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Positive graphsMay 29 2012Jan 30 2014We study "positive" graphs that have a nonnegative homomorphism number into every edge-weighted graph (where the edgeweights may be negative). We conjecture that all positive graphs can be obtained by taking two copies of an arbitrary simple graph and ... More

A Whirlwind Tour of the World of $(\infty,1)$-categoriesMar 19 2013Sep 05 2013This introduction to higher category theory is intended to a give the reader an intuition for what $(\infty,1)$-categories are, when they are an appropriate tool, how they fit into the landscape of higher category, how concepts from ordinary category ... More

The mod 2 homology of free spectral Lie algebrasNov 27 2016The Goodwillie derivatives of the identity functor on pointed spaces form an operad in spectra. Adapting a definition of Behrens, we introduce mod 2 homology operations for algebras over this operad and prove these operations account for all the mod 2 ... More

Nilpotent $n$-tuples in $SU(2)$Nov 18 2016Let $F_n/\Gamma^q_n$ denote the finitely generated free $q$-nilpotent group. We describe the connected components of the spaces of homomorphisms $Hom(F_n/\Gamma^q_n,SU(2))$, $Hom(F_n/\Gamma^q_n,SO(3))$ and $Hom(F_n/\Gamma^q_n,U(2))$. We also describe ... More

Corrigendum to "Groupoids, the Phragmen-Brouwer Property, and the Jordan Curve Theorem", J. Homotopy and Related Structures 1 (2006) 175-183Apr 02 2014Aug 08 2014Omar Antol{\'\i}n Camarena pointed out a gap in the proofs in \cite{Brown15,BrownJordan} of a condition for the Phragmen--Brouwer Property not to hold; this note gives the correction in terms of a result on a pushout of groupoids, and some additional ... More

Chromatic fracture cubesOct 27 2014In this note, we construct a general form of the chromatic fracture cube, using a convenient characterization of the total homotopy fiber, and deduce a decomposition of the E(n)-local stable homotopy category.

A simple universal property of Thom ring spectraNov 28 2014We give a simple universal property of the multiplicative structure on the Thom spectrum of an $n$-fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax $\mathcal{O}$-monoidal functor. This allows ... More

Classifying spaces for commutativity of low-dimensional Lie groupsFeb 10 2018For each of the groups $G = O(2), SU(2), U(2)$, we compute the integral and $\mathbb{F}_2$-cohomology rings of $B_\text{com} G$ (the classifying space for commutativity of $G$), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy ... More

Topology of Fermi Surfaces and Anomaly InflowsSep 04 2015Aug 08 2016We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems with Born-von Karman ... More

Topology of Fermi Surfaces and anomaly inflowsSep 04 2015Nov 16 2016We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems on an infinite crystal ... More

Cosmological constraints on the radiation released during structure formationAug 31 2016Sep 06 2016During the process of structure formation in the universe matter is converted into radiation through a variety of processes such as light from stars, infrared radiation from cosmic dust and gravitational waves from binary black holes/neutron stars and ... More

On the classifying space for proper actions of groups with cyclic torsionJul 04 2011Oct 24 2011In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of products of locally ... More

The Haagerup property is stable under graph productsMay 29 2013Feb 21 2014The Haagerup property, which is a strong converse of Kazhdan's property $(T)$, has translations and applications in various fields of mathematics such as representation theory, harmonic analysis, operator K-theory and so on. Moreover, this group property ... More

A note on the Farrell-Jones conjecture for relatively hyperbolic groupsOct 22 2013Oct 27 2013For a group G relatively hyperbolic to a family of residually finite groups satisfying the Farrell-Jones conjecture, we reduce the solution of the Farrell-Jones conjecture for G to the case of certain nice cyclic extensions in G.

Nilspaces, nilmanifolds and their morphismsSep 20 2010Jun 10 2012Recent developments in ergodic theory, additive combinatorics, higher order Fourier analysis and number theory give a central role to a class of algebraic structures called nilmanifolds. In the present paper we continue a program started by Host and Kra. ... More

Farrell-Jones via Dehn fillingsOct 27 2015Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order elements have a certain structure of a free product. We then apply this result to show that groups ... More

Degree of commutativity of infinite groupsNov 23 2015We prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where the group has polynomial growth ... More

On the asymptotics of visible elements and homogeneous equations in surface groupsMay 12 2011Let $F$ be a group whose abelianization is $\Z^k$, $k\geq 2.$ An element of $F$ is called visible if its image in the abelianization is visible, that is, the greatest common divisor of its coordinates is 1. In this paper we compute three types of densities, ... More

Conjugacy in Houghton's GroupsMay 09 2013Jun 30 2014Let $n\in \mathbb{N}$. Houghton's group $H_n$ is the group of permutations of $\{1,\dots, n\}\times \mathbb{N}$, that eventually act as a translation in each copy of $\mathbb{N}$. We prove the solvability of the conjugacy problem and conjugator search ... More

Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic BeamsOct 13 2016The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately ... More

Kurosh rank of intersections of subgroups of free products of orderable groupsSep 01 2011Jan 21 2014We prove that the reduced Kurosh rank of the intersection of two subgroups $H$ and $K$ of a free product of right-orderable groups is bounded above by the product of the reduced Kurosh ranks of $H$ and $K$. In particular, taking the fundamental group ... More

I am 4 vho: new approach to improve seamless vertical hanover in heterogeneous wireless networksJun 06 2013Two mechanisms have been proposed independently by IEEE and 3GPP; namely, Media Independent Handover (MIH) and Access Network Discovery and Selection Function (ANDSF), respectively. These mechanisms enable a seamless Vertical Handover (VHO) between the ... More

Computation of the incomplete gamma function for negative values of the argumentAug 14 2016An algorithm for computing the incomplete gamma function $\gamma^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincar\'e-type expansions, uniform ... More

Wavelets in weighted norm spacesOct 17 2014We give a complete characterization of the classes of weight functions for which the Haar wavelet system for $m$-dilations, $m= 2,3,\ldots$ is an unconditional basis in $L^p(\mathbb{R},w)$. Particulary it follows that higher rank Haar wavelets are unconditional ... More

Role of intracluster supernovae in radio mini-halos in galaxy clustersFeb 08 2019A possibility of generating a population of cosmic-ray particles accelerated in supernovae typeIa (SNIa) remnants in the intracluster medium (ICM) is discussed. The presently constrained host-less SNIa rates in the clusters are found to be sufficient ... More

Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetryJul 13 2010Jul 20 2010The kinetic energy operator with position-dependent-mass in cylindrical coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed within radial cylindrical mass settings. Azimuthal symmetry is assumed and spectral ... More

Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signaturesMar 09 2007Aug 20 2007The (3+1)-dimensional Dirac equation with position dependent mass in 4-vector electromagnetic fields is considered. Using two over-simplified examples (the Dirac-Coulomb and Dirac-oscillator fields), we report energy-levels crossing as a spectral property ... More

A new deformed Schioberg-type potential and ro-vibrational energies for some diatomic moleculesSep 24 2014Apr 24 2015We suggest a new deformed Schioberg-type potential for diatomic molecules. We show that it is equivalent to Tietz-Hua oscillator potential. We discuss how to relate our deformed Schi\"oberg potential to Morse, to Deng-Fan , to the improved Manning-Rosen, ... More

Dirac and Klein-Gordon particles in complex Coulombic fields; a similarity transformationJan 14 2003Mar 06 2003The observation that the existance of the amazing reality and discreteness of the spectrum need not be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic ... More

On spectroscopic structure of two interacting electrons in a quantum dotFeb 07 2001Mar 12 2003The shifted 1/N expansion technique, used by El-Said (Phys. Rev. B 61, 13026 (2000)), to study the relative Hamiltonian of two interacting electrons confined in a quantum dot, is investigated. El-Said's results from SLNT are revised and results from an ... More

Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvabilityNov 17 2014May 08 2015A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related Euler-Lagrange equations ... More

Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetryNov 25 2007Jan 24 2008A non-Hermitian P$_{\phi}$T$_{\phi}$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H$_{r}$, H$_{\theta}$, and H$_{\phi}$ play essential roles and offer some user-feriendly options as ... More

On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfinedJan 27 2001Oct 10 2001The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt, their solution ... More

New variant of ElGamal signature schemeJan 15 2013In this paper, a new variant of ElGamal signature scheme is presented and its security analyzed. We also give, for its theoretical interest, a general form of the signature equation.

On the discretization of backward doubly stochastic differential equationsJul 09 2009In this paper, we are dealing with the approximation of the process (Y,Z) solution to the backward doubly stochastic differential equation with the forward process X . After proving the L2-regularity of Z, we use the Euler scheme to discretize X and the ... More

Position-dependent mass harmonic oscillator: classical-quantum mechanical correspondence and ordering-ambiguityAug 10 2012Feb 22 2013We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical and quantum position-dependent mass (PDM) oscillators. To elaborate on the ordering ambiguity, we properly amend some of the results reported in their work and discuss the classical ... More

Radial power-law position-dependent mass; Cylindrical coordinates, separability, and spectral signaturesApr 07 2011We discuss the separability of the position-dependent mass Hamiltonian in cylindrical coordinates in the framework of a radial power-law position-dependent mass. We consider two particular radial mass settings; a harmonic oscillator type, and a Coulombic ... More

On the ro-vibrational energies for the lithium dimer; maximum-possible rotational levelsJul 04 2014Mar 02 2015The Deng-Fan potential is used to discuss the reliability of the improved Greene-Aldrich approximation and the factorization recipe of Badawi et al.'s [17] for the central attractive/repulsive core. The factorization recipe is shown to be a more reliable ... More

Reply to the Comment 'On large-N expansion'Dec 13 2002Fernandez Comment [1] on our pseudo-perturbative shifted-l expansion technique [2,3] is either unfounded or ambiguous.

Complex geometric optics for symmetric hyperbolic systems II: nonlinear theory in one space dimensionFeb 12 2008This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \emph{naive} ... More

String model of the Hydrogen AtomJan 31 2007A non-moving electron hydrogen model is proposed, resolving a long standing contradiction (94 years) in the hydrogen atom. This, however, forces to not use the "in an orbit point particle kinetic energy" as the phenomenon responsible for the atom stability. ... More

Asymptotic solutions of pseudodifferential wave equationsNov 10 2004The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of electromagnetic ... More

The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics methodApr 26 2004Nov 04 2005The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, ... More

Is the Equation of State of strongly interacting matter observable ?Jun 06 2002I review the available empirical information on the equation of state of cold strongly interacting matter, as well as the prospects for obtaining new insights from the experimental study of gravitational waves emitted by neutron stars.

Interpretation of the Neutrino-Nucleus Cross SectionDec 05 2016I discuss the near-degeneracy between models of neutrino-nucleus interactions based on diverse assumptions, and analyze a specific example illustrating how the different reaction mechanisms taken into account, as well as the approximations associated ... More

Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$Dec 21 2012Mar 03 2014The Hecke algebra of the pair $(S_{2n},B_n)$, where $B_n$ is the hyperoctahedral subgroup of $S_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property ... More

Algorithm for factoring some RSA and Rabin moduliMar 21 2013In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on factoring integers. ... More

Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances modelJul 26 2009Oct 27 2010We study models of continuous-time, symmetric, $\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$ with a power law with an exponent $\gamma$ near 0. We are interested ... More

Note on the Heat-Kernel Decay for Random Walk among Random Conductances with Heavy TailMar 18 2009Dec 31 2009Results have been moved to a published article, see arXiv:0812.2669v4[math.PR]

$k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebraFeb 06 2019We generalize the concept of partial permutations of Ivanov and Kerov and introduce $k$-partial permutations. This allows us to show that the structure coefficients of the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra are polynomials ... More

Holograms in the brain: focusing arbitrary ultrasonic fields through the skull using holographic phase platesFeb 18 2019We report 3D-printed acoustic holographic lenses for the formation of ultrasonic fields of complex spatial distribution inside the skull. Using holographic lenses, we experimentally, numerically and theoretically produce acoustic beams whose spatial distribution ... More

Transgression forms as source for topological gravity and Chern-Simons-Higgs theoriesNov 06 2014Two main gauge invariant off-shell models are studied in this Thesis. I) Poincare-invariant topological gravity in even dimensions is formulated as a transgression field theory whose gauge connections are associated to linear and nonlinear realizations ... More

Area Versus Speed Trade-off Analysis of a WiMAX Deinterleaver Circuit DesignOct 10 2014Trade-off is one of the main design parameters in the field of electronic circuit design. Whereas smaller electronics devices which use less hardware due to techniques like hardware multiplexing or due to smaller devices created due to techniques developed ... More

Final state interactions in the nuclear response at large momentum transferJan 15 2013The convolution approach, widely employed to describe final state interactions in the response of many-body systems, is derived from the expression of the nuclear response in the zeroth-order ladder approximation. Within this framework, the folding function, ... More

A particular case of the Level increasing Conjecture for Type A fusion algebrasApr 27 2011A particular case of the level increasing conjecture for type A fusion coefficientes is proved for when one the weights is a multiple of the first fundamental weight.

Insecure primitive elements in an ElGamal signature protocolSep 04 2015Consider the classical ElGamal digital signature scheme based on the modular relation $\alpha^m\equiv y^r\, r^s\ [p]$. In this work, we prove that if we can compute a natural integer $i$ such that $\alpha^i\ mod\ p$ is smooth and divides $p-1$, then it ... More

Many-Body Theory of the Electroweak Nuclear ResponseJul 08 2008After a brief review of the theoretical description of nuclei based on nonrelativistic many-body theory and realistic hamiltonians, these lectures focus on its application to the analysis of the electroweak response. Special emphasis is given to electron-nucleus ... More

An algorithm for finding the Independence Number of a graphJan 03 2008Jan 09 2008In this paper, we prove that for every connected graph G, there exists a split graph H with the same independence number and the same order. Then we propose a first algorithm for finding this graph, given the degree sequence of the input graph G. Further, ... More

An algorithm for solving the Independent Set problemSep 17 2007Sep 21 2007This paper has been withdrawn by the author, due an error in claim 1.

The Flat DeuteronOct 18 2005The new model was applied to the femtometer toroidal structures found for the deuteron. It was possible to relate the magnetic moment and the energy of the particle to the torus geometric parameters. Excellent agreement between the magnetic moment of ... More

A different view of deep inelastic electron-proton scatteringDec 11 2000Deep inelastic electron-proton scattering is analyzed in the target rest frame using a theoretical approach suitable to describe many-body systems of {\em bound} constituents subject to {\em interactions}. At large three-momentum transfer $\magq$, this ... More

On Dirac equation for a Coulomb scalar, vector, and tensor interactionAug 30 2011In their recent paper (Inter. J. Mod. Phys. A 26 (2011) 1011), Zarrinkamar and coauthors have considered the radial Dirac equation for a Coulomb scalar, vector and tensor interaction. The exact solutions for the energy eigenvalues they have reported for ... More

On the nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator: Lagrange and Newton equations' equivalenceApr 19 2013Using a generalized coordinate along with a proper invertible coordinate transformation, we show that the Euler-Lagrange equation used by Bagchi et al. 16 is in clear violation of the Hamilton's principle. We also show that Newton's equation of motion ... More

Auxiliary quantization constraints on the von Roos ordering-ambiguity at zero binding energies; azimuthally symmetrized cylindrical coordinatesAug 29 2011Aug 01 2012Using azimuthally symmetrized cylindrical coordinates, we report the consequences of zero-energy quantal states on the von Roos Hamiltonian. A position-dependent mass M({\rho},\phi,z)=bz^{j}{\rho}^{2\u{psion}+1}/2 is used. We show that the zero-energy ... More

Perturbed Coulombic potentials in Dirac and Klein-Gordon equationsJul 10 2003Feb 17 2004A relativistic extension of our pseudo-shifted $\ell$-expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical ... More

Conditions on the generator for forging ElGamal signatureJan 14 2013This paper describes new conditions on parameters selection that lead to an efficient algorithm for forging ElGamal digital signature. Our work is inspired by Bleichenbacher's ideas.

A general framework for the polynomiality property of the structure coefficients of double-class algebrasApr 07 2015Take a sequence of couples $(G_n,K_n)_n$, where $G_n$ is a group and $K_n$ is a sub-group of $G_n.$ Under some conditions, we are able to give a formula that shows the form of the structure coefficients that appear in the product of double-classes of ... More

The Adaptive LQ RegulatorJan 14 2019The optimal adaptive control of a linear system in a signal-plus-noise setting with infinite horizon LQ regulator cost is studied. The class of partially observed linear systems for which the certainty equivalence property holds is identified. It is also ... More

Nuclear Physics with Electroweak ProbesFeb 26 2009In recent years, the italian theoretical Nuclear Physics community has played a leading role in the development of a unified approach, allowing for a consistent and fully quantitative description of the nuclear response to electromagnetic and weak probes. ... More

Matter and Light in FlatlandJan 28 2004Using a non-material current through three new dimensions. It was possible to build a particle-space model (a higher dimensional object intersecting a lower dimensional world). The new dimensions solve the old problem of equal sign walls huge electric ... More

Scaling in many-body systems and proton structure functionOct 17 2001The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system simply reflects the dominance of incoherent scattering off target constituents. While a suitably defined scaling function ... More

Global and local existence for the dissipative critical SQG equation with small oscillationsAug 04 2013Jun 03 2015This article is devoted to the study of the critical dissipative surface quasi-geostrophic $(SQG)$ equation in $\mathbb{R}^2$. For any initial data $\theta_{0}$ belonging to the space $\Lambda^{s} ( H^{s}_{uloc}(\mathbb{R}^2)) \cap L^\infty(\mathbb{R}^2)$, ... More

Schedulability Analysis of Distributed Real-Time Applications under Dependence and Several Latency ConstraintsJan 21 2013This paper focuses on the analysis of real-time non preemptive multiprocessor scheduling with precedence and several latency constraints. It aims to specify a schedulability condition which enables a designer to check a priori -without executing or simulating- ... More

Weak error expansion of the implicit Euler schemeApr 25 2013In this paper, we extend the Talay Tubaro theorem to the implicit Euler scheme.

On submeasures on Boolean algebrasDec 31 2012Mar 04 2013We present a collection of observations and results concerning submeasures on Boolean algebras. They are all motivated by Maharam's problem and Talagrand's construction that solved it.

On the Differentiability of Quaternion FunctionsMar 26 2012Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show that the elementary ... More

Large-scale multiscale particle models in inhomogeneous domains: modelling and implementationSep 13 2016In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each particle has ... More

Entangled Bloch Spheres: Bloch Matrix and Two Qubit State SpaceFeb 04 2016Jun 20 2016We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix ... More

On a 1D nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusionMar 16 2016Apr 11 2016We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space $H^{k}(w_{\lambda,\kappa}) \cap L^{\infty},$ with $k=\max(0,3/2-\alpha)$ and $w_{\lambda, \kappa}$ is a given ... More

On the correlation energies for two interacting electrons in a parabolic quantum dotJul 09 2001Jul 10 2001The correlation energies for two interacting electrons in a parabolic quantum dot are studied via a pseudo-perturbation recipe. It is shown that the central spike term, ($m^2-1/4)/r^2$, plays a distinctive role in determining the spectral properties of ... More

(1+1)-Dirac bound states in one-dimension; position-dependent Fermi velocity and massSep 29 2012Jan 28 2013We extend Panella and Roy's [13] work on one-dimensional heterostructure for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where both the mass and velocity are position-dependent. Bound states in the continuum ... More

A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairsFeb 06 2015We generalise some well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs. This leads to a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients of its associated ... More

Heat-kernel estimates for random walk among random conductances with heavy tailDec 14 2008Dec 30 2009We study models of discrete-time, symmetric, $\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$, with polynomial tail near 0 with exponent $\gamma>0$. We first prove ... More

Computing arithmetic invariants for hyperbolic reflection groupsAug 15 2007We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in $\mathbb{H}^3$, the commensurability invariants known as the invariant trace field and invariant quaternion algebra. ... More

Reasoning about Body-Parts Relations for Sign Language RecognitionJul 21 2016Over the years, hand gesture recognition has been mostly addressed considering hand trajectories in isolation. However, in most sign languages, hand gestures are defined on a particular context (body region). We propose a pipeline to perform sign language ... More

PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikesJun 25 2002Aug 24 2002The pseudo-perturbation shifted-l expansion technique PSLET is shown applicable in the non-Hermitian PT-symmetric context. The construction of bound states for several PT-symmetric potentials is presented, with special attention paid to V(r) = ir^3-alpha ... More

Pseudo perturbative expansion method; the non-polynomial, cutoff - Coulomb, and Coulomb plus logarithmic potentialsJan 27 2001We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a conclusion reached ... More

Nonrelativistic shifted-l expansion technique for three- and two-dimensional Schrodinger equationOct 26 1999The shifted-l expansion technique (SLET) has been developed to get eigenvalues of Schrodinger equation in three (3D) and two dimensions (2D). SLET simply consists of 1/\bar{l} as a perturbation parameter, where \bar{l}=l-\beta, \beta is a suitable shift, ... More

Relativistic shifted-l expansion technique for Dirac and Klein-Gordon equationsOct 25 1999The shifted-i expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or 4-vector potentials. A parameter {\lambda}=0,1 is introduced in such a way that one can obtain the Klein-Gordon (KG) bound ... More

2D H-atom in an arbitrary magnetic field via pseudoperturbation expansions through the quantum number lNov 01 1999The pseudoperturbative shifted-l expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrodinger equation with an arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb ... More

Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission conditionFeb 19 2010We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale Galerkin method proposed ... More

Global well-posedness for the 2D stable Muskat problem in $H^{3/2}$Mar 20 2018Apr 22 2018We prove a global existence result of a unique strong solution in $\dot H^{5/2} \cap \dot H^{3/2}$ with small $\dot H^{3/2}$ norm for the 2D stable Muskat problem, hence allowing the interface to have arbitrary large finite slopes and finite energy (thanks ... More

On Maximal Displacement of Bridges in the Random Conductance modelMar 21 2016Dec 18 2016We study a discrete time random walk in an environment of i.i.d. non-negative conductances in $\mathbb{Z}^d$. We consider the maximum displacements for bridges, i.e. we condition the random walk on returning to the origin, and we prove first a normal ... More

Magnetic fingerprints on the spectra of one-electron and two-electrons interacting in parabolic quantum dotsOct 22 2000Feb 22 2001Magnetic fingerprints on the spectra of an interacting electron with a negatively charged ion in a parabolic quantum dot (QD), and of two interacting electrons in such a dot, are investigated via a pseudoperturbative methodical proposal. The effect of ... More

Energy levels of neutral atoms via a new perturbation methodJul 14 2000The energy levels of neutral atoms supported by Yukawa potential, $V(r)=-Z exp(-\alpha r)/r$, are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrodinger ... More

Anharmonic oscillators energies via artificial perturbation methodJan 12 2000Feb 25 2000A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=\alpha_o q^2 + \alpha q^4. ... More

Bound states for spiked harmonic oscillators and truncated Coulomb potentialsOct 19 1999We propose a new analytical method to solve for the nonexactly solvable Schrodinger equation. Successfully, it is applied to a class of spiked harmonic oscillators and truncated Coulomb potentials. The utility of this method could be extended to study ... More

On presimplifiable group ringsFeb 13 2014Dec 11 2014A ring A is called presimplifiable if whenever a; b belongs to A and a = ab, then either a = 0 or b is a unit in A. Let A be a commutative ring and G be an abelian torsion group. For the group ring A[G], we prove that A[G] is presimplifiable if and only ... More

On the model companion of partial differential fields with an automorphismSep 13 2013Jul 09 2014We prove that the class of partial differential fields of characteristic zero with an automorphism has a model companion. We then establish the basic model theoretic properties of this theory and prove that it satisfies the Zilber dichotomy for finite ... More

Devasthal Fast Optical Telescope observations of Wolf-Rayet dwarf galaxy Mrk 996Jul 17 2013The Devasthal Fast Optical Telescope (DFOT) is a 1.3 meter aperture optical telescope, recently installed at Devasthal, Nainital. We present here the first results using an \Ha filter with this telescope on a Wolf-Rayet dwarf galaxy Mrk 996. The instrumental ... More