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Energy-Efficient Data Collection and Wireless Power Transfer Using A MIMO Full-Duplex UAVNov 22 2018In this paper, we propose a novel energy-efficient data collection and wireless power transfer (WPT) framework for internet of things (IoT) applications, via a multiple-input multiple-output (MIMO) full-duplex (FD) unmanned aerial vehicle (UAV). To exploit ... More

Wireless Network Coding in Network MIMO: A New Design for 5G and BeyondJan 22 2018May 21 2018Physical layer network coding (PNC) has been studied to serve wireless network MIMO systems with much lower backhaul load than approaches such as Cloud Radio Access Network (Cloud-RAN) and coordinated multipoint (CoMP). In this paper, we present a design ... More

Cache Placement in Two-Tier HetNets with Limited Storage Capacity: Cache or Buffer?Jun 06 2018In this paper, we aim to minimize the average file transmission delay via bandwidth allocation and cache placement in two-tier heterogeneous networks with limited storage capacity, which consists of cache capacity and buffer capacity. For average delay ... More

Transmission Capacity of Full-Duplex MIMO Ad-Hoc Network with Limited Self-Interference CancellationApr 29 2018Sep 09 2018In this paper, we propose a joint transceiver beamforming design to simultaneously mitigate self-interference (SI) and partial inter-node interference for full-duplex multiple-input and multiple-output ad-hoc network, and then derive the transmission ... More

Cross-layer Design in Cognitive Radio StandardsNov 26 2017The growing demand for wireless applications and services on the one hand, and limited available radio spectrum on the other hand have made cognitive radio (CR) a promising solution for future mobile networks. It has attracted considerable attention by ... More

Edge Computing and Dynamic Vision Sensing for Low Delay Access to Visual Medical InformationNov 10 2017A new method is proposed to decrease the transmission delay of visual and non-visual medical records by using edge computing and Dynamic Vision Sensing (DVS) technologies. The simulation results show that the proposed scheme can decrease the transmission ... More

Evaluation of Availability of Initial-segments of Video Files in Device-to-Device (D2D) NetworkOct 19 2017We propose a new caching concept in which wireless nodes in Device-to-Device (D2D) network can cache the initial-segments of the popular video files and may share to users in their proximity upon request. We term this approach as Bootstrapping- D2D (B-D2D) ... More

Joint Time-Frequency Splitting for Multiuser SWIPT OFDM NetworksFeb 08 2019In this paper, we propose a joint time-frequency splitting (TFS) strategy for a multiuser orthogonal frequency division multiplexing (OFDM) system with simultaneous wireless information and power transfer (SWIPT). In TFS, the time sharing factors for ... More

Energy Efficient Resource Allocation for Mobile-Edge Computation Networks with NOMASep 04 2018Feb 14 2019This paper investigates an uplink non-orthogonal multiple access (NOMA)-based mobile-edge computing (MEC) network. Our objective is to minimize the total energy consumption of all users including transmission energy and local computation energy subject ... More

Resource Allocation in Full-Duplex Mobile-Edge Computing Systems with NOMA and Energy HarvestingJul 31 2018This paper considers a full-duplex (FD) mobile-edge computing (MEC) system with non-orthogonal multiple access (NOMA) and energy harvesting (EH), where one group of users simultaneously offload task data to the base station (BS) via NOMA and the BS simultaneously ... More

An Adaptive Optimal Mapping Selection Algorithm for PNC using Variable QAM ModulationMay 15 2018Fifth generation (5G) wireless networks will need to serve much higher user densities than existing 4G networks, and will therefore require an enhanced radio access network (RAN) infrastructure. Physical layer network coding (PNC) has been shown to enable ... More

Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019Feb 13 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More

Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More

A Physical Layer Network Coding Design for 5G Network MIMOMay 01 2018This paper presents a physical layer network coding (PNC) approach for network MIMO (N-MIMO) systems to release the heavy burden of backhaul load. The proposed PNC approach is applied for uplink scenario in binary systems, and the design guideline serves ... More

Symbol-Level Selective Full-Duplex Relaying with Power and Location OptimizationDec 20 2017Jun 02 2018In this paper, a symbol-level selective transmission for full-duplex (FD) relaying networks is proposed to mitigate error propagation effects and improve system spectral efficiency. The idea is to allow the FD relay node to predict the correctly decoded ... More

Joint Altitude, Beamwidth, Location and Bandwidth Optimization for UAV-Enabled CommunicationsJun 06 2018This letter investigates an uplink power control problem for unmanned aerial vehicles (UAVs) assisted wireless communications. We jointly optimize the UAV's flying altitude, antenna beamwidth, UAV's location and ground terminals' allocated bandwidth and ... 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

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

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

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

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

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

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

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

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

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

Advanced refinements of Young and Heinz inequalitiesJun 22 2016Oct 08 2016In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*} A\#_{\nu}B&+&\sum_{j=1}^{N}s_{j}(\nu)\left(A\#_{\alpha_j(\nu)}B+A\#_{2^{1-j}+\alpha_j(\nu)}B-2A\#_{2^{-j}+\alpha_j(\nu)}B\right)\leq ... 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

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

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

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

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

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

Relative symmetric polynomials and money change problemDec 14 2010This article is devoted to the number of non-negative solutions of the linear Diophantine equation $$ a_1t_1+a_2t_2+... a_nt_n=d, $$ where $a_1, ..., a_n$, and $d$ are positive integers. We obtain a relation between the number of solutions of this equation ... 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

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.

Diamond can fail at the least inaccessible cardinalJul 04 2016Starting from suitable large cardinals, we force the failure of diamond at the least inaccessible cardinal. The result improves an unpublished theorem of Woodin.

Polytropic gas scalar field models of dark energyJun 04 2012Jul 16 2013In this work we investigate the polytropic gas dark energy model in the non flat universe. We first calculate the evolution of EoS parameter of the model as well as the cosmological evolution of Hubble parameter in the context of polytropic gas dark energy ... More

(Weak) diamond can fail at the least inaccessible cardinalJul 04 2016Oct 31 2016Starting from suitable large cardinals, we force the failure of (weak) diamond at the least inaccessible cardinal. The result improves an unpublished theorem of Woodin and a recent result of Ben-Neria, Garti and Hayut.

Almost Souslin Kurepa treesOct 10 2015We show that the existence of an almost Souslin Kurepa tree is consistent with $ZFC$. We also prove their existence in $L$. These results answer two questions from Zakrzewski.

Character Sums, Gaussian Hypergeometric Series, and a Family of Hyperelliptic CurvesJul 03 2015Dec 08 2015We study the character sums \[\phi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left(x(x^{m}+a)(x^{n}+b)\right),\textrm{ and, } \psi_{(m,n)}(a,b)=\sum_{x\in\mathbb{F}_q}\phi\left((x^{m}+a)(x^{n}+b)\right)\] where $\phi$ is the quadratic character defined ... More

On the notion of generic cut for models of ZFCJan 28 2015We define the notion of generic cut between models of ZFC and give some examples.

Hyperbolic Lagrangian coherent structures align with contours of path-averaged scalarsJan 21 2015Jul 26 2015While inequality (9) is mathematically correct, it does not imply alignment between path-averaged scalars and the hyperbolic LCSs.

Convex functions and means of matricesJun 26 2016In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality, the arithmetic-harmonic ... More

Power set at $\aleph_ω$: On a theorem of WoodinJan 16 2016We give Woodin's original proof that if there exists a $(\kappa+2)-$strong cardinal $\kappa,$ then there is a generic extension of the universe in which $\kappa=\aleph_\omega,$ $GCH$ holds below $\aleph_\omega$ and $2^{\aleph_\omega}=\aleph_{\omega+2}.$ ... More

Generalized injectivity of Banach modulesFeb 16 2015Feb 25 2015In this paper, we study the notion of $\phi$-injectivity in the special case that $\phi=0$. For an arbitrary locally compact group $G$, we characterize the 0-injectivity of $L^{1}(G)$ as a left $L^{1}(G)$ module. Also, we show that $L^{1}(G)^{**}$ and ... More

K(X,Y) as subspace complemented of L(X,Y)Nov 09 2014Mar 23 2016Let X,Y be two Banach spaces ; in the first part of this work, we show that K(X,Y) contains a complemented copy of c0 if Y contains a copy of c0 and each bounded sequence in Y has a subsequece which is w* convergente. Afterward we obtain some results ... More

Clustering Fossils in Solid InflationSep 10 2014In solid inflation the single field non-Gaussianity consistency condition is violated. As a result, the long tensor perturbation induces observable clustering fossils in the form of quardupole anisotropy in large scale structure power spectrum. In this ... More

New Coefficients For Hopf Cyclic CohomologyFeb 15 2012Jan 03 2014In this note the categories of coefficients for Hopf cyclic cohomology of comodule algebras and comodule coalgebras are extended. We show that these new categories have two proper different subcategories where the smallest one is the known category of ... More

Estimation of mean vector in elliptical modelsMar 06 2012In this paper, we are basically discussing on a class of Baranchik type shrinkage estimators of the vector parameter in a location model, with errors belonging to a sub-class of elliptically contoured distributions. We derive conditions under Schwartz ... More