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Thermal transport across grain boundaries in polycrystalline silicene: a multiscale modelingJan 03 2019During the fabrication process of large scale silicene through common chemical vapor deposition (CVD) technique, polycrystalline films are quite likely to be produced, and the existence of Kapitza thermal resistance along grain boundaries could result ... More

Thermal conductivity and thermal rectification of nanoporous graphene: A molecular dynamics simulationJun 11 2019Using non-equilibrium molecular dynamics (NEMD) simulation, we study thermal properties of the so-called nanoporous graphene (NPG) sheet which contains a series of nanoporous in an ordered way and was synthesized recently (Science 360 (2018), 199). The ... More

Thermal transport in silicene nanotubes: Effects of length, grain boundary and strainJan 03 2019Thermal transport behavior in silicene nanotubes has become more important due to the application of these promising nanostructures in the engineering of next-generation nanoelectronic devices. We apply non-equilibrium molecular dynamics (NEMD) simulations ... More

Phonon Heat Conduction in Corrugated Silicon Nanowires Below the Casimir LimitFeb 18 2013Apr 17 2013The thermal conductance of straight and corrugated monocrystalline silicon nanowires has been measured between 0.3 K and 5 K. The difference in the thermal transport between corrugated nanowires and straight ones demonstrates a strong reduction in the ... More

Inter-layer and Intra-layer Heat Transfer in Bilayer/Monolayer Graphene van der Waals Heterostructure: Is There a Kapitza Resistance Analogous?Nov 24 2017Van der Waals heterostructures have exhibited interesting physical properties. In this paper, heat transfer in hybrid coplanar bilayer/monolayer (BL-ML) graphene, as a model layered van der Waals heterostructure, was studied using non-equilibrium molecular ... More

The effect of water/carbon interaction strength on interfacial thermal resistance and the surrounding molecular nanolayer of CNT and graphene nanoparticlesJan 10 2019Heat transfer at the liquid/solid interface, especially at the nanoscale, has enormous importance in nanofluids. This study investigates liquid/solid interfacial thermal resistance and structure of the formed molecular nanolayer around a carbon-based ... More

Influence of long-range interactions on the critical behavior of the Ising modelNov 28 2012Mar 27 2013We study the ferromagnetic Ising model with long-range interactions in two dimensions. We first present results of a Monte Carlo study which shows that the long-range interactions dominate over the short-range ones in the intermediate regime of interaction ... More

Thermal transport at a nanoparticle-water interface: A molecular dynamics and continuum modeling studyJan 10 2019Heat transfer between a silver nanoparticle and surrounding water has been studied using molecular dynamics (MD) simulations. The thermal conductance (Kapitza conductance) at the interface between a nanoparticle and surrounding water has been calculated ... More

Classification of the sign of the critical Casimir force in two dimensional systemsSep 20 2016We classify the sign of the critical Casimir force between two finite objects separated by a large distance in the two dimensional systems that can be described by conformal field theory (CFT). In particular, we show that as far as the smallest scaling ... More

Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact resultsDec 12 2015Apr 12 2016We calculate analytically the R\'enyi bipartite entanglement entropy $S_{\alpha}$ of the ground state of $1+1$ dimensional conformal field theories (CFT) after performing a projective measurement in a part of the system. We show that the entanglement ... More

Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theoriesJul 24 2016We calculate formation probabilities of the ground state of the finite size quantum critical chains using conformal field theory (CFT) techniques. In particular, we calculate the formation probability of one interval in the finite open chain and also ... More

Fate of the area-law after partial measurement in quantum field theoriesMar 26 2015Mar 28 2016We calculate numerically the R\'enyi bipartite entanglement entropy of the ground state of Klein-Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators in $d=1,2$ and $3$ dimensions. ... More

Winding Number of Fractional Brownian MotionJul 23 2008Feb 26 2009We find the exact winding number distribution of Riemann-Liouville fractional Brownian motion for large times in two dimensions using the propagator of a free particle. The distribution is similar to the Brownian motion case and it is of Cauchy type. ... More

Formation probabilities in quantum critical chains and Casimir effectDec 03 2015Jan 26 2016We find a connection between logarithmic formation probabilities of two disjoint intervals of quantum critical spin chains and the Casimir energy of two aligned needles in two dimensional classical critical systems. Using this connection we provide a ... More

Post measurement bipartite entanglement entropy in conformal field theoriesJan 30 2015Aug 06 2015We derive exact formulas for bipartite von Neumann entanglement entropy after partial projective local measurement in $1+1$ dimensional conformal field theories with periodic and open boundary conditions. After defining the set up we will check numerically ... More

Conformal symmetry in non-local field theoriesMar 18 2011Jun 25 2011We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the translation, rotation ... More

Area Distribution of Elastic Brownian MotionJun 17 2009Nov 14 2009We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion ... More

Bessel Process and Conformal Quantum MechanicsJun 09 2009Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint ... More

Loop models for CFTsJun 27 2008Feb 26 2009By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary operator. ... More

Boundary conformal field theories and loop modelsAug 01 2008Apr 20 2009We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as adjacency matrices. ... More

Quantum quench in long-range field theoriesSep 23 2014Jan 21 2015We study equilibration properties of observables in long-range field theories after the mass quench in $d=1,2$ and $3$ dimensions. We classify the regimes where we expect equilibration or its absence in different dimensions. In addition we study the effect ... More

Full counting statistics of the subsystem energy in the free fermions and the quantum spin chainsOct 24 2017Dec 15 2017We calculate the full counting statistics (FCS) of a subsystem energy in free fermionic systems by means of the Grassmann variables. We demonstrate that the generating function of these systems can be written as a determinant formula with respect to the ... More

Entanglement entropy after selective measurements in quantum chainsAug 14 2016Dec 23 2016We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement ... More

Quantum Quench of the trap frequency in the harmonic Calogero modelJul 29 2013Nov 27 2013We consider a quantum quench of the trap frequency in a system of bosons interacting through an inverse-square potential and confined in a harmonic trap (the harmonic Calogero model). We determine exactly the initial state in terms of the post-quench ... More

Entanglement entropy of two disjoint intervals from fusion algebra of twist fieldsDec 06 2011We study the entanglement and Renyi entropies of two disjoint intervals in minimal models of conformal field theory. We use the conformal block expansion and fusion rules of twist fields to define a systematic expansion in the elliptic parameter of the ... More

Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorderSep 23 2006Sep 25 2007We investigate the explicit renormalization group for fermionic field theoretic representation of two-dimensional random bond Ising model with long-range correlated disorder. We show that a new fixed point appears by introducing a long-range correlated ... More

Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillatorsJul 23 2019We study general entanglement properties of the excited states of the one dimensional translational invariant free fermions and coupled harmonic oscillators. In particular, using the integrals of motion, we prove that these Hamiltonians independent of ... More

Discretely Holomorphic Parafermions in Lattice Z(N) ModelsAug 28 2007Nov 20 2007We construct lattice parafermions - local products of order and disorder operators - in nearest-neighbor Z(N) models on regular isotropic planar lattices, and show that they are discretely holomorphic, that is they satisfy discrete Cauchy-Riemann equations, ... More

Entanglement entropy after selective measurements in quantum chainsAug 14 2016Aug 27 2016We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement ... More

Formation probabilities and Shannon information and their time evolution after quantum quench in transverse-field XY-chainNov 19 2015Mar 28 2016We first provide a formula to calculate the probability of occurrence of different configurations (formation probabilities) in a generic free fermion system. We then study the scaling of these probabilities with respect to the size in the case of critical ... More

Area law and universality in the statistics of subsystem energyJun 06 2018Jan 27 2019We introduce R\'enyi entropy of a subsystem energy as a natural quantity which closely mimics the behavior of the entanglement entropy and can be defined for all the quantum many body systems. For this purpose, consider a quantum chain in its ground state ... More

Spin interfaces in the Ashkin-Teller model and SLENov 14 2011We investigate the scaling properties of the spin interfaces in the Ashkin-Teller model. These interfaces are a very simple instance of lattice curves coexisting with a fluctuating degree of freedom, which renders the analytical determination of their ... More

Ashkin-Teller model on the iso-radial graphsMar 31 2010We find the critical surface of the Ashkin-Teller model on the generic iso-radial graphs by using the results for the anisotropic Ashkin-teller model on the square lattice. Different geometrical aspects of this critical surface are discussed, especially ... More

Amenability of groups and semigroups characterized by ConfigurationJan 25 2015In 2005, Abdollahi and Rejali, studied the relations between paradoxical decompositions and configurations for semigroups. In the present paper, we introduce another concept of amenability on semigroups and groups which includes amenability of semigroups ... More

Stability in a many-to-one job market with general increasing functionsMar 04 2017We consider an occupation market in which preferences of members are treated as non linear general increasing functions. The arrangement of members is separated into two non over-lapping sets, set of workers and set of firms. We consider that firms have ... More

Recent Results on Photoproduction of Vector Mesons and Mass Dependent Pomeron TrajectorySep 13 2002It is shown that the recent results on photoproduction of vector mesons can be naturally explained by using a mass dependent pomeron trajectory.

Customers perception of mbanking adoption in Kingdom of Bahrain: an empirical assessment of an extended tam modelMar 12 2014Mar 25 2014Mobile applications have been rapidly changing the way business organizations deliver their services to their customers and how customers can interact with their service providers in order to satisfy their needs. The use of mobile applications increases ... More

Discrete holomorphic parafermions in the Ashkin-Teller model and SLESep 17 2010Nov 24 2010We find discrete holomorphic parafermions of the Ashkin-Teller model on the critical line, by mapping appropriate interfaces of the model to the $O(n=1)$ model. We give support to the conjecture that the curve created by the insertion of parafermionic ... More

Conformal Curves in Potts Model: Numerical CalculationMar 16 2010We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal ... More

Perturbed Logarithmic CFT and Integrable ModelsOct 09 2005Feb 05 2006Perturbation of logarithmic conformal field theories is investigated using Zamolodchikov's method. We derive conditions for the perturbing operator, such that the perturbed model be integrable. We also consider an example where integrable models arise ... More

Error Correction Coding Meets Cyber-Physical Systems: Message-Passing Analysis of Self-Healing Interdependent NetworksSep 25 2016Coupling cyber and physical systems gives rise to numerous engineering challenges and opportunities. An important challenge is the contagion of failure from one system to another, which can lead to large-scale cascading failures. However, the \textit{self-healing} ... More

Finite Size Scaling and Conformal CurvesNov 06 2005In this letter we investigate the finite size scaling effect on SLE($\kappa,\rho$) and boundary conformal field theories and find the effect of fixing some boundary conditions on the free energy per length of SLE($\kappa,\rho$). As an application, we ... More

Return amplitude after a quantum quench in the XY chainMay 03 2019We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local $z$-magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude ... More

Message Passing for Analysis and Resilient Design of Self-Healing Interdependent Cyber-Physical NetworksJun 03 2016Coupling cyber and physical systems gives rise to numerous engineering challenges and opportunities. An important challenge is the contagion of failure from one system to another, that can lead to large scale cascading failures. On the other hand, self-healing ... More

Message Passing for Analysis and Resilient Design of Self-Healing Interdependent Cyber-Physical NetworksJun 03 2016Dec 29 2016Coupling cyber and physical systems gives rise to numerous engineering challenges and opportunities. An important challenge is the contagion of failure from one system to another, that can lead to large scale cascading failures. On the other hand, self-healing ... More

Discrete scale invariance and stochastic Loewner evolutionOct 08 2010Dec 03 2010In complex systems with fractal properties the scale invariance has an important rule to classify different statistical properties. In two dimensions the Loewner equation can classify all the fractal curves. Using the Weierstrass-Mandelbrot (WM) function ... More

Return amplitude after a quantum quench in the XY chainMay 03 2019May 12 2019We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local $z$-magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude ... More

Quantum entanglement entropy and classical mutual information in long-range harmonic oscillatorsJun 05 2013Jul 18 2013We study different aspects of quantum von Neumann and R\'enyi entanglement entropy of one dimensional long-range harmonic oscillators that can be described by well-defined non-local field theories. We show that the entanglement entropy of one interval ... More

Contour lines of the discrete scale invariant rough surfacesNov 04 2010Mar 08 2011We study the fractal properties of the 2d discrete scale invariant (DSI) rough surfaces. The contour lines of these rough surfaces show clear DSI. In the appropriate limit the DSI surfaces converge to the scale invariant rough surfaces. The fractal properties ... More

Two-dimensional conformal field theories with matrix-valued levelSep 19 2015We study the chiral algebra of holomorphic currents with an operator product expansion characterized by a matrix-valued level $K_{AB}$. We use the Sugawara construction to compute the energy-momentum tensor, the central charge, and the spectrum of conformal ... More

Remarks on inhomogeneous anisotropic cosmologyMar 10 2016Aug 06 2016Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow of spacelike ... More

New Brane Solutions from Killing Spinor EquationsApr 27 2000May 02 2000In a recent paper, we have pointed out a relation between the Killing spinor and Einstein equations. Using this relation, new brane solutions of D=11 and D=10 type IIB supergravity theories are constructed. It is shown that in a brane solution, the flat ... More

On Renyi entropy convergence of the max domain of attractionFeb 05 2014Apr 22 2014In this paper, we prove that the Renyi entropy of linearly normalized partial maxima of independent and identically distributed random variables is convergent to the corresponding limit Renyi entropy when the linearly normalized partial maxima converges ... More

DEBH: Detection and Elimination Black Holes in Mobile Ad Hoc NetworkAug 20 2016Mobile Ad hoc Network MANET is a self-configurable, easy to setup and decentralize network with mobile wireless nodes. Special features of MANET like hop-by-hop communications, dynamic topology and open network boundary made security highly challengeable. ... More

Analysis and Evaluation of the Link and Content Based Focused Treasure-CrawlerJun 01 2013Indexing the Web is becoming a laborious task for search engines as the Web exponentially grows in size and distribution. Presently, the most effective known approach to overcome this problem is the use of focused crawlers. A focused crawler applies a ... More

A Focused Crawler Combinatory Link and Content Model Based on T-Graph PrinciplesMay 30 2013The two significant tasks of a focused Web crawler are finding relevant topic-specific documents on the Web and analytically prioritizing them for later effective and reliable download. For the first task, we propose a sophisticated custom algorithm to ... More

A short review on techniques for processes and process simulation of scaffold-free tissue engineeringNov 01 2015The invention of three-dimensional printers has led to major innovations in tissue engineering. They have enabled the printing of complex geometries such as those that occur in natural tissues, that were not possible with traditional manufacturing techniques. ... More

Analysis of Quantum Correlation in Successive Spin Measurements, Classical Communication of Spin $S$ Singlet States and Quantum Nonlocality of two Qubit Entangled StatesJul 04 2008In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for ... More

A Differential Integrability Condition for Two-Dimensional Hamiltonian SystemsJan 06 2014We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial differential equations. ... More

Pseudo-Hermitian Quantum Mechanics with Unbounded Metric OperatorsMar 28 2012Dec 18 2012We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space, observables, and ... More

Optical Spectral Singularities as Threshold ResonancesFeb 23 2011Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral singularity appears ... More

PT-Symmetric Quantum Mechanics: A Precise and Consistent FormulationJul 27 2004The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical equivalence of PT-symmetric ... More

Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian FermionsApr 05 2004We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic ... More

A Critique of PT-Symmetric Quantum MechanicsOct 28 2003We study the physical content of the PT-symmetric complex extension of quantum mechanics as proposed in Bender et al, Phys. Rev. Lett. 80, 5243 (1998) and 89, 270401 (2002), and show that as a fundamental probabilistic physical theory it is neither an ... More

Exact PT-Symmetry Is Equivalent to HermiticityApr 11 2003Jun 23 2003We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with ... More

Pseudo-Unitary Operators and Pseudo-Unitary Quantum DynamicsFeb 21 2003Dec 18 2003We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, ... More

Pseudo-Hermiticity for a Class of Nondiagonalizable HamiltoniansJul 04 2002Sep 12 2002We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such an operator ... More

On a Factorization of Symmetric Matrices and Antilinear SymmetriesMar 14 2002We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.

Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian HamiltonianJul 01 2001Oct 10 2001We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian ... More

Relativistic Adiabatic Approximation and Geometric PhaseJul 01 1998A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical phases are calculated. ... More

Adiabatic Approximation, Semiclassical Scattering, and Unidirectional InvisibilityJan 17 2014Feb 27 2014The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that the application of the adiabatic approximation to H(t) ... More

Imaginary-Scaling versus Indefinite-Metric Quantization of the Pais-Uhlenbeck OscillatorJul 10 2011Dec 09 2011Using the Pais-Uhlenbeck Oscillator as a toy model, we outline a consistent alternative to the indefinite-metric quantization scheme that does not violate unitarity. We describe the basic mathematical structure of this method by giving an explicit construction ... More

Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status reportAug 27 2010We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum system and its representations ... More

Pseudo-Hermiticity and Electromagnetic Wave Propagation in Dispersive MediaJan 15 2010Pseudo-Hermitian operators appear in the solution of Maxwell's equations for stationary non-dispersive media with arbitrary (space-dependent) permittivity and permeability tensors. We offer an extension of the results in this direction to certain stationary ... More

Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical ApplicationsSep 09 2009We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study ... More

Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric OperatorJun 13 2007Oct 29 2007The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the existence of ... More

Delta-Function Potential with a Complex CouplingJun 23 2006Nov 28 2006We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at E=-z^2/4. For \Re(z)<0, ... More

A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon FieldsJul 08 2003Jun 08 2006Generalized parity (P), time-reversal (T), and charge-conjugation (C)operators were initially definedin the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein-Gordon fields and show that in this ... More

On a Z_3-Graded Generalization of the Witten IndexDec 10 2001We construct a realization of the algebra of the Z_3-graded topological symmetry of type (1,1,1) in terms of a pair of operators D_1: H_1 -> H_2, and D_2: H_2 -> H_3 satisfying [D_1D_1^\dagger,D_2^\dagger D_2]=0. We show that the sequence of the restriction ... More

Variational Sturmian Approximation: A nonperturbative method of solving time-independent Schrödinger equationMay 11 2001A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian potential. ... More

Perturbative Calculation of the Adiabatic Geometric Phase and Particle in a Well with Moving WallsOct 25 1999We use the Rayleigh-Schr\"odinger perturbation theory to calculate the corrections to the adiabatic geometric phase due to a perturbation of the Hamiltonian. We show that these corrections are at least of second order in the perturbation parameter. As ... More

Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical InvariantsOct 22 1998For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions ... More

Topological Aspects of ParasupersymmetryJun 22 1995Parasupersymmetric quantum mechanics is exploited to introduce a topological invariant associated with a pair of parameter dependent Fredholm (respectively elliptic differential) operators satisfying two compatibility conditions. An explicit algebraic ... More

Geometric Phase, Bundle Classification, and Group RepresentationDec 21 1993The line bundles which arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the Borel-Weil-Bott theorem of the representation theory. The remarkable relation of the geometric ... More

From $e$ to $π$: Derivation of the Wallis formula for $π$ from $e$Jun 23 2016In this Note, we start off with the primary representation of e and from there present an elementary short proof for the Wallis formula for $\pi$.

On Periodic Solutions Of Lienard EquationsSep 30 2004We Prove That The Uniform Upper Bound for the Number Of Limit Cycles Of The Lienard Equation of Degree 4 Can be equals to 2. Further We Suggest to Embedding Planar Lienard Equations In Higher Dimension and Present question of completly integrabiolity ... More

On the configuration of limit cycles in planar vector fieldsSep 22 2004We prove that coexistence of two limit cycles with disjoint interior can not occur in certain quadratic systems

Real time electron dynamics in an interacting vibronic molecular quantum dotOct 16 2010We employ the time-dependent non-crossing approximation to investigate the joint effect of strong electron-electron and electron-phonon interaction on the instantaneous conductance of a single molecule transistor which is abruply moved into the Kondo ... More

Atoms deform or stretch, do not ionize, those having electronic transitions are the source of photonic current while inherently making terminals of inert gas atoms switch photonic current into photonsNov 16 2016The phenomenon whereby atoms take a positive or negative charge by losing or gaining one or more electrons forms the basis of the known chemical or physical processes. However, atoms that have outer shell of valence electrons unfilled execute electronic ... More

A Banach algebraic Approach to the Borsuk-Ulam TheoremOct 01 2011Oct 15 2013Using methods from the theory of commutative graded Banach algebras, we obtain a generalization of the two dimensional Borsuk-Ulam theorem as follows: Let $\phi:S^{2} \rightarrow S^{2}$ be a homeomorphism of order n and $\lambda\neq 1$ be an nth root ... More

Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-dualitySep 13 2014Feb 04 2015The equations of motion of a super non-Abelian T-dual sigma model on the Lie supergroup $(C^1_1+A)$ in the curved background are explicitly solved by the super Poisson-Lie T-duality. To find the solution of the flat model we use the transformation of ... More

Structure evolution in atoms of electron transitions under confined inter-state electron-dynamicsNov 04 2016May 09 2019It is ambiguous to understand the structure evolution in atoms executing confined inter-state electron-dynamics. Such atoms evolve structure on amalgamation under significant attained-dynamics. A structure evolution is in different format depending on ... More

On the metric dimension of a class of distance transitive graphsMay 25 2019Let $\Gamma=Cay(\mathbb{Z}_n, S_k)$ be the Cayley graph on the cyclic additive group $\mathbb{Z}_n$, where $S_1=\{1, n-1\}$, ..., $S_k=S_ {k-1}\cup\{k, n-k\}$ are the inverse closed subsets of $\mathbb{Z}_n-\{0\}$ for any $k\in \mathbb{N}$, $1\leq k\leq ... More

The Cabello Nonlocal Argument is Stronger Control than the Hardy Nonlocal Argument for Detecting Post-Quantum CorrelationsJan 21 2017Sep 03 2017In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context ... More

Thin Hessenberg PairsNov 20 2009A square matrix is called {\it Hessenberg} whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. Let $V$ denote a nonzero finite-dimensional vector space over a field $\fld$. We consider an ordered pair of linear ... More

Thin Hessenberg Pairs and Double Vandermonde MatricesJul 27 2011A square matrix is called {\it Hessenberg} whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. Let $V$ denote a nonzero finite-dimensional vector space over a field $\fld$. We consider an ordered pair of linear ... More

An Overview of Datatype Quantization Techniques for Convolutional Neural NetworksAug 22 2018Convolutional Neural Networks (CNNs) are becoming increasingly popular due to their superior performance in the domain of computer vision, in applications such as objection detection and recognition. However, they demand complex, power-consuming hardware ... More

Cauchy's Equations and Ulam's ProblemJun 08 2014Our aim is to study the Ulam's problem for Cauchy's functional equations. First, we present some new results about the superstability and stability of Cauchy exponential functional equation and its Pexiderized for class functions on commutative semigroup ... More

On growth of the set $A(A+1)$ in arbitrary finite fieldsJul 29 2018Let $\mathbb{F}_q$ be a finite field of order $q$, where $q$ is a power of a prime. For a set $A \subset \mathbb{F}_q$, under certain structural restrictions, we prove a new explicit lower bound on the size of the product set $A(A + 1)$. Our result improves ... More

Self-adjoint boundary value problems of automorphic formsSep 24 2015We apply some ideas of Bombieri and Garrett to construct natural self-adjoint operators on spaces of automorphic forms whose only possible discrete spectrum is $\lambda_{s}$ for $s$ in a subset of on-line zeros of an $L$-function, appearing as a compact ... More