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Entropic effects in the self-assembly of open lattices from patchy particlesMar 02 2013Open lattices are characterized by low volume-fraction arrangements of building blocks, low coordination number, and open spaces between building blocks. The self-assembly of these lattices faces the challenge of mechanical instability due to their open ... More

Finite temperature mechanical instability in disordered latticesMar 18 2015Mechanical instability takes different forms in various ordered and disordered systems. We study the effect of thermal fluctuations in two disordered central-force lattice models near mechanical instability: randomly diluted triangular lattice and randomly ... More

Rigidity percolation on the square latticeJul 20 2011The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation transition which ... More

Self-assembly of three-dimensional open structures using patchy colloidal particlesMar 04 2014Open structures can display a number of unusual properties, including a negative Poisson's ratio, negative thermal expansion, and holographic elasticity, and have many interesting applications in engineering. However, it is a grand challenge to self-assemble ... More

Coherent potential approximation of random nearly isostatic kagome latticeAug 12 2010The kagome lattice has coordination number $4$, and it is mechanically isostatic when nearest neighbor ($NN$) sites are connected by central force springs. A lattice of $N$ sites has $O(\sqrt{N})$ zero-frequency floppy modes that convert to finite-frequency ... More

Elasticity of Filamentous Kagome LatticeJan 05 2013Jan 16 2013The diluted kagome lattice, in which bonds are randomly removed with probability $1-p$, consists of straight lines that intersect at points with a maximum coordination number of four. If lines are treated as semi-flexible polymers and crossing points ... More

Effective Medium Theory of Filamentous Triangular LatticeNov 07 2011Jan 05 2013We present an effective medium theory that includes bending as well as stretching forces, and we use it to calculate mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending ... More

Topological mechanics in quasicrystalsSep 24 2018We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy ... More

Fiber networks below the isostatic point: fracture without stress concentrationDec 28 2016Crack nucleation is a ubiquitous phenomena during materials failure, because stress focuses on crack tips. It is known that exceptions to this general rule arise in the limit of strong disorder or vanishing mechanical stability, where stress distributes ... More

Transformable topological mechanical metamaterialsOct 21 2015Mechanical metamaterials are engineered materials that gain their remarkable mechanical properties, such as negative Poisson's ratios, negative compressibility, phononic bandgaps, and topological phonon modes, from their structure rather than composition. ... More

Nonlinear elasticity of disordered fiber networksJul 27 2015Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated ... More

Mechanical instability at finite temperatureJul 08 2014Many physical systems including lattices near structural phase transitions, glasses, jammed solids, and bio-polymer gels have coordination numbers that place them at the edge of mechanical instability. Their properties are determined by an interplay between ... More

Jamming as a Multicritical PointSep 25 2018Jan 10 2019The discontinuous jump in the bulk modulus $B$ at the jamming transition is a consequence of the formation of a critical contact network of spheres that resists compression. We introduce lattice models with underlying under-coordinated compression resistant ... More

Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite FrequenciesMay 07 2018Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted experimental characterization ... More

Elastic heterogeneity of soft random solidsOct 16 2006Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel, which induces randomness ... More

Elasticity of highly cross-linked random networksAug 17 2006Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the elastic energy of ... More

Fracturing of topological Maxwell latticesJan 25 2018We present fracturing analysis of topological Maxwell lattices when they are stretched by applied stress. Maxwell lattices are mechanical structures containing equal numbers of degrees of freedom and constraints in the bulk and are thus on the verge of ... More

Non-affine displacements in flexible polymer networksNov 28 2010The validity of the affine assumption in model flexible polymer networks is explored. To this end, the displacements of fluorescent tracer beads embedded in polyacrylamide gels are quantified by confocal microscopy under shear deformation, and the deviations ... More

Capillary-driven binding of thin triangular prisms at fluid interfacesFeb 08 2018We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $\mu m$, and the thickness of the prism is varied between 2 and 20 $\mu m$. For thickness ... More

Finite-temperature buckling of an extensible rodJul 09 2015Thermal fluctuations can play an important role in the buckling of elastic objects at small scales, such as polymers or nanotubes. In this paper, we study the finite-temperature buckling transition of an extensible rod by analyzing fluctuation corrections ... More

A general comparison theorem for 1-dimensional anticipated BSDEsNov 03 2009Oct 28 2011Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the generators depending ... More

Generating the mapping class groups by torsionsJun 14 2015Feb 26 2018Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ ... More

The Extended Mapping Class Group Can Be Generated by Two TorsionsJul 14 2016Feb 26 2018Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these ... More

Folding mechanisms at finite temperatureFeb 08 2018Folding mechanisms are zero elastic energy motions essential to the deployment of origami, linkages, reconfigurable metamaterials and robotic structures. In this paper, we determine the fate of folding mechanisms when such structures are miniaturized ... More

Topological edge floppy modes in disordered fiber networksAug 13 2017Disordered fiber networks are ubiquitous in a broad range of natural (e.g., cytoskeleton) and manmade (e.g., aerogels) materials. In this paper, we discuss the emergence of topological floppy edge modes in these fiber networks as a result of deformation ... More

Soft modes and elasticity of nearly isostatic lattices: randomness and dissipationSep 14 2009Apr 15 2010The square lattice with central-force springs on nearest-neighbor bonds is isostatic. It has a zero mode for each row and column, and it does not support shear. Using the Coherent Potential Approximation (CPA), we study how the random addition, with probability ... More

New upper bound on block sensitivity and certificate complexity in terms of sensitivityJun 19 2013Jun 24 2013Sensitivity \cite{CD82,CDR86} and block sensitivity \cite{Nisan91} are two important complexity measures of Boolean functions. A longstanding open problem in decision tree complexity, the "Sensitivity versus Block Sensitivity" question, proposed by Nisan ... More

Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome latticesDec 05 2011Model lattices consisting of balls connected by central-force springs provide much of our understanding of mechanical response and phonon structure of real materials. Their stability depends critically on their coordination number $z$. $d$-dimensional ... More

Soft random solids and their heterogeneous elasticityDec 20 2008Apr 15 2010Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also ... More

Cavity Approach to the Random Solid StateJun 08 2005The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal motion. This ... More

Elasticity of randomly diluted honeycomb and diamond lattices with bending forcesJan 22 2016Mar 01 2016We use numerical simulations and an effective-medium theory to study the rigidity percolation transition of the honeycomb and diamond lattices when weak bond-bending forces are included. We use a rotationally invariant bond-bending potential, which, in ... More

Convergence analysis of the direct extension of ADMM for multiple-block separable convex minimizationSep 23 2016Recently, the alternating direction method of multipliers (ADMM) has found many efficient applications in various areas; and it has been shown that the convergence is not guaranteed when it is directly extended to the multiple-block case of separable ... More

New separation between $s(f)$ and $bs(f)$Aug 17 2011In this note we give a new separation between sensitivity and block sensitivity of Boolean functions: $bs(f)=(2/3)s(f)^2-(1/3)s(f)$.

Consensus Control for Linear Systems with Optimal Energy CostDec 01 2016In this paper, we design an optimal energy cost controller for linear systems asymptotic consensus given the topology of the graph. The controller depends only on relative information of the agents. Since finding the control gain for such controller is ... More

An Efficient and Distribution-Free Two-Sample Test Based on Energy Statistics and Random ProjectionsJul 14 2017A common disadvantage in existing distribution-free two-sample testing approaches is that the computational complexity could be high. Specifically, if the sample size is $N$, the computational complexity of those two-sample tests is at least $O(N^2)$. ... More

A Statistically and Numerically Efficient Independence Test based on Random Projections and Distance CovarianceJan 21 2017Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous advantages, comparing ... More

Optimal output consensus for linear systems: A topology free approachOct 14 2015In this paper, for any homogeneous system of agents with linear continuous time dynamics, we formulate an optimal control problem. In this problem a convex cost functional of the control signals of the agents shall be minimized, while the outputs of the ... More

Alignment and Nonlinear Elasticity in Biopolymer GelsFeb 12 2014Oct 14 2014We present a Landau type theory for the non-linear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the non-linear elastic behavior of these materials to fiber alignment ... More

Random Walker Models for DurotaxisJun 01 2018Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for durotaxis based ... More

Performance Analysis and Optimization for Interference Alignment over MIMO Interference Channels with Limited FeedbackFeb 03 2014In this paper, we address the problem of interference alignment (IA) over MIMO interference channels with limited channel state information (CSI) feedback based on quantization codebooks. Due to limited feedback and hence imperfect IA, there are residual ... More

Joint Optimization of Spectrum Sensing and Accessing in Multiuser MISO Cognitive NetworksJun 30 2014In this paper, a joint spectrum sensing and accessing optimization framework for a multiuser cognitive network is proposed to significantly improve spectrum efficiency. For such a cognitive network, there are two important and limited resources that should ... More

Consensus Control for Linear Systems with Optimal Energy CostDec 01 2016Oct 25 2017In this paper, we design an optimal energy cost controller for linear systems asymptotic consensus given the topology of the graph. The controller depends only on relative information of the agents. Since finding the control gain for such controller is ... More

On the Sensitivity Complexity of $k$-Uniform Hypergraph PropertiesAug 24 2016In this paper we investigate the sensitivity complexity of hypergraph properties. We present a $k$-uniform hypergraph property with sensitivity complexity $O(n^{\lceil k/3\rceil})$ for any $k\geq3$, where $n$ is the number of vertices. Moreover, we can ... More

On Interference Alignment with Imperfect CSI: Characterizations of Outage Probability, Ergodic Rate and SERJan 25 2015In this paper, we give a unified performance analysis of interference alignment (IA) over MIMO interference channels. Rather than the asymptotic characterization, i.e. degree of freedom (DOF) at high signal-to-noise ratio (SNR), we focus on the other ... More

Analysis and simulations of a Viscoelastic Model of AngiogenesisOct 15 2010The work analyzes a one-dimensional viscoelastic model of blood vessel growth under nonlinear friction with surroundings, and provides numerical simulations for various growing cases. For the nonlinear differential equations, two sufficient conditions ... More

Collisionless periodic orbits in the free-fall three-body problemMay 21 2018Although the free-fall three-body problem have been investigated for more than one century, however, only four collisionless periodic orbits have been found. In this paper, we report 234 collisionless periodic orbits of the free-fall three-body system ... More

More than six hundreds new families of Newtonian periodic planar collisionless three-body orbitsApr 26 2017Jul 11 2017The famous three-body problem can be traced back to Isaac Newton in 1680s. In the 300 years since this "three-body problem" was first recognized, only three families of periodic solutions had been found, until 2013 when \v{S}uvakov and Dmitra\v{s}inovi\'c ... More

Diffusion-controlled Alloying of Single-phase Multi-principal Covalent Transition Metal Carbides with Enhanced Damage tolerance and Exceptional Thermal PropertiesSep 02 2018Multicomponent alloying has displayed extraordinary potential for producing exceptional structural and functional materials. However, the synthesis of single-phase, multi-principal covalent compounds remains a challenge. Here we present a diffusion-controlled ... More

Interference-Aware Resource Control in Multi-Antenna Cognitive Ad Hoc Networks with Heterogeneous Delay ConstraintsApr 05 2013In this work, we consider a multi-antenna cognitive ad hoc network (CAHNet) with heterogeneous delay requirements. To fulfill the interference and delay constraints simultaneously, we propose to perform adaptive zero-forcing beamforming (ZFBF) at cognitive ... More

Phonons and elasticity in critically coordinated latticesMar 04 2015Much of our understanding of vibrational excitations and elasticity is based upon analysis of frames consisting of sites connected by bonds occupied by central-force springs, the stability of which depends on the average number of neighbors per site $z$. ... More

Tighter Relations Between Sensitivity and Other Complexity MeasuresNov 13 2014Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related ... More

Elasticity of colloidal gels: structural heterogeneity, foppy modes, and rigidityAug 04 2018Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant. ... More

Correlated rigidity percolation and colloidal gelsJul 23 2018Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid ... More

Criticality and isostaticity in fiber networksNov 30 2010The rigidity of elastic networks depends sensitively on their internal connectivity and the nature of the interactions between constituents. Particles interacting via central forces undergo a zero-temperature rigidity-percolation transition near the isostatic ... More

On the Fundamental Relationship Determining the Capacity of Static and Mobile Wireless NetworksJul 05 2012Studying the capacity of wireless multi-hop networks is an important problem and extensive research has been done in the area. In this letter, we sift through various capacity-impacting parameters and show that the capacity of both static and mobile networks ... More

Relativistic quantum transport theory for heavy-ion collisionsOct 29 2001Oct 26 2003This paper was withdrawn by the author.

Degree reduction of disk rational Bézier curvesSep 08 2014This paper presents an algorithm for optimal multi-degree reduction of rational disk B\'ezier curve in the $L^{2}$ norm. We start by introducing a novel disk rational B\'ezier based on parallel projection, whose properties are also discussed. Then we ... More

Smarandache Multi-Space Theory(II)--Multi-spaces on graphsApr 22 2006A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. ... More

Combinatorial Structure of Manifolds with Poincaré ConjectureApr 08 2010Jun 18 2010A manifold $M^n$ inherits a labeled $n$-dimensional graph $\widetilde{M}[G^L]$ structure consisting of its charts. This structure enables one to characterize fundamental groups of manifolds, classify those of locally compact manifolds with finite non-homotopic ... More

Automorphism groups of maps, surfaces and Smarandache geometriesMay 16 2005A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism group of a Klein surface and a Smarandache manifold, also applied ... More

Pseudo-Manifold Geometries with ApplicationsOct 10 2006A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and ... More

Pions in magnetic field at finite temperatureAug 30 2018Pions in external magnetic field are investigated in the frame of a Pauli-Villars regularized Nambu--Jona-Lasinio model. The meson propagators in terms of quark bubbles in Ritus and Schwinger schemes are analytically derived, and pion masses are numerically ... More

Inverse Magnetic Catalysis in Nambu--Jona-Lasinio Model beyond Mean FieldFeb 21 2016May 13 2016We study inverse magnetic catalysis in the Nambu--Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis ... More

Structure of Compact Stars in Pion Superfluid PhaseFeb 19 2014Jul 19 2014The gross structure of compact stars composed of pion superfluid quark matter is investigated in the frame of Nambu-Jona-Lasinio model. Under the Pauli-Villars regularization scheme, the uncertainty of the thermodynamic functions for inhomogeneous states ... More

Gravitational Microlensing: Past, Present and FutureSep 17 1999Ongoing microlensing surveys have already yielded more than five hundred microlensing events, most of which have been identified in real-time. In this review I present the basic theory and observational status of these surveys. I highlight the discoveries ... More

Rigidity percolation by next-nearest-neighbor braces on generic and regular isostatic latticesDec 20 2014We study rigidity percolation transitions in two-dimensional central-force isostatic lattices, including the square and the kagome lattices, as next-nearest-neighbor bonds ("braces") are randomly added to the system. In particular, we focus on the differences ... More

Research on Wireless Multi-hop Networks: Current State and ChallengesAug 22 2011Wireless multi-hop networks, in various forms and under various names, are being increasingly used in military and civilian applications. Studying connectivity and capacity of these networks is an important problem. The scaling behavior of connectivity ... More

Information Resources Management Framework for Virtual EnterpriseDec 09 2015Dec 14 2015Virtual enterprise is a new form of organization in recent years which adapt to the IT environment. Information resources management implemented in the virtual enterprise is determined by the form of business organization and information exchange mechanisms. ... More

Smarandache Multi-Space Theory(I)-Algebraic multi-spacesApr 22 2006A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. ... More

A new view of combinatorial maps by Smarandache's notionJun 13 2005On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are Smarandache geometries ... More

What PhD students really wantJun 23 2010The road to becoming an astronomer is exciting, but often fraught with danger and conflicting messages. A PhD student is inundated with catch-phrases such as "publish or perish" and "it's not about the quantity, but the quality of work". How do we know ... More

Quantum Algorithm to Solve Satisfiability ProblemsNov 29 2004Feb 28 2005A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit Exact Cover problems. ... More

Forced hyperbolic mean curvature flowMar 12 2012In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}. For the first hyperbolic flow, as in \cite{klw}, by using support function, ... More

On Multi-Vector SpacesOct 22 2005A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. ... More

Geometrical Theory on Combinatorial ManifoldsDec 26 2006For an integer $m\geq 1$, a combinatorial manifold $\widetilde{M}$ is defined to be a geometrical object $\widetilde{M}$ such that for $\forall p\in\widetilde{M}$, there is a local chart $(U_p,\phi_p)$ enable $\phi_p:U_p\to B^{n_{i_1}}\bigcup B^{n_{i_2}}\bigcup...\bigcup ... More

A Generalization of Seifert-Van Kampen Theorem for Fundamental GroupsJun 18 2010As we known, the {\it Seifert-Van Kampen theorem} handles fundamental groups of those topological spaces $X=U\cup V$ for open subsets $U, V\subset X$ such that $U\cap V$ is arcwise connected. In this paper, this theorem is generalized to such a case of ... More

On Multi-Metric SpacesOct 22 2005A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some characteristics of ... More

Rational Bézier Curves Approximated by Bernstein-Jacobi Hybrid Polynomial CurvesMay 13 2016In this paper, we propose a linear method for $C^{(r,s)}$ approximation of rational B\'{e}zier curve with arbitrary degree polynomial curve. Based on weighted least-squares, the problem be converted to an approximation between two polynomial curves. Then ... More

Efficiency of Ground State Quantum ComputerNov 03 2004Feb 28 2005The energy gap is calculated for the ground state quantum computer circuit, which was recently proposed by Mizel et.al. When implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap $1/\Delta$ is ... More

Effect of tensor couplings in a relativistic Hartree approach for finite nucleiNov 12 2002The relativistic Hartree approach describing the bound states of both nucleons and anti-nucleons in finite nuclei has been extended to include tensor couplings for the $\omega$- and $\rho$-meson. After readjusting the parameters of the model to the properties ... More

Construction of the Poincare sheaf for higher genus curvesJan 08 2018Let $X$ be a smooth projective curve of genus $g$ and $L$ be a degree $l$ line bundle on $X$ with $l\geq 2g-1$. Denote the stack of rank two Higgs bundles on $X$ with value in $L$ by $\mathcal{H}iggs$ and the semistable part by $\mathcal{H}iggs_{ss}$. ... More

A note on convergence analysis of NURBS curve when weights approach infinityApr 15 2016This article considers the convergence of NURBS curve when weights approach infinity. We shows that limit of NURBS curve dose not exist when independent variables weights approach infinity. Further, pointwise convergence uniform convergence and $L^1$ ... More

Drell-Yan process with jet vetoes: breaking of generalized factorizationJul 07 2015Oct 29 2015Resummation of hadron collision cross sections, when the measurement imposes a hierarchy of scales, relies on factorization. Cancellation of Glauber / Coulomb gluons is a necessary condition for factorization. For Drell-Yan-like processes, the known proofs ... More

A multi-space model for Chinese bids evaluation with analyzingMay 18 2006A tendering is a negotiating process for a contract through by a tenderer issuing an invitation, bidders submitting bidding documents and the tenderer accepting a bidding by sending out a notification of award. As a useful way of purchasing, there are ... More

Combinatorial Speculations and the Combinatorial Conjecture for MathematicsJun 28 2006Jul 04 2006Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to find combinatorial ... More

Smarandache Multi-Space Theory(IV)--Application to theoretical physicsApr 22 2006A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. ... More

Parallel bundles in planar map geometriesJun 20 2005Parallel lines are very important objects in Euclid plane geometry and its behaviors can be gotten by one's intuition. But in a planar map geometry, a kind of the Smarandache geometries, the sutation is complex since it may contains elliptic or hyperbolic ... More

Introduction to the Symbolic Integration SystemSep 23 2013Symbolic integration is an important module of a typical Computer Algebra System. As for now, Mathematica, Matlab, Maple and Sage are all mainstream CAS. They share the same framework for symbolic integration at some points. In this book first we review ... More

Monotonicity of the first eigenvalue of the Laplace and the p-Laplace operators under a forced mean curvature flowOct 21 2013Dec 23 2013In this paper, we would like to give an answer to \textbf{Problem 1} below issued firstly in [J. Mao, Eigenvalue estimation and some results on finite topological type, Ph.D. thesis, IST-UTL, 2013]. In fact, by imposing some conditions on the mean curvature ... More

The vertex-rainbow index of a graphJan 31 2015The $k$-rainbow index $rx_k(G)$ of a connected graph $G$ was introduced by Chartrand, Okamoto and Zhang in 2010. As a natural counterpart of the $k$-rainbow index, we introduced the concept of $k$-vertex-rainbow index $rvx_k(G)$ in this paper. For a graph ... More

A Generic Top-Down Dynamic-Programming Approach to Prefix-Free CodingSep 26 2008Given a probability distribution over a set of n words to be transmitted, the Huffman Coding problem is to find a minimal-cost prefix free code for transmitting those words. The basic Huffman coding problem can be solved in O(n log n) time but variations ... More

Malliavin calculus for backward stochastic differential equations and application to numerical solutionsFeb 21 2012In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does ... More

Inverse Quadratic Optimal Control for Discrete-Time Linear SystemsOct 30 2018In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear time-invariant system, ... More

Exploiting Large-Scale MIMO Techniques for Physical Layer Security with Imperfect Channel State InformationJul 28 2014In this paper, we study the problem of physical layer security in large-scale multiple input multiple output (LS-MIMO) systems. The large number of antenna elements in LS-MIMO system is exploited to enhance transmission security and improve system performance, ... More

Resource Allocation for Cost Minimization in Limited Feedback MU-MIMO Systems with Delay GuaranteeNov 05 2013In this paper, we design a resource allocation framework for the delay-sensitive Multi-User MIMO (MU-MIMO) broadcast system with limited feedback. Considering the scarcity and interrelation of the transmit power and feedback bandwidth, it is imperative ... More

Adaptive Mode Selection in Multiuser MISO Cognitive Networks with Limited Cooperation and FeedbackOct 16 2013In this paper, we consider a multiuser MISO downlink cognitive network coexisting with a primary network. With the purpose of exploiting the spatial degree of freedom to counteract the inter-network interference and intra-network (inter-user) interference ... More

Continuous-Time Inverse Quadratic Optimal Control ProblemOct 31 2018In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first ... More

Smarandache Multi-Space Theory(III)--Map geometries and pseudo-plane geometriesApr 22 2006A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. ... More

Constraining Gravitational and Cosmological Parameters with Astrophysical DataAug 15 2008We use astrophysical data to shed light on fundamental physics by constraining parametrized theoretical cosmological and gravitational models. Gravitational parameters are those constants that parametrize possible departures from Einstein's general theory ... More

Spectra of anti-nucleons in the vacuum of finite nucleiDec 25 2003The quantum vacuum in a many-body system of finite nuclei has been investigated within the relativistic Hartree approach which describes the bound states of nucleons and anti-nucleons consistently. The contributions of the Dirac sea to the source terms ... More