laser beams forming the OL. We investigate the effect of increasing the modulation coefficient in the system which enhances the chaos, while raising the OL height softens it. It is evident from the numerical simulations that, as the coefficient of modulation is increased BEC becomes more chaotic

Application of a Newly Developed Recurrence Matrix and Finite State Machines for Data Security 
Sheela Bhatt 

Abstract
In the present modern digitized world, information theory has its own importance. Today’s computer era demands more security over digital communications. Cryptography is one such useful security tool for transmission and reception of secret messages. This paper presents a new cryptography scheme. The objective of the paper is to construct a new Recurrence matrix and apply the same for security in data transmission using finite state machines.

Computing the ClujIlmenau Index of VPhenylenic Nanotubes and Nanotori 
Mohammad Reza Farahani, Muhammad Imran , DaeWon Lee and M.R. Rajesh Kanna 

Abstract
G(V,E) be a connected molecular graph without multiple edges and loops, with the vertex set V(G) and edge set E(G). A counting polynomial, called the Omega Ω(G,x), was proposed by M.V. Diudea. It is defined on the ground of “opposite edge strips” ops. Also, M.V. Diudea introduced a counting index for counting QOC strips in G on based the Omega polynomial, called the ClujIlmenau index CI(G) and is equal to CI(G)=[Ω(G,x)’^{2}Ω(G,x)’Ω(G,x)”]x=1. In this paper we compute an exact formula of the ClujIlmenau index for the VPhenylenic Nanotubes and Nanotori

A Theoretical Study for Search of Better Metal Plasmonic Materials and Evaluation of Quality Factor for Localized Plasmons Resonances (QLSPR) for Ag, Au, Na, K and Al Metals 
Chandeshwar Prasad , S.K. Shrivastav and L.K. Mishra 

Abstract
Using the theoretical formalism of P R West etal (Laser Photonic Rev. 2010) and M D Arnold & M G Blaber (Opt. Exp. 2009), we have theoretically studied the search of metals for better plasmonic materials. We have evaluated real and imaginary part of permittivities ε’ and ε” as a function of wavelength for metals like Ag, Au, Al and alkali metals Na, K, Li. Our theoretically evaluated results for ε’ and ε” indicate that ε’ is always negative and ε” is always positive for the above mentioned metals as a function of frequency. We have also evaluated the quality factor for localized surface plasmon resonance (QLSPR) as a function of frequency for these metals. Our theoretically evaluated results are in good agreement with the experimental data and also with other theoretical workers.

LRS Bianchi Type  V String Dust Cosmological Models with Decaying Vacuum Energy 
Varun Humad, Harish Nagar and Sapna Shrimali 

Abstract
We have investigated LRS Bianchi Type  V string dust cosmological models with decaying vacuum energy. To get the deterministic model of the universe, we assume that rest energy density (ρ) is equal to the string tension density(ρ) and vacuum energyΛ∝𝐻^{2}, H being mean Hubble parameter. Some physical and geometrical features of the model are also discussed.

A Theoretical Evaluation of Quality Factor of Surface PlasmonPolaritons (QSPP) As a Function of Wavelength (Nm) and Comparative Studies of Metals for Better Plasmonic Materials 
Chandeshwar Prasad , S.K. Shrivastav2 and L.K. Mishra 

Abstract
Using the theoretical formalism of P R West etal (Laser Photonic Rev. 2010) and H. Reather, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (SpringerVerlag, Berlin , 1988), we have theoretically evaluated Quality factor for surface plasmonpolaritons QSPP as a function of wavelength (nm) for metals like Ag, Au, Al, Na and K. We have also performed comparative studies of these metals by taking the maximum value of the quality factor for four wide applications. The comparative studies show that there is not a single clear choice for best lowloss plasmon materials (Metals) for all applications at all frequencies. It also suggest that a variety of materials combinations must be finetuned and optimizrd for individual studies and applications. An improved plasmonic material has the potential to make an enormous impact on both optics and nanoelctronics by allowing for a new generation of unparrelled device applications.

MarichevSaigoMaeda Fractional Calculus Operators Involving Generalized MittagLeffler Function 
Rajeev Kumar Gupta,* Bhupender Singh Shaktawat and Dinesh Kumar 

Abstract
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized MittagLeffler function defined by Salim and Faraj ^{1}. The considered generalized fractional calculus operators contain the Appell’s function _{3}F^{2} [p.224] as kernel and are introduced by Saigo and Maeda^{3}. The MarichevSaigoMaeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide extensions of the results given by Gupta and Parihar ^{4}, Saxena and Saigo ^{5}, Samko et al^{6}. On account of the general nature of the generalized MittagLeffler function and generalized Wright function, a number of known results can easily be found as special cases of our main results.

Power Function of CST Procedure Based on two PTS in FourStage Unbalanced Nested Designs 
Anita Mehta 

Abstract
In this paper we have been derived the expression for power and size of the CST procedure for fourstage partially balanced nested designs. Further, we have derived the formulae for power and size of the CST procedure for balance at thirdstage as well as at fourthstage within ith firststage. The power of CST procedure denoted by P_{T}(θ) can be obtained by adding different power components P_{11}, P_{12},P_{13} and P._{14} i.e. P_{T}(θ) )P_{11}+ P _{12}+ p _{13} + P_{14}.Where P_{11},P _{12 ,}P_{13} and P _{14} be the probabilities of events E_{11, }E_{12} , E _{13} and E _{14 } respectively.

RadiationType of Problems Using Generalized Hankel Type Integral Transformation 
V. R. Lakshmi Gorty 

Abstract
In this paper, the generalized Hankel type integral transformation of three real parameters is used to solve boundary value problems. Three problems of heat conduction in an infinite, semiinfinite and a finite circular cylinder bounded by given surfaces with radiationtype boundary value conditions are solved using the transforms

Linear Fractional NonHomogeneous Differential Equations with Jumarie Fractional Derivative 
Dinesh Kumar and Jitendra Daiya 

Abstract
In this paper we develop a method to solve the linear nonhomogeneous fractional differential equations, composed with Jumarie type Fractional Derivative. The solutions are obtained in terms of MittagLeffler functions, fractional sine and cosine functions. This method proposed by us is useful as it is having conjugation with the classical methods of solving nonhomogeneous linear differential equations composed via Jumarie fractional derivative, and also useful in understanding physical systems described by fractional differential equations.

A Note on 𝚽_{𝒅}Frames in Banach Spaces 
H. K. Pathak and Mayur Puri Goswami 

Abstract
In this note, we introduce and study a new notion of Φ_{𝑑}frames in Banach spaces. A necessary and sufficient condition for the existence of Φ_{𝑑} frames has been discussed. It has been proved that the linear homeomorphic image of a Φ_{𝑑} frame is a Φ_{𝑑} frame. In the sequel, we have shown the productivity of Φ_{𝑑}frames by realizing that the product of two Φ_{𝑑}frames in Banach spaces yields a Φ_{𝑑}frame. Finally, we provide an application of Φ_{𝑑}frame in boundary value problems

Single and MultiChannel Queuing Models (A Comparison Study) 
Tariq Ahmad Koka and V.H. Badshah 

Abstract
Queues or waiting lines are a common phenomenon in everyday life. The essence of this phenomenon is the low efficiency of queuing system. In this paper we treat two elementary queuing models. Attention is paid to methods for analysis of these models and also to application of queuing models. The queuing number, the service windows number, and the optimal service rate are investigated by means of queuing theory. The time of customer queuing is reduced. The customer satisfaction is increased. By the example, the results are effective and practical.

A Note on GSemiClosure and GSemiInterior 
J.K. maitra and H.K. tripathi 

Abstract
In this paper we have introduced the notions of gsemiclosure and gsemiinterior of a set in a generalized topological space and obtained its significant properties. We have constructed some important examples.

On Some Expansion Theorems Involving Confluent Hypergeometric_{2} 2F_{2} (x) Polynomial 
Yashoverdhan Vyas and Kalpana Fatawat 

Abstract
Recently, Rathie and Kılıçman (2014) employed Kummertype transformation for _{2} F _{2} (a,d +1;b,d ; x) to develop certain classes of expansions theorems for_{2}F_{2} (x) hypergeometric polynomial. Our aim is to deduce Kummertype transformation for_{2} F_{2} (a,d + 2;b,d ; x) and utilize it to develop some new expansion theorems for the confluent hypergeometric_{2} F_{2} (x) polynomial. We also obtain a wellknown result given by Kim et al. (Integral Transforms Spec. Funct. 23(6); 435444, 2012) and many other new results as particular cases of our theorems.

On transformation formulae for SrivastavaDaoust type qhypergeometric series 
Yashoverdhan Vyas , Kalpana Fatawat 

Abstract
We present here the qanalogues of certain transformations or reduction formulae for SrivastavaDaoust type double hypergeometric series. These reduction formulae are derived by utilizing the extended Bailey’s Transform developed and studied by Joshi and Vyas [Int. J. Math. Sci., (12), 2005, 19091927]. A number of wellknown qhypergeometric transformations are also obtained as special cases of our results
