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Thermal management and non-reciprocal control of phonon flow via optomechanicsOct 24 2017Mar 23 2018Engineering phonon transport in physical systems is a subject of interest in the study of materials and plays a crucial role in controlling energy and heat transfer. Of particular interest are non-reciprocal phononic systems, which in direct analogy to ... More

Measuring topological invariants in photonic systemsOct 29 2013Motivated by the recent theoretical and experimental progress in implementing topological orders with photons, we analyze photonic systems with different topologies and present a scheme to probe their topological features. Specifically, we propose a scheme ... More

Cavity Higgs-PolaritonsMay 08 2019Motivated by the dramatic success of realizing cavity exciton-polariton condensation in experiment we consider the formation of polaritons from cavity photons and the amplitude or Higgs mode of a superconductor. Enabled by the recently predicted and observed ... More

Photonic quantum transport in a nonlinear optical fiberJul 29 2009Nov 26 2009We theoretically study the transmission of few-photon quantum fields through a strongly nonlinear optical medium. We develop a general approach to investigate non-equilibrium quantum transport of bosonic fields through a finite-size nonlinear medium and ... More

Optomechanically induced non-reciprocity in microring resonatorsOct 16 2011Mar 16 2012We describe a new approach for on-chip optical non-reciprocity which makes use of strong optomechanical interaction in microring resonators. By optically pumping the ring resonator in one direction, the optomechanical coupling is only enhanced in that ... More

Photon pair condensation by engineered dissipationMar 29 2019Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, ... More

Emergent equilibrium in many-body optical bistabilityNov 07 2016Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body ... More

Nonlinear Optics Quantum Computing with Circuit-QEDAug 14 2012Nov 20 2012One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED ... More

Two coupled nonlinear cavities in a driven-dissipative environmentAug 28 2016Dec 18 2016We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical ... More

A topological source of quantum lightSep 28 2017Mar 21 2019Quantum light sources are characterized by their distinctive statistical distribution of photons. For example, single photons and correlated photon pairs exhibit antibunching and reduced variance in the number distribution that is impossible with classical ... More

Induced self-stabilization in fractional quantum Hall states of lightFeb 27 2014Mar 11 2014Recent progress in nanoscale quantum optics and superconducting qubits has made the creation of strongly correlated, and even topologically ordered, states of photons a real possibility. Many of these states are gapped and exhibit anyon excitations, which ... More

Engineering three-body interaction and Pfaffian states in circuit QED systemsAug 01 2013We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling dynamics, in the form of a synthesized magnetic field, for the ... More

Anisotropic exciton transport in transition-metal dichalcogenidesMar 02 2018Due to the Coulomb interaction exciton eignestates in monolayer transitional metal dichalcogenides are coherent superposition of two valleys. The exciton band which couples to the transverse electric mode of light has parabolic dispersion for the center ... More

Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological OrderNov 15 2017Dec 19 2017In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and fusion rules ... More

Measurement of many-body chaos using a quantum clockJun 30 2016There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-time-ordered (OTO) correlation functions ... More

Topologically robust transport of entangled photons in a 2D photonic systemMay 16 2016Aug 01 2016We theoretically study the transport of time-bin entangled photon pairs in a two-dimensional topological photonic system of coupled ring resonators. This system implements the integer quantum Hall model using a synthetic gauge field and exhibits topologically ... More

Two coupled nonlinear cavities in a driven-dissipative environmentAug 28 2016We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical ... More

Minimal Injective Resolutions and Auslander-Gorenstein Property for Path AlgebrasMay 18 2015Apr 24 2016Let $R$ be a ring and $\mathcal{Q}$ be a finite and acyclic quiver. We present an explicit formula for the injective envelopes and projective precovers in the category $\rm{Rep} (\mathcal{Q} ,R)$ of representations of $\mathcal{Q}$ by left $R$-modules. ... More

Auslander's Formula for contravariantly finite subcategoriesDec 31 2016Feb 21 2018A relative version of Auslander's formula with respect to a contravariantly finite subcategory will be given. Dual version will be treated. Several examples and applications will be provided. In particular, we show that under certain circumstances, if ... More

Topological growing of Laughlin states in synthetic gauge fieldsJun 10 2014Sep 26 2014We suggest a scheme for the preparation of highly correlated Laughlin (LN) states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on ... More

Robust optical delay lines via topological protectionFeb 16 2011Phenomena associated with topological properties of physical systems are naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we ... More

Fractional Quantum Hall Effect in Optical LatticesJun 06 2007We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate conditions under ... More

Hardware-efficient fermionic simulation with a cavity-QED systemJul 15 2017Mar 26 2018In digital quantum simulation of fermionic models with qubits, non-local maps for encoding are often encountered. Such maps require linear or logarithmic overhead in circuit depth which could render the simulation useless, for a given decoherence time. ... More

Measurement Protocol for the Entanglement Spectrum of Cold AtomsMay 27 2016Nov 22 2016Entanglement, and, in particular the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because ... More

Non-equilibrium Fractional Quantum Hall state of lightJan 07 2013Jun 18 2013We investigate the quantum dynamics of systems involving small numbers of strongly interacting photons. Specifically, we develop an efficient method to investigate such systems when they are externally driven with a coherent field. Furthermore, we show ... More

Quantum transport of strongly interacting photons in a one-dimensional nonlinear waveguideNov 25 2009We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is governed by the quantum ... More

Two-Dimensionally Confined Topological Edge States in Photonic CrystalsMay 28 2016We present an all-dielectric photonic crystal structure that supports two-dimensionally confined helical topological edge states. The topological properties of the system are controlled by the crystal parameters. An interface between two regions of differing ... More

A Measurement Protocol for the Entanglement Spectrum of Cold AtomsMay 27 2016Entanglement plays a major role in characterizing many-body quantum systems. In particular, the entanglement spectrum holds a great promise to characterize essential physics of quantum many-body systems. While there has been a surge of theoretical works ... More

Slowing and stopping light using an optomechanical crystal arrayJun 19 2010Nov 21 2010One of the major advances needed to realize all-optical information processing of light is the ability to delay or coherently store and retrieve optical information in a rapidly tunable manner. In the classical domain, this optical buffering is expected ... More

Optical Lattice with Torus TopologyMay 03 2018May 10 2018We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed high resolution ... More

Characterization of topological states on a lattice with Chern numberJun 06 2007Dec 04 2007We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where conventional overlap ... More

Measurement of topological invariants in a 2D photonic systemApr 01 2015Mar 01 2016A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall ... More

Fractional Quantum Hall States of Rydberg PolaritonsNov 24 2014We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array ... More

Recollements of Cohen-Macaulay Auslander algebras and Gorenstein derived categoriesJan 20 2014Jul 10 2014Let $A$, $B$ and $C$ be associative rings with identity. Using a result of Koenig we show that if we have a $\mathbb{D}^{{\rm{b}}}({\rm{{mod\mbox{-}}}} )$ level recollement, writing $A$ in terms of $B$ and $C$, then we get a $\mathbb{D}^-({\rm{Mod\mbox{-}}} ... More

Homotopy category of N-complexes of projective modulesApr 04 2015Apr 20 2015In this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective T_{N-1}(R)- modules where T_{N-1}(R) is the ring of triangular matrices of order N-1 with entries in ... More

Machine learning assisted readout of trapped-ion qubitsApr 20 2018May 01 2018We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the ... More

Photon pair condensation by engineered dissipationMar 29 2019Apr 03 2019Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, ... More

High-Order Multipole Radiation from Quantum Hall States in Dirac MaterialsJan 12 2017Jun 23 2017We investigate the optical response of strongly disordered quantum Hall states in two-dimensional Dirac materials and find qualitatively different effects in the radiation properties of the bulk versus the edge. We show that the far-field radiation from ... More

Optical control over bulk excitations in fractional quantum Hall systemsAug 08 2018Local excitations in fractional quantum Hall systems are amongst the most intriguing objects in condensed matter, as they behave like particles of fractional charge and fractional statistics. In order to experimentally reveal these exotic properties and ... More

Ultra-Sensitive Chip-Based Photonic Temperature Sensor Using Ring Resonator StructuresDec 18 2013Resistance thermometry provides a time-tested method for taking temperature measurements. However, fundamental limits to resistance-based approaches has produced considerable interest in developing photonic temperature sensors to leverage advances in ... More

Collective phases of strongly interacting cavity photonsJan 26 2016Sep 16 2016We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-$\frac{1}{2}$ model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, ... More

A topological quantum optics interfaceNov 01 2017The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although significant progress on topological phenomena has been achieved in the classical domain, the realization of ... More

Maximal Violation of Bell Inequalities using Continuous Variables MeasurementsNov 12 2002We propose a whole family of physical states that yield a violation of the Bell CHSH inequality arbitrarily close to its maximum value, when using quadrature phase homodyne detection. This result is based on a new binning process called root binning, ... More

Cavity Quantum Eliashberg Enhancement of SuperconductivityMay 03 2018Aug 03 2018Driving a conventional superconductor with an appropriately tuned classical electromagnetic field can lead to an enhancement of superconductivity via a redistribution of the quasiparticles into a more favorable non-equilibrium distribution -- a phenomenon ... More

Thermal radiation as a probe of one-dimensional electron liquidsApr 02 2018Motivated by recent developments in the field of plasmonics, we develop the theory of radiation from one-dimensional electron liquids, showing that the spectrum of thermal radiation emitted from the system exhibits signatures of non-Fermi liquid behavior. ... More

Photonic quadrupole topological phasesDec 21 2018Jan 05 2019The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest themselves as ... More

A synthetic gauge field for two-dimensional time-multiplexed quantum random walksFeb 17 2019Temporal multiplexing provides an efficient and scalable approach to realize a quantum random walk with photons that can exhibit topological properties. But two dimensional time-multiplexed topological quantum walks studied so far have relied on generalizations ... More

Photonic Anomalous Quantum Hall EffectApr 01 2019We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has zero net gauge flux threading ... More

Cavity Quantum Eliashberg Enhancement of SuperconductivityMay 03 2018Feb 27 2019Driving a conventional superconductor with an appropriately tuned classical electromagnetic field can lead to an enhancement of superconductivity via a redistribution of the quasiparticles into a more favorable non-equilibrium distribution -- a phenomenon ... More

Interference of multiple temporally distinguishable photons using frequency-resolved detectionApr 05 2019We demonstrate quantum interference of three photons that are distinguishable in time, by resolving them in the conjugate parameter, frequency. We show that the multi-photon interference pattern in our setup can be manipulated by tuning the relative delays ... More

Temporal and spectral manipulations of correlated photons using a time-lensApr 14 2017Sep 11 2017A common challenge in quantum information processing with photons is the limited ability to manipulate and measure correlated states. An example is the inability to measure picosecond scale temporal correlations of a multi-photon state, given state-of-the-art ... More

Cavity Quantum Eliashberg Enhancement of SuperconductivityMay 03 2018Apr 30 2019Driving a conventional superconductor with an appropriately tuned classical electromagnetic field can lead to an enhancement of superconductivity via a redistribution of the quasiparticles into a more favorable non-equilibrium distribution -- a phenomenon ... More

Auslander's Formula: Variations and ApplicationsMay 16 2016According to the Auslander's formula one way of studying an abelian category $\mathcal{C}$ is to study ${\rm{{mod\mbox{-}}}} \mathcal{C}$, that has nicer homological properties than $\mathcal{C}$, and then translate the results back to $\mathcal{C}$. ... More

Anyonic interferometry and protected memories in atomic spin latticesNov 08 2007Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic ... More

Observation of chiral photocurrent transport in the quantum Hall regime in grapheneMar 04 2019Optical excitation provides a powerful tool to investigate non-equilibrium physics in quantum Hall systems. Moreover, the length scale associated with photo-excited charge carries lies between that of local probes and global transport measurements. Here, ... More

$(1+2u)$-constacyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$Apr 14 2015Let $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u^2=0$. In the present paper, we introduce a new Gray map from $R^n$ to $\mathbb{Z}_{4}^{2n}.$ We study $(1+2u)$-constacyclic codes over $R$ of odd lengths ... More

On relative Auslander algebrasNov 19 2017Relative Auslander algebras were introduced and studied by Beligiannis. In this paper, we apply intermediate extension functors associated to certain recollements of functor categories to study them. In particular, we study the existence of tilting-cotilting ... More

Topological PhotonicsFeb 12 2018Topological photonics is a rapidly-emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators ... More

Topological PhotonicsFeb 12 2018Apr 02 2019Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators ... More

Cosmography of interacting generalized QCD ghost dark energyDec 18 2012Aug 24 2013Exploring the accelerated expansion of the universe, we investigate the generalized ghost dark energy (GGDE) model from the statefinder diagnosis analysis in a flat FRW universe. First we calculate the cosmological evolution and statefinder trajectories ... More

Maximally transitive semigroups of $n\times n$ matricesDec 30 2011We prove that, in both real and complex cases, there exists a pair of matrices that generates a dense subsemigroup of the set of $n\times n$ matrices.

A Collatz-type conjecture on the set of rational numbersOct 18 2010Define $\theta(x)=(x-1)/3$ if $x\geq 1$, and $\theta(x)=2x/(1-x)$ if $x<1$. We conjecture that the orbit of every positive rational number ends in 0. In particular, there does not exist any positive rational fixed point for a map in the semigroup $\Omega$ ... More

Means refinements via convexityJun 22 2016The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well established inequalities ... More

On dependence of rational points on elliptic curvesMay 10 2016Let $E$ be an elliptic curve defined over $\mathbb Q$. Let $\Gamma$ be a subgroup of $E(\mathbb Q)$ and $P\in E(\mathbb Q)$. In [1], it was proved that if $E$ has no nontrivial rational torsion points, then $P\in\Gamma$ if and only if $P\in \Gamma$ mod ... More

Optimal initial condition of passive tracers for their maximal mixing in finite timeApr 05 2016The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here, we address the natural corollary question: Given the best available ... More

Optimal regularity for variational problems with nonsmooth non-strictly convex gradient constraintsFeb 10 2016May 19 2016We prove the optimal regularity for variational problems with nonsmooth gradient constraints. Furthermore, we obtain the optimal regularity in two dimensions without assuming the strict convexity of the constraints. We also characterize the set of singular ... More

DataGrinder: Fast, Accurate, Fully non-Parametric Classification Approach Using 2D Convex HullsNov 11 2015It has been a long time, since data mining technologies have made their ways to the field of data management. Classification is one of the most important data mining tasks for label prediction, categorization of objects into groups, advertisement and ... More

An introdution to forcingMar 27 2015The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic predicate logic, ... More

Sequence Modeling using Gated Recurrent Neural NetworksJan 01 2015In this paper, we have used Recurrent Neural Networks to capture and model human motion data and generate motions by prediction of the next immediate data point at each time-step. Our RNN is armed with recently proposed Gated Recurrent Units which has ... More

Lower bounds for warping functions on warped-product AHE manifoldsOct 14 2007Let $[\gamma]$ be the conformal boundary of a warped product $C^{3,\alpha}$ AHE metric $g=g_M+u^2h$ on $N=M \times F$, where $(F,h)$ is compact with unit volume and nonpositive curvature. We show that if $[\gamma]$ has positive Yamabe constant, then $u$ ... More

On Cyclic Cohomology of x-Hopf algebrasMar 12 2012Feb 20 2014In this paper we study the cyclic cohomology of certain x-Hopf algebras: universal enveloping algebras, quantum algebraic tori, the Connes-Moscovici x-Hopf algebroids and the Kadison bialgebroids. Introducing their stable anti Yetter-Drinfeld modules ... More

Separating detection and catalog productionNov 19 2016In the coming era of massive surveys (e.g. LSST, SKA), the role of the database designers and the algorithms they choose to adopt becomes the decisive factor in scientific progress. Systems that allow/encourage users/scientists to be more creative with ... More

Operateurs absolument continus et interpolationMay 10 2017In the first part of this work, we study the absolutely continuous operators which are defined on fuction spaces with wide sense. In the second part, we show some results concerning the absoltely continuous operators when the function spaces (with wide ... More

Representations of Finite Polyadic GroupsNov 03 2010We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite groups to the ... More

Learning Analytics in Massive Open Online CoursesFeb 17 2018Educational technology has obtained great importance over the last fifteen years. At present, the umbrella of educational technology incorporates multitudes of engaging online environments and fields. Learning analytics and Massive Open Online Courses ... More

Isomorphismes entre des espaces de mesures à valeurs vectoriellesMar 29 2016Let $(\Omega_1, \mathcal{F}_1, \mu_1)$, $(\Omega_2, \mathcal{F}_2, \mu_2)$ be two probabilty spaces, $1\leq p\leq +\infty$ and $X$ a Banach space. In this work we show that $L^p(\mu_1, X)$, $VB^p (\mu_1,X),$ $cabv(\mu_{1},X)$ are isomorphic to $L^p(\mu_2, ... More

The free boundary of variational inequalities with gradient constraintsJan 21 2015Aug 09 2015In this paper we prove that the free boundary of some variational inequalities with gradient constraints is as regular as the tangent bundle of the boundary of the domain. To this end, we study a generalized notion of ridge of a domain in the plane, which ... More

Deformations of unbounded convex bodies and hypersurfacesDec 15 2009May 02 2010We study the topology of the space $\d\K^n$ of complete convex hypersurfaces of $\R^n$ which are homeomorphic to $\R^{n-1}$. In particular, using Minkowski sums, we construct a deformation retraction of $\d\K^n$ onto the Grassmannian space of hyperplanes. ... More

Tangent lines, inflections, and vertices of closed curvesJan 06 2012Mar 06 2013We show that every smooth closed curve C immersed in Euclidean 3-space satisfies the sharp inequality 2(P+I)+V >5 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of vertices (or ... More

Vertices of closed curves in Riemannian surfacesJun 21 2010We uncover some connections between the topology of a complete Riemannian surface M and the minimum number of vertices, i.e., critical points of geodesic curvature, of closed curves in M. In particular we show that the space forms with finite fundamental ... More

On Izumi's theorem on comparison of valuationsOct 14 2008Mar 18 2010We prove that the sequence of MacLane key polynomials constructed in \cite{Mac1} and \cite{Sp2} for a valuation extension $(K,\nu)\subset (K(x),\mu)$ is finite, provided that both $\nu$ and $\mu$ are divisorial and $\mu$ is centered over an analytically ... More

Global optimal regularity for variational problems with nonsmooth non-strictly convex gradient constraintsJul 02 2018Jan 18 2019We prove the optimal $W^{2,\infty}$ regularity for variational problems with convex gradient constraints. We do not assume any regularity of the constraints; so the constraints can be nonsmooth, and they need not be strictly convex. When the domain is ... More

Tree property at successor of a singular limit of measurable cardinalsJan 16 2016Sep 26 2016Assume $\lambda$ is a singular limit of $\eta$ supercompact cardinals, where $\eta \leq \lambda$ is a limit ordinal. We present two forcing methods for making $\lambda^+$ the successor of the limit of the first $\eta$ measurable cardinals while the tree ... More

Lagrangian analysis of the laminar flat plate boundary layerApr 05 2016Sep 17 2016The flow properties at the leading edge of a flat plate represent a singularity to the Blasius laminar boundary layer equations, by applying the Lagrangian approach the leading edge velocity profiles of the laminar boundary layer over a flat plate are ... More

HOD, V and the GCHDec 19 2015Starting from large cardinals we construct a model of $ZFC$ in which the $GCH$ fails everywhere, but such that $GCH$ holds in its $HOD$. The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we produce a model ... More

An Easton like theorem in the presence of Shelah CardinalsMar 08 2016Sep 27 2016We show that Shelah cardinals are preserved under the canonical $GCH$ forcing notion. We also show that if $GCH$ holds and $F:REG\rightarrow CARD$ is an Easton function which satisfies some weak properties, then there exists a cofinality preserving generic ... More

Minimal regular models of quadratic twists of genus two curvesNov 08 2015Let $K$ be a complete discrete valuation field with ring of integers $R$ and residue field $k$ of characteristic $p>2$. We assume moreover that $k$ is algebraically closed. Let $C$ be a smooth projective geometrically connected curve of genus $2$. If ... More

On solubility of groups with finitely many centralizersMay 03 2012For any group G, let C(G) denote the set of centralizers of G. We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n. In this note, we prove that every finite Cn-group with n ? 21 is soluble and this estimate is sharp. Moreover, we ... More

On Representation Theory of Total (Co)IntegralsFeb 08 2014Feb 18 2014In this paper, we show that total integrals and cointegrals are new sources of stable anti Yetter-Drinfeld modules. We explicitly show that how special types of total (co)integrals can be used to provide both (stable) anti Yetter-Drinfeld and Yetter- ... More

Quartic Quasi-Topological-Born-Infeld GravityMar 30 2015Sep 08 2015In this paper, quartic quasi-topological black holes in the presence of a nonlinear electromagnetic Born-Infeld field is presented. By using the metric parameters, the charged black hole solutions of quasi-topological Born-Infeld gravity is considered. ... More

A Note on Derivations of Lie AlgebrasNov 07 2010In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is necessarily solvable. ... More

The Capacity of Degraded Cognitive Interference Channel with Unidirectional Destination CooperationJan 22 2018Previous works established the capacity region for some special cases of discrete memoryless degraded cognitive interference channel (CIC) with unidirectional destination cooperation (UDC). In this letter, we characterize the capacity region of the general ... More

On the matrix harmonic meanMay 17 2018The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a new type of ... More

Refactoring Software Packages via Community Detection from Stability Point of ViewNov 26 2018As the complexity and size of software projects increases in real-world environments, maintaining and creating maintainable and dependable code becomes harder and more costly. Refactoring is considered as a method for enhancing the internal structure ... More

Smart False Data Injection attacks against State Estimation in Power GridSep 19 2018In this paper a new class of cyber attacks against state estimation in the electric power grid is considered. This class of attacks is named false data injection attacks. We show that with the knowledge of the system configuration an attacker could successfully ... More

Multi-species Stochastic Model And Effective Stochastic Generator with Site-Dependent InteractionsApr 28 2019May 01 2019The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective processes can ... More

A Note on the Construction of Complex and Quaternionic Vector Fields on SpheresMay 16 2016A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard $(4n-1)$-sphere ... More

A new construction of the degree of maximal monotone mapsMay 18 2018Apr 02 2019The inclusion equations of the type $f \in T ( x)$ where $T: X \to 2^{X^{\ast}}$ is a maximal monotone map, are extensively studied in nonlinear analysis. In this paper, we present a new construction of the degree of maximal monotone maps of the form ... More

On a question related to bounded approximate identities of ideals in Banach algebrasDec 18 2018In this paper we give an example of a Banach algebra $A$ and a closed ideal $I$ of $A$ such that the multiplier algebra of $I$ is equal to $A$ but $I$ does not have any bounded approximate identity. In the case that $I$ has an approximate identity, we ... More