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A Neural Network Prediction Based Adaptive Mode Selection Scheme in Full-Duplex Cognitive NetworksApr 12 2019We propose a neural network (NN) predictor and an adaptive mode selection scheme for the purpose of both improving secondary user's (SU's) throughput and reducing collision probability to the primary user (PU) in full-duplex (FD) cognitive networks. SUs ... 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

Adaptive Full Duplex Communications in Cognitive Radio NetworksOct 16 2017In this paper we propose a novel adaptive scheme for full duplex communication of secondary users (SUs) in a cognitive radio network. The secondary network operates in three modes; Cooperative Sensing (CS), Full Duplex Transmit and Sensing (FDTS), and ... 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

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

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

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

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

Performance Analysis of Energy Consumption in Cache-Enabled Multicast D2D CommunicationsOct 11 2017Device-to-Device (D2D) communication as a promising technology in 5G cellular networks provides the communication of the users in the vicinity and thereby decreases end-to-end delay and power consumption. In addition to the aforementioned advantages, ... More

Optimization of Rate Allocation and Power Control for Rate Splitting Multiple Access (RSMA)Mar 19 2019In this paper, the sum-rate maximization problem is studied for wireless networks that use downlink rate splitting multiple access (RSMA). In the considered model, each base station (BS) divides the messages that must be transmitted to its users into ... 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 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

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

Full-Duplex Device-to-Device Collaboration for Low-Latency Wireless Video DistributionApr 12 2017Apr 18 2017Growing demand for video services is the main driver for increasing traffic in wireless cellular data networks. Wireless video distribution schemes have recently been proposed to offload data via Device-to-Device (D2D) communications. These offloading ... More

Performance Analysis of Inband FD-D2D Communications with Imperfect SI Cancellation for Wireless Video DistributionJun 19 2017Tremendous growing demand for high data rate services is the main driver for increasing traffic in wireless cellular networks. Device-to-Device (D2D) communications have recently been proposed to offload data via direct communications by bypassing cellular ... 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

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

Multi-Antenna Assisted Virtual Full-Duplex Relaying with Reliability-Aware Iterative DecodingJul 13 2017Oct 18 2017In this paper, a multi-antenna assisted virtual full-duplex (FD) relaying with reliability-aware iterative decoding at destination node is proposed to improve system spectral efficiency and reliability. This scheme enables two half-duplex relay nodes, ... More

Spectral Efficiency of OFDMA Cognitive Radios under Imperfect Cross-Link KnowledgeOct 19 2017We analyze the spectral efficiency performance and limits of orthogonal frequency-division multiple access (OFDMA) cognitive radios (CRs) with an imperfect availability of cross-link knowledge. In particular, in contrast to the conventional `average' ... More

Square Deviation Based Symbol-Level Selection for Virtual Full-Duplex Relaying NetworksJul 14 2017Nov 02 2017In this paper, a symbol-level selective transmission for virtual full-duplex (FD) relaying networks is proposed, which aims to mitigate error propagation effects and improve system spectral efficiency. The idea is to allow two half-duplex relays, mimicked ... 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

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

Sum-Rate Maximization of Uplink Rate Splitting Multiple Access (RSMA) CommunicationJun 10 2019In this paper, the problem of maximizing the wireless users' sum-rate for uplink rate splitting multiple access (RSMA) communications is studied. In the considered model, each user transmits a superposition of two messages to a base station (BS) with ... More

Spectral Efficiency of Multi-User Adaptive Cognitive Radio NetworksSep 13 2017In this correspondence, the comprehensive problem of joint power, rate, and subcarrier allocation have been investigated for enhancing the spectral efficiency of multi-user orthogonal frequency-division multiple access (OFDMA) cognitive radio (CR) networks ... More

Adaptive Modulation and Coding and Cooperative ARQ in a Cognitive Radio SystemSep 12 2017In this paper, a joint cross-layer design of adaptive modulation and coding (AMC) and cooperative automatic repeat request (C-ARQ) scheme is proposed for a secondary user in a shared-spectrum environment. First, based on the statistical descriptions of ... More

On the Ergodic Rate of OFDMA Cognitive Radios under Imperfect Cross-Link InformationNov 17 2017The ergodic rate performance and limits of orthogonal frequency-division multiple access (OFDMA) cognitive radios (CRs) is studied under imperfect cross-link knowledge. We propose a novel stochastic interference management and exploitation technique to ... More

Traveling Waves for a Microscopic Model of Traffic FlowSep 26 2017Dec 19 2017We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a local density ... 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

$(1+2u)$-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

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

A generalization of Browder degreeJan 10 2018May 18 2018Let $X$ be a Banach space, $X^*$ its topological dual, and let $Y$ be a reflexive separable Banach space continuously embedded in $X$. For a bounded demi-continuous map $A:Y \to X^*$ satisfying the $(S)_+$ condition, a topological index is defined in ... 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

On Antipodes Of Hom-Hopf algebrasMar 05 2018Mar 24 2019In the recent definition of Hom-Hopf algebras the antipode S is the relative Hominverse of the identity map with respect to the convolution product. We observe that some fundamental properties of the antipode of Hopf algebras and Hom-Hopf algebras, with ... 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

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

A Novel Square Wave Generator Based on the Translinear Circuit Scheme of Second Generation Current Controlled Current Conveyor-CCCIINov 06 2018Mar 08 2019A robust square wave generator employing a sole capacitor and two resistors has been presented in this study. Low power and popular translinear circuit scheme of Second generation current controlled current conveyor-CCCII has been taken as an active element ... More

On the stationary solutions of Doi-Onsager model in general dimensionMar 06 2018We give new results of the phase transition of dilute colloidal solutions of rod-like molecules in dimension $D \geq 3$. For the low concentration of particles in a carrier fluid, we prove that the isotropic phase is the unique solution to the Doi-Onsager ... 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

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

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

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

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

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

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

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

Multiscale analysis of accelerated gradient methodsJul 30 2018May 20 2019Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow. Using geometric ... 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

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

Lagrange's Theorem For Hom-GroupsMar 20 2018Dec 07 2018Hom-groups are nonassociative generalizations of groups where the unitality and associativity are twisted by a map. We show that a Hom-group (G, {\alpha}) is a pointed idempotent quasigroup (pique). We use Cayley table of quasigroups to introduce some ... 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 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

A Survey on Cloud Video Multicasting Over Mobile NetworksJul 02 2017Since multimedia streaming has become very popular research topic in the recent years, this paper surveys the state of art techniques introduced for multimedia multicasting over mobile networks. In this paper, we give an overview of multimedia multicasting ... More

A Survey of Bandwidth and Latency Enhancement Approaches for Mobile Cloud Game MulticastingJul 02 2017Among mobile cloud applications, mobile cloud gaming has gained a significant popularity in the recent years. In mobile cloud games, textures, game objects, and game events are typically streamed from a server to the mobile client. One of the challenges ... 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

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

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

More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphismJan 21 2017For two Banach algebras $A$ and $B$, the $T$-Lau product $A\times_T B$, was recently introduced and studied for some bounded homomorphism $T:B\to A$ with $\|T\|\leq 1$. Here, we give general nessesary and sufficent conditions for $A\times_T B$ to be (approximately) ... 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

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

The length, width, and inradius of space curvesMay 04 2016Jan 16 2018The 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

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

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 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