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Magnetic fields on young, moderately rotating Sun-like stars - I: HD~35296 and HD~29615Feb 20 2015Observations of the magnetic fields of young solar-type stars provide a way to investigate the signatures of their magnetic activity and dynamos. Spectropolarimetry enables the study of these stellar magnetic fields and was thus employed at the T\'{e}lescope ... More

Nuclear Corrections in Neutrino Deep Inelastic Scattering and the Extraction of the Strange Quark DistributionJun 18 1998Jun 23 1998Recent measurement of the structure function $F_2^\nu$ in neutrino deep inelastic scattering allows us to compare structure function measured in neutrino and charged lepton scattering for the first time with reasonable precision. The comparison between ... More

Light-Cone Meson-Baryon Fluctuations and Single-Spin AsymmetriesJun 15 1998Feb 09 1999We show that energetically favored meson-baryon fluctuations present in the light-cone wave function of a transversely polarized proton can account for the left-right asymmetries measured in inclusive meson production processes.

Random Coupling of Chaotic Maps leads to Spatiotemporal SynchronisationMay 04 2002We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our system, randomly ... More

New results of the Berliner relativistic quark modelOct 27 1995It is pointed out that the recently measured left-right asymmetries in inclusive pion and lambda hyperon production processes are in very good agreement with the relativistic quark model, proposed some time ago. Further predictions based on this model ... More

On the dependence of the existence of the positive steady states on the rate coefficients for deficiency-one mass action systems: single linkage classMay 15 2013The Deficiency-One Theorem states that there exists a unique positive steady state in each positive stoichiometric class for weakly reversible deficiency-one mass action systems with one linkage class (regardless of the values of the rate coefficients). ... More

Existence of Positive Steady States for Weakly Reversible Mass-Action SystemsOct 12 2017Nov 28 2018We prove the following. For each weakly reversible mass-action system, there exists a positive steady state in each positive stoichiometric class.

On the defining equations of Rees algebra of a height two perfect ideal using the theory of $D$-modulesSep 20 2018Let $k$ be a field of characteristic zero, and $R=k[x_1, \ldots, x_d]$ with $d \geq 3$ be a polynomial ring in $d$ variables. Let $\m=(x_1, \ldots, x_d)$ be the homogeneous maximal ideal of $R$. Let $\mathcal{K}$ be the kernel of the canonical map $\alpha: ... More

On units generated by Euler systemsOct 08 2009In the context of cyclotomic fields, it is still unknown whether there exist Euler systems other than the ones derived from cyclotomic units. Nevertheless, we first give an exposition on how norm-compatible units are generated by any Euler system, following ... More

Ratchet effect in an underdamped periodic potential and its characterisationAug 28 2016Ratchet effect in a driven underdamped periodic potential system is studied. The presence of a space dependent and periodic friction coefficient, but with a phase difference with the symmetric periodic potential is shown to generate substantial ratchet ... More

Particle dynamics and Stochastic Resonance in Periodic potentialsSep 02 2016We have studied the dynamics of a particle in a periodically driven underdamped periodic potential. Recent studies have reported the occurrence of Stochastic Resonance (SR) in such systems in the high frequency regime, using input energy per period of ... More

Selmer Groups of Elliptic Curves with Complex MultiplicationOct 08 2009This paper contains some results regarding the Iwasawa module structure of Selmer groups of elliptic curves with complex multiplication.

Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage ClassMar 07 2019We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent.

Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in $L^p$Oct 25 2011We generalize the idea of a multiplier in two different ways and generalize a recent result of Geiss, Montomery-Smith and Saksman. First of all, we consider multipliers in the form of a vector acting on a scalar function. Using this technique we compute ... More

Hyers--Ulam stability of derivations and linear functionsJul 02 2013In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in consideration, ... More

Ribet's construction of a suitable cusp eigenformOct 08 2009Oct 16 2009This article gives a self-contained exposition on Ribet's construction of a Hecke eigenform of weight 2 with certain congruence properties.

Planar S-systems: PermanenceMay 25 2018We characterize permanence of planar S-systems. Further, we construct a planar S-system with three limit cycles.

Localization of Excitons by Molecular Layer Formation in a Polymer FilmJan 20 2005Atactic polystyrene of two different molecular weights (560900 g.mol-1 and 212400 g.mol-1) have been studied as spin-coated films of thickness varying from ~30 nm to ~250 nm, i.e., ~2Rg to ~12Rg where Rg is the unperturbed radius of gyration of polystyrene, ... More

Asymptotic Behavior of the $T^3 \times R$ Gowdy SpacetimesSep 16 1992We present new evidence in support of the Penrose's strong cosmic censorship conjecture in the class of Gowdy spacetimes with $T^3$ spatial topology. Solving Einstein's equations perturbatively to all orders we show that asymptotically close to the boundary ... More

Permanence of Weakly Reversible Mass-Action Systems with a Single Linkage ClassMar 07 2019Mar 13 2019We give a new proof of the fact that each weakly reversible mass-action system with a single linkage class is permanent.

On Quadratization of Pseudo-Boolean FunctionsApr 25 2014We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of terms based on ... More

The Mixmaster Spacetime, Geroch's Transformation and Constants of MotionSep 09 1993We show that for $U(1)$-symmetric spacetimes on $S^3 \times R$ a constant of motion associated with the well known Geroch transformation, a functional $K[h_{ij},\pi^{ij}]$, quadratic in gravitational momenta, is strictly positive in an open subset of ... More

Tunable Self-assembly of Au-nanoparticles with Near-Perfect MonodispersityMar 29 2006Au nanoparticles with near perfect monodispersity in shape and size self-assemble, very slowly and at room temperature, on polystyrene films for film thickness < 4R_{g}$, R_{g} being unperturbed polymer gyration radius. Nanoparticle shape and size can ... More

Non-universal dependence of spatiotemporal regularity on randomness in coupling connectionsApr 03 2008We investigate the spatiotemporal dynamics of a network of coupled nonlinear oscillators, modeled by sine circle maps, with varying degrees of randomness in coupling connections. We show that the change in the basin of attraction of the spatiotemporal ... More

Distribution of Husimi Zeroes in Polygonal BilliardsApr 26 1999The zeroes of the Husimi function provide a minimal description of individual quantum eigenstates and their distribution is of considerable interest. We provide here a numerical study for pseudo- integrable billiards which suggests that the zeroes tend ... More

A q-deformed nonlinear mapAug 19 2004A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic ... More

Evidence of universality for the May-Wigner stability theorem for random networks with local dynamicsFeb 02 2004Apr 29 2005We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of nodes that persist ... More

Balance of interactions determines optimal survival in multi-species communitiesAug 21 2015We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric matrix J, with fraction 1-C of zero entries, where C reflects the over-all connectivity of the system. The non-zero elements ... More

Robust Emergent Activity in Dynamical NetworksOct 22 2005We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a ... More

On A New Asymptotic Norming PropertyOct 16 1995In this work, we introduce a new Asymptotic Norming Property (ANP) which lies between the strongest and weakest of the existing ones, and obtain isometric characterisations of it. The corresponding w*-ANP turns out to be equivalent on the one hand, to ... More

Spin content of Lambda and its longitudinal polarization in $e^+e^-$ annihilation at high energiesMar 03 1998Longitudinal polarization of Lambda produced in $e^+e^-$ annihilation at LEP energies is calculated in a picture for the spin content of Lambda which is consistent with the polarized deep inelastic lepton-nucleon scattering data and SU(3) flavor symmetry ... More

Pion Exchange and the H1 Forward Spectrometer DataDec 07 1998Mar 02 1999We point out that the $\Delta\pi$ component of the nucleon wave function is vital to the interpretation of the recent H1 data for leading baryon production. While the $n/p$ ratio is equal to two with the $N\pi$ component alone, the inclusion of the $\Delta\pi$ ... More

Single spin asymmetries in inclusive high energy hadron-hadron collision processesJan 31 2000It has been realized for quite a long time that single-spin experiments, in which one of the colliding objects is transversely polarized, can be helpful in studying the properties of strong interaction in general and in testing Quantum Chromodynamics ... More

Lambda polarization and single-spin left-right asymmetry in diffractive hadron-hadron collisionsJan 31 2000We discuss Lambda polarization and single-spin left-right asymmetry in diffractive hadron-hadron scattering at high energies. We show that the physical picture proposed in a recent Letter is consistent with the experimental observation that $\Lambda$ ... More

Bounding Hilbert coefficients of parameter idealsNov 10 2016Let $(R,\mathfrak{m})$ be a Noetherian local ring of dimension $d>0$ and depth R$\geq d-1$. Let $Q$ be a parameter ideal of $R$. In this paper, we derive uniform lower and upper bounds for the Hilbert coefficient $e_i(Q)$ under certain assumptions on ... More

Supercongruences for truncated hypergeometric series and p-adic gamma functionJul 27 2015Sep 03 2015We prove several supercongruences for truncated hypergeometric series and $p$-adic Gamma function. Recently, A. Deines, J. Fuselier, L. Long, H. Swisher and F. Tu posed some open problems on supercongruences based on numeric observations. We prove one ... More

A characterization of a prime $p$ from the binomial coefficient ${n \choose p}$Sep 07 2012May 01 2014We complete a proof of a theorem that was inspired by an Indian Olympiad problem, which gives an interesting characterization of a prime number $p$ with respect to the binomial coefficients ${n\choose p}$. We also derive a related result which generalizes ... More

Periodic Sequences modulo $m$Sep 10 2012Sep 26 2015We give a few remarks on the periodic sequence $a_n=\binom{n}{x}~(mod~m)$ where $x,m,n\in \mathbb{N}$, which is periodic with minimal length of the period being $$\ell(m,x)={\displaystyle\prod^w_{i=1}p^{\lfloor\log_{p_i}x\rfloor+b_i}_i}=m{\displaystyle\prod^w_{i=1}p^{\lfloor\log_{p_i}x\rfloor}_i}$$ ... More

A Study of Kummer's Proof of Fermat's Last Theorem for Regular PrimesJul 11 2013We study Kummer's approach towards proving the Fermat's last Theorem for regular primes. Some basic algebraic prerequisites are also discussed in this report, and also a brief history of the problem is mentioned. We review among other things the Class ... More

An Interesting Number Theoretic ProblemAug 13 2012In this short note we prove a result that is an extension of an old Olympiad problem and is a very simple variant of the question of finding an approximation for $k$, where it is a nonzero constant and it satisfies the equation $a^k+b^k=c$, where $a,b,c$ ... More

Summation identities and transformations for hypergeometric seriesSep 22 2016We find summation identities and transformations for the McCarthy's $p$-adic hypergeometric series by evaluating certain Gauss sums which appear while counting points on the family $$Z_{\lambda}: x_1^d+x_2^d=d\lambda x_1x_2^{d-1}$$ over a finite field ... More

Hyperon production mechanisms and single-spin asymmetry in high energy hadron-hadron collisionsOct 17 1995It is shown that the existence of left-right asymmetry in single-spin inclusive Lambda production, together with the characteristic features of the data, should be considered as another clear signature for the existence of orbiting valence quarks in polarized ... More

Suppression of chaos through coupling to an external chaotic systemJul 02 2016We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system manages to suppress ... More

Control of Hierarchical Networks by Coupling to an External Chaotic SystemJun 02 2018We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the mean-field of the ... More

Dynamic Transitions in Small World Networks: Approach to EquilibriumJul 07 2005We study the transition to phase synchronization in a model for the spread of infection defined on a small world network. It was shown (Phys. Rev. Lett. {\bf 86} (2001) 2909) that the transition occurs at a finite degree of disorder $p$, unlike equilibrium ... More

Numerical simulations of particle sedimentation using the immersed boundary methodApr 02 2013Nov 07 2013We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction problem is simulated ... More

Landen transformations and the integration of rational functionsJul 26 2007We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm for the numerical ... More

Polarization of radio cores as a test of the unified schemesNov 20 1998In the unified schemes for extragalactic radio sources, the quasars and BL Lac objects are intrinsically similar to the Fanaroff-Riley class II and I radio galaxies respectively, but appear to be different because they are viewed at different angles to ... More

Certain character sums and hypergeometric seriesFeb 13 2018We prove two transformations for the $p$-adic hypergeometric series which can be described as $p$-adic analogues of a Kummer's linear transformation and a transformation of Clausen. We first evaluate two character sums, and then relate them to the $p$-adic ... More

Explicit Solutions for $u^{2}-pv^{2}=\pm 2$ and a Conjecture of MordellOct 14 2018We obtain an explicit solution of the Pell's equation ${{u^{2}-pv^{2}=\pm 2}}$ in terms of the convergents of the continued fraction of the prime $p$. Then we show that Mordell's conjecture concerning the fundamental unit of $\mathbb{Q}(\sqrt{p})$ holds ... More

Graded components of Local cohomology modules IIAug 04 2017Let $A$ be a commutative Noetherian ring containing a field $K$ of characteristic zero and let $R= A[X_1, \ldots, X_m]$. Consider $R$ as standard graded with $\deg A=0$ and $\deg X_i=1$ for all $i$. We present a few results about the behavior of the graded ... More

Hyperon polarization and single spin left-right asymmetry in inclusive production processes at high energiesAug 29 1997Nov 25 1997It is shown that the polarization of hyperons observed in high energy collisions using unpolarized hadron beams and unpolarized nucleon or nuclear targets is closely related to the left-right asymmetries observed in single spin inclusive hadron production ... More

A dichotomy property for the graphs of monomialsOct 30 2014Jul 31 2015We prove that the graph of a discontinuous $n$-monomial function $f:\mathbb{R}\to\mathbb{R}$ is either connected or totally disconnected. Furthermore, the discontinuous monomial functions with connected graph are characterized as those satisfying a certain ... More

Protocols for characterizing quantum transport through nano-structuresMay 17 2012Sep 05 2012In this work, we have analyzed the exact closed-form solutions for transport quantities through a mesoscopic region which may be characterized by a polynomial functional of resonant transmission functions. These are then utilized to develop considerably ... More

Graded components of local cohomology modules of invariant ringsSep 28 2017Let $A$ be a regular domain containing a field $K$ of characteristic zero, $G$ be a finite subgroup of the group of automorphisms of $A$ and $B=A^G$ be the ring of invariants of $G$. Let $S= A[X_1,\ldots, X_m]$ and $R= B[X_1, \ldots, X_m]$ be standard ... More

Linear Hahn Banach Type Extension Operators in Banach Algebras of OperatorsOct 07 2017The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz (1982). Previously, J. Lindenstrauss (1966) studied similar versions of this notion in the context of non separable reflexive Banach spaces. Subsequently, ... More

Supercongruences for truncated hypergeometric series and p-adic gamma functionJul 27 2015Jul 10 2018We prove three more general supercongruences between truncated hypergeometric series and $p$-adic Gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez-Villegas and proved by E. Mortenson using the theory ... More

Enumeration of Domino Tilings of an Aztec Rectangle with boundary defectsMay 30 2016Helfgott and Gessel gave the number of domino tilings of an Aztec Rectangle with defects of size one on the boundary of one side. In this paper we extend this to the case of domino tilings of an Aztec Rectangle with defects on all boundary sides.

Quantum critical Mott transitions in a bilayer Kondo insulator-metal model systemNov 20 2015Sep 09 2016A bilayer system comprising a Kondo insulator coupled to a simple metal (KI-M) is considered. Employing the framework of dynamical mean field theory, the model system is shown to exhibit a surface of quantum critical points (QCPs), that separates a Kondo ... More

How Crucial is Small World Connectivity for Dynamics?May 21 2004We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties occur only at ... More

The bend elastic constant in a mixture of (4,4')-n-octyl-cyanobiphenyl and biphenylMar 12 2001The effect of a rigid, non-polar and nonmesogenic solute biphenyl ((C_{6}H_{5}-C_{6}H_{5})) on the divergence of the bend elastic constant K_{33} of (4,4^{\prime}) -n-octyl-cyanobiphenyl (8CB) near the smecticA-nematic transition is reported. The exponent ... More

The $L^p-$Operator Norm of a Quadratic Perturbation of the Real Part of the Ahlfors--Beurling OperatorSep 19 2011Sep 22 2011We will explain how to compute the exact $L^p$ operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a new approach of constructing a sequence of laminates (probability measures ... More

Equistarable bipartite graphsFeb 23 2015Recently, Milani\v{c} and Trotignon introduced the class of equistarable graphs as graphs without isolated vertices admitting positive weights on the edges such that a subset of edges is of total weight $1$ if and only if it forms a maximal star. Based ... More

On global stability of the Lotka reactions with generalized mass-action kineticsNov 17 2016Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and ... More

Deterministic inhomogeneous inertia ratchetsApr 05 2010We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the potential ... More

A radio study of the superwind galaxy NGC1482Nov 23 2004We present multifrequency radio continuum as well as HI observations of the superwind galaxy NGC1482, with both the GMRT and the VLA. This galaxy has a remarkable hourglass-shaped optical emission line outflow as well as bi-polar soft X-ray bubbles on ... More

Dispersionless motion in a driven periodic potentialAug 07 2009Recently, dispersionless (coherent) motion of (noninteracting) massive Brownian particles, at intermediate time scales, was reported in a sinusoidal potential with a constant tilt. The coherent motion persists for a finite length of time before the motion ... More

HI absorption towards low luminosity radio-loud AGNs of different accretion modes and WISE coloursJul 04 2016Oct 18 2016H{\sc i} absorption studies of active galaxies enable us to probe their circumnuclear regions and the general interstellar medium, and study the supply of gas which may trigger the nuclear activity. In this paper, we investigate the detection rate of ... More

Froissart Bound and Transverse Momentum Dependent Parton Distribution Functions (TMDPDF) with self-similarityOct 12 2017Froissart Bound implies that the total proton-proton cross-section (or equivalently structure function) cannot rise faster than the logarithmic growth $\log^2 s \sim \log^2 (1/x)$, where \textit{s} is the square of the center of mass energy and \textit{x} ... More

On some families of integrals solvable in terms of polygamma and negapolygamma functionsMay 09 2003Beginning with Hermite's integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type $\int_0^\infty f(t)K(q,t)dt$ with ... More

Unification scheme and the distribution of neutral gas in compact radio sourcesMay 17 2006We examine the consistency of HI properties with the unification scheme for radio galaxies and quasars, and any correlation with the symmetry parameters for a sample of CSS and GPS sources. In our sample, 15 out of 23 galaxies exhibit 21-cm absorption ... More

Polarization asymmetry in CSS sources: evidence of AGN fuel?Apr 29 2003The compact steep spectrum and gigahertz peaked spectrum sources are widely believed to be young radio sources, with ages <10^6 yr. If the activity in the nucleus is fuelled by the supply of gas, one might find evidence of this gas by studying the structural ... More

Recurrent Activity in Active Galactic NucleiFeb 09 2010There has been a growing body of evidence to suggest that AGN activity, which is powered by mass accretion on to a supermasive black hole, could be episodic, although the range of time scales involved needs to be explored further. The structure and spectra ... More

Double-double radio galaxies from the FIRST surveyAug 09 2012The radio structures and optical identifications of a sample of 242 sources classified as double-double radio sources by Proctor (2011) from a morphological study of sources in the FIRST (Faint Images of the Radio Sky at Twenty centimeters) survey (2003 ... More

An HI study of three long-tailed irregular galaxies in the cluster Abell1367Jun 21 2007We present the results on the distribution and kinematics of H$\sc{i}$ gas with higher sensitivity and in one case of higher spectral resolution as well than reported earlier, of three irregular galaxies CGCG 097073, 097079 and 097087 (UGC 06697) in the ... More

Singularity free analysis of a self-similar model of proton structure function at small \textit{x}Sep 01 2014In this paper we make re-analysis of a self-similarity based model of the proton structure function at small \textit{x} pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range $0<\textit{x}<1$. ... More

A Simple Number Theoretic ResultJul 28 2012We derive an interesting congruence relation motivated by an Indian Olympiad problem. We give three different proofs of the theorem and mention a few interesting related results.

Transverse Momentum Dependent Parton Distributions with self-similarity at small $x$ and models of proton structure functionMay 04 2016In this paper we make re-analysis of a self-similarity based model of the proton structure function at small $x$ pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range $0\leq \textit{x}\leq ... More

Some remarks on extrapolation with "flat" weightsApr 18 2012We prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded on some L^{p_{0}}(w), for all "flat" weights, w in A_{p_{0}}, 1 < p_{0} ... More

On Equistable, Split, CIS, and Related Classes of GraphsMay 21 2015We consider several graphs classes defined in terms of conditions on cliques and stable sets, including CIS, split, equistable, and other related classes. We pursue a systematic study of the relations between them. As part of this study, we introduce ... More

The 2-adic valuation of the coefficients of a polynomialAug 07 2003In this paper we compute the 2-adic valuations of some polynomials associated with the definite integral $\int_{0}^{\infty} \frac{dx}{(x^4+2*a*x^2+1)^(m+1)}$

Ratchet effect in inhomogeneous inertial systems: II. The square-wave drive caseJul 28 2008The underdamped Langevin equation of motion of a particle, in a symmetric periodic potential and subjected to a symmetric periodic forcing with mean zero over a period, with nonuniform friction, is solved numerically. The particle is shown to acquire ... More

Radio bubbles in the composite AGN-starburst galaxy NGC6764Jul 20 2006We present multi-frequency radio continuum as well as HI observations of the composite galaxy NGC6764, which has a young, circumnuclear starburst and also harbours an active galactic nucleus (AGN). These observations have been made at a number of frequencies ... More

Froissart bound and self-similarity based models of proton structure functionsApr 11 2017Froissart Bound implies that the total proton-proton cross-section (or equivalently structure function) cannot rise faster than the logarithmic growth $\log^2 s \sim \log^2 1/x$, where \textit{s} is the square of the center of mass energy and \textit{x} ... More

Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial SequencesSep 19 2012Jun 10 2015In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, ... More

A new proof of Lucas' TheoremJan 16 2013We give a new proof of Lucas' Theorem in elementary number theory.

An attempt for an Emergent Scenario with Modified Chaplygin GasJan 06 2016The present work is an attempt for emergent universe scenario with modified Chaplygin gas. The universe is chosen as spatially flat FRW space-time with modified Chaplygin gas as the only cosmic substratum. It is found that emergent scenario is possible ... More

Evidence for directed percolation universality at the onset of spatiotemporal intermittency in coupled circle mapsOct 16 2002We consider a lattice of coupled circle maps, a model arising naturally in descriptions of solid state phenomena such as Josephson junction arrays. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation ... More

Effect of asynchronicity on the universal behaviour of coupled map latticesMay 10 2002We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchronous (parallel) updating on one hand and asynchronous (random) updating rules on the other. Synchronous evolution of extended spatiotemporal systems, such ... More

On CIS CirculantsFeb 14 2013A circulant is a Cayley graph over a cyclic group. A well-covered graph is a graph in which all maximal stable sets are of the same size, or in other words, they are all maximum. A CIS graph is a graph in which every maximal stable set and every maximal ... More

Separable discrete functions: recognition and sufficient conditionsNov 17 2017A discrete function of $n$ variables is a mapping $g : X_1 \times \ldots \times X_n \rightarrow A$, where $X_1, \ldots, X_n$, and $A$ are arbitrary finite sets. Function $g$ is called {\em separable} if there exist $n$ functions $g_i : X_i \rightarrow ... More

New optimization algorithms for neural network training using operator splitting techniquesApr 29 2019In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique for some associated dynamical systems. Furthermore, we investigate through ... More

Electrical and magnetic transport study on strain driven ferromagnetic insulating thin film of low doped manganiteDec 31 2012In this paper we have created a strain driven single crystal like ferromagnetic insulating (FMI) state in a PLD grown thin film of low doped LCMO(X = 0.15)on NGO(100) substrate and make a thorough study of strain effects on the electric and magnetic transport ... More

Emergence of non-Fermi liquid dynamics through non-local correlations in an interacting disordered systemAug 14 2017Jul 12 2018We provide strong evidence of a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. A unique crossover energy scale, $\omega^*$ separating the ... More

Collimation of extragalactic radio jets in compact steep spectrum and larger sourcesApr 19 1999Oct 05 1999We study the collimation of radio jets in the high-luminosity Fanaroff-Riley class II sources by examining the dependence of the sizes of hotspots and knots in the radio jets on the overall size of the objects for a sample of compact steep-spectrum or ... More

Binomial Symbols and Prime ModuliSep 07 2012We try to improve a problem asked in an Indian Math Olympiad. We give a brief overview of the work done in Saikia and Vogrinc (2011) and Saikia and Vogrinc where the authors have found a periodic sequence and the length of its period, all inspired from ... More

Laminates Meet Burkholder FunctionsSep 22 2011Dec 07 2011We will explain how to compute the exact $L^p$ operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a new approach of constructing a sequence of laminates (probability measures ... More

Anticipating Persistent InfectionMay 04 2018We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual within a given range. We ... More

Threshold-activated transport stabilizes chaotic populations to steady statesApr 27 2017We explore Random Scale-Free networks of populations, modelled by chaotic Ricker maps, connected by transport that is triggered when population density in a patch is in excess of a critical threshold level. Our central result is that threshold-activated ... More

Emergence of Persistent Infection due to HeterogeneityMay 27 2016We explore the emergence of persistent infection in a patch of population, where the disease progression of the individuals is given by the SIRS model and an individual becomes infected on contact with another infected individual. We investigate the persistence ... More