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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Duality and Serre functor in homotopy categoriesMay 25 2017For a (right and left) coherent ring $A$, we show that there exists a duality between homotopy categories ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A^{{\rm op}})$ and ${\mathbb{K}}^{{\rm{b}}}({\rm mod}{\mbox{-}}A)$. If $A=\Lambda$ is an artin algebra ... 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

$(1+2u)$-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 skew cyclic codes over $F_q+vF_q+v^2F_q$Apr 16 2015In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. ... More

Dense 2-generator subsemigroups of $2\times 2$ matricesApr 27 2011We show that the semigroup of real linear fractional transformations on a proper subinterval of the real line does not admit any 2-generator dense subsemigroups, and then we construct a 3-parameter family of examples of 3-generator dense subsemigroups. ... More

Kinematics and Structure of Clumps in Broad-line Regions in Active Galactic NucleiJul 14 2016We use the Jeans equations for an ensemble of collisionless particles to describe the distribution of broad-line region (BLR) cloud in three classes: (A) non disc (B) disc-wind (c) pure disc structure. We propose that clumpy structures in the brightest ... More

Finding HeavyPaths in Weighted Graphs and a Case-Study on Community DetectionDec 13 2015A heavy path in a weighted graph represents a notion of connectivity and ordering that goes beyond two nodes. The heaviest path of length l in the graph, simply means a sequence of nodes with edges between them, such that the sum of edge weights is maximum ... More

More on almost Souslin Kurepa treesOct 10 2015It is consistent that there exists a Souslin tree $T$ such that after forcing with it, $T$ becomes an almost Souslin Kurepa tree. This answers a question of Zakrzewski.

An adjoint-based approach for finding invariant solutions of Navier-Stokes equationsAug 26 2015Mar 14 2016We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave ... More

Singular cofinality conjecture and a question of GorelicJun 25 2015We give an affirmative answer to a question of Gorelic \cite{Gorelic}, by showing it is consistent, relative to the existence of large cardinals, that there is a proper class of cardinals $\alpha$ with $cf(\alpha)=\omega_1$ and $\alpha^\omega > \alpha.$ ... More

BSE property for some certain Segal algebras with applications to the Fourier algebraJun 07 2015Aug 12 2015In this paper, we study the BSE-property for some certain Segal algebras. As an application, we give some results on subalgebras of the Fourier algebra and provide a wide range of Banach algebras with the BSE-property. Also, we give a generalization of ... More

On the notions of dimension and transcendence degree for models of ZFCJan 25 2015We define notions of generic dimension and generic transcendence degree between models of ZFC and give some examples.

Woodin's surgery methodJan 12 2015In this short paper we give an overview of Woodin's surgery method.

On J-orders of elements of $KO(CP^m)$Jun 03 1999Let $KO(CP^m)$ be the KO-ring of the complex projective space $CP^m.$ By means of methods of rational D-series, a formula for the J-orders of elements of $KO(CP^m)$ is given. Explicit formulas are given for computing the J-orders of the canonical generators ... More

A note on the localization of J-groupsMay 25 1999Let $\widetilde{JO}(X)=\widetilde{KO}(X)/TO(X)$ be the J-group of a connected finite CW complex X. We Obtain two computable formulas of $TO(X)_{(p)}$, the localization of $TO(X)$ at a prime p. Then we show how to use these two formulas of $TO(X)_{(p)}$ ... More

On certain product of Banach modulesJun 15 2016Let $A$ and $B$ be Banach algebras and let $B$ be an algebraic Banach $A-$bimodule. Then the $\ell^1-$direct sum $A\times B$ equipped with the multiplication $$(a_1,b_1)(a_2,b_2)=(a_1a_2,a_1\cdot b_2+b_1\cdot a_2+b_1b_2),~~ (a_1, a_2\in A, b_1, b_2\in ... More

An example of non-embedability of the Ricci flowAug 10 2014For an evolution of metrics $(M,g_{t})$ there is a t-smooth family of embeddings $e_{t}:M\to\mathbb{R}^{N}$ inducing $g_{t}$, but in general there is no family of embeddings extending a given initial embedding $e_{0}$. We give an example of this phenomenon ... More

On elliptic curves whose conductor is a product of two prime powersJun 16 2012Oct 14 2012We find all elliptic curves defined over $\mathbb{Q}$ that have a rational point of order $N$, $N\ge 4$, and whose conductor is of the form $p^aq^b$, where p, q are two distinct primes, a, b are two positive integers. In particular, we prove that Szpiro's ... More

Effective Capacity of Receive Antenna Selection MIMO-OSTBC Systems in Co-Channel InterferenceAug 02 2016In this paper, delay constrained performance of a multiple-input multiple-output (MIMO) communication system in a dense environment with co-channel interference is investigated. We apply orthogonal space-time block coding (OSTBC) at the transmitter, and ... More

Nonnilpotent subsets in the susuki groupsSep 22 2013Let G be a group and N be the class of nilpotent groups. A subset A of G is said to be nonnilpotent if for any two distinct elements a and b in A, ha, bi 62 N. If, for any other nonnilpotent subset B in G, |A| ? |B|, then A is said to be a maximal nonnilpotent ... More

Non-nilpotent subgroups of locally graded groupsDec 04 2014In this paper, we show that a locally graded group with a finite number m of non-(nilpotent of class at most n) subgroups is (soluble of class at most [log2(n)] + m + 3)-by-(finite of order $\le$ m!). Also we show that the derived length of a soluble ... More

Hopf Galois (Co)Extensions In Noncommutative GeometryApr 09 2012May 25 2013We introduce an alternative proof, with the use of tools and notions for Hopf algebras, to show that Hopf Galois coextensions of coalgebras are the sources of stable anti Yetter-Drinfeld modules. Furthermore we show that two natural cohomology theories ... More

Searching for quantum speedup in quasistatic quantum annealersMar 13 2015Nov 19 2015We argue that a quantum annealer at very long annealing times is likely to experience a quasistatic evolution, returning a final population that is close to a Boltzmann distribution of the Hamiltonian at a single (freeze-out) point during the annealing. ... More

Directed immersions of closed manifoldsOct 12 2010Oct 25 2010Given any finite subset X of the sphere S^n, n>1, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space R^{n+1} whose Gauss map misses X. In particular, this answers a ... More

From Once Upon a Time to Happily Ever After: Tracking Emotions in Novels and Fairy TalesSep 23 2013Today we have access to unprecedented amounts of literary texts. However, search still relies heavily on key words. In this paper, we show how sentiment analysis can be used in tandem with effective visualizations to quantify and track emotions in both ... More

The length, width, and inradius of space curvesMay 04 2016The width $w$ of a curve $\gamma$ in Euclidean space $R^n$ is the infimum of the distances between all pairs of parallel hyperplanes which bound $\gamma$, while its inradius $r$ is the supremum of the radii of all spheres which are contained in the convex ... More

Shadows and convexity of surfacesSep 20 2004We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H. Wente.

The regularity of some vector-valued variational inequalities with gradient constraintsJan 21 2015Apr 16 2015We prove the optimal regularity for some class of vector-valued variational inequalities with gradient constraints. We also give a new proof for the optimal regularity of some scalar variational inequalities with gradient constraints. In addition, we ... More

On non-commuting sets and centralizers in infinite groupDec 14 2014A subset X of a group G is a set of pairwise non-commuting ele- ments if ab 6= ba for any two distinct elements a and b in X. If jXj ? jY j for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise ... More

Fraïssé limit via forcingFeb 17 2019Given a Fra\"{i}ss\'{e} class $\mathcal{K}$ and an infinite cardinal $\kappa,$ we define a forcing notion which adds a structure of size $\kappa$ using elements of $\mathcal{K}$, which extends the Fra\"{i}ss\'{e} construction in the case $\kappa=\omega.$ ... More

Hom-Groups, Representations and Homological AlgebraJan 23 2018Mar 24 2018A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples of Homalgebras, ... More

The generalized Kurepa hypothesis at singular cardinalsDec 07 2017We discuss the generalized Kurepa hypothesis $KH_{\lambda}$ at singular cardinals $\lambda$. In particular, we answer questions of Erd\"{o}s-Hajnal [1] and Todorcevic [6], [7] by showing that $GCH$ does not imply $KH_{\aleph_\omega}$ nor the existence ... More

Self-biased current, magnetic interference response, and superconducting vortices in tilted Weyl semimetals with disorderNov 28 2018Jan 21 2019We have generalized a quasiclassical model for Weyl semimetals with a tilted band in the presence of an externally applied magnetic field. This model is applicable to ballistic, moderately disordered, and samples containing a high density of nonmagnetic ... 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

A Simplification in the proof presented for non existence of periodic solutions in time invariant fractional order systemsFeb 27 2012In this note, a short-cut is proposed to shorten the proof which has been previously presented for non existence of periodic solutions in time invariant fractional order systems.

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

A Game-Theoretic Framework for Studying Dynamics of Multi Decision-maker SystemsDec 24 2014System Dynamics (SD) main aim is to study dynamic behavior of systems based on causal relations. The other purpose of the science is to design policies, both in initial values and causal relation, to change system behavior as we desire. Especially we ... 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 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 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

Boundary torsion and convex caps of locally convex surfacesJan 29 2015Sep 11 2015We prove that the torsion of any closed space curve which bounds a simply connected locally convex surface vanishes at least 4 times. This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of positively curved ... More

Semigroups of real functions with dense orbitsAug 23 2009Let ${\mathcal F}_I=\{f:I \to I| f(x)= (Ax+B)/(Cx+D); AD-BC \neq 0 \}$, where $I$ is an interval. For $x\in I$, let ${\Omega}_x$ be the orbit of $x$ under the action of the semigroup of functions generated by $f,g \in {\mathcal F}_I$. Our main result ... More

Affine unfoldings of convex polyhedraMay 14 2013Apr 21 2014We show that every convex polyhedron admits a simple edge unfolding after an affine transformation. In particular there exists no combinatorial obstruction to a positive resolution of Durer's unfoldability problem, which answers a question of Croft, Falconer, ... More

On the norm of the centralizers of a groupJul 14 2015For any group G, let C(G) denote the intersection of the normal- izers of centralizers of all elements of G. Set C0 = 1. Define Ci+1(G)=Ci(G) = C(G=Ci(G)) for i ? 0. By C1(G) denote the terminal term of the ascending series. In this paper, we show that ... More

Periodic continued fractions and elliptic curves over quadratic fieldsNov 22 2014Nov 25 2014Let $f(x)$ be a square free quartic polynomial defined over a quadratic field $K$ such that its leading coefficient is a square. If the continued fraction expansion of $\displaystyle \sqrt{f(x)}$ is periodic, then its period $n$ lies in the set \[\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,22,26,30,34\}.\] ... More

Searching Lattice Data Structures of Varying Degrees of SortednessMay 13 2016Lattice data structures are space efficient and cache-suitable data structures. The basic searching, insertion, and deletion operations are of time complexity $O(\sqrt{N})$. We give a jump searching algorithm of time complexity $O(J(L)\log(N))$, where ... More

O-segments on topological measure spacesJun 06 2008Let $X$ be a topological space and $\mu$ be a nonatomic finite measure on a $\sigma$-algebra $\Sigma$ containing the Borel $\sigma$-algebra of $X$. We say $\mu$ is weakly outer regular, if for every $A \in \Sigma$ and $\epsilon>0$, there exists an open ... More

Consistency in Distributed Data StoresApr 26 2016This paper focuses on the problem of consistency in distributed data stores.We define strong consistency model which provides a simple semantics for application programmers, but impossible to achieve with availability and partition-tolerance. We also ... More

Power Allocation and Effective Capacity of AF Successive RelaysSep 13 2016In the relay based telecommunications with $K$ relays between the source and destination, $K+1$ time or frequency slots are required for a single frame transmission. However, without the relays, only one time or frequency slot is used for a single frame ... More

Lagrangian analysis of the laminar flat plate boundary layerApr 05 2016Nov 06 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

Cryptanalysis of some protocols using matrices over group ringsMar 16 2015We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.

Definable tree property can hold at all uncountable regular cardinalsAug 24 2016Aug 31 2016Starting from a supercompact cardinal and a measurable above it, we construct a model of ZFC in which definable tree property holds at all uncountable regular cardinals. This answers a question from [1].

All uncountable regular cardinals can be inaccessible in HODAug 02 2016Assuming the existence of a supercompact cardinal and an inaccessible above it, we construct a model of ZFC, in which all uncountable regular cardinals are inaccessible in HOD.

Tree property at successor of a singular limit of measurable cardinalsJan 16 2016Oct 18 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

Detecting Cognitive Appraisals from Facial Expressions for Interest RecognitionSep 30 2016Oct 10 2016Interest makes one hold her attention on the object of interest. Automatic recognition of interest has numerous applications in human-computer interaction. In this paper, we study the facial expressions associated with interest and its underlying and ... More

Notes on countably generated complete Boolean algebrasNov 08 2016We give a necessary and sufficient condition for an atomless Boolean algebra to be countably generated, and use it to give new proofs of some some know facts due to Gaifman-Hales and Solovay and also due to Jech, Kunen and Magidor. We also show that Jensen's ... More

Amenable groups and bounded $Δ$-weak approximate identitiesApr 08 2014Let $A$ be a Banach algebra with a non-empty character space. We say that a bounded net $\{e_{\alpha}\}$ in $A$ is a bounded $\Delta$-weak approximate identity for $A$ if, for each $a\in A$ and compact subset $K$ of $\Delta(A)$, $||\widehat{e_{\alpha}a}-\widehat{a}||_{K}=\sup_{\phi\in ... More

Une remarque sur les espaces d'interpolation faiblement localement uniformément convexesJun 21 2012Let $(A_0, A_1)$ be an interpolation couple, and let $B_j$ be the closure of $A_0^\ast \cap A_1^\ast$ in $A_j^\ast$, $j = 0, 1$. For every $\theta \in \, ]0, 1[$, there exists a natural one to one contraction $R^\theta : A^\theta \rightarrow (B_0^\ast, ... More