synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

synchronization in dynamic networks with nonsymmetrical time delay coupling based on linear feedback controllers based on a general complex dynamic network model with nonsymmetrical time delay coupling and without assuming irreducibility a strategy for global exponential synchronization is proposed based on the approach of linear state feedback controllers especially the criteria for controller design can be expressed by inequalities instead of matrix inequalities thus the proposed controllers can be easily constructed without relying on any numerical toolbox the efficiency of the control scheme is revealed by simulations on a network consisting of the unified chaotic systems with nearest neighbour unidirectional time delay coupling

generalized q bosons and their squeezed states generalized q boson operators associated with the simultaneous creation of several q bosons are introduced these operators give rise to a realization of the quantum weyl heisenberg algebra and are applied to the construction of corresponding holstein primakoff realizations of the quantum algebras suq 2 and suq 1 1 coherent states of these algebras are defined in the various ways suggested by the equivalent definitions of the harmonic oscillator coherent states and some of their properties are studied particular attention is devoted to the squeezing properties of the quadrature of the electromagnetic field in these states

an analogue of the unitary displacement operator for the q oscillator using the concept of a non standard hilbert space over the quantum complex plane recently introduced by kowalski et al 1993 we construct a unitary q analogue of the weyl displacement operator we investigate the q displaced vacuum states and show that they exhibit properties analogous to coherent states in the undeformed theory they are however distinct from any q coherent states previously found in the literature

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

energy spectrum potential and inertia functions of a generalized f oscillator we consider a generalized four parameter q algebra aa q a a q n n a a n a a associating with operators a and a the nonlinear f oscillator operators defined in terms of the usual harmonic oscillator operators as a af n and a f n a where a and a are operators of the weyl heisenberg algebra and n a a the function f n is determined from the commutation relations we write the hamiltonian for the free f oscillator and obtain its energy spectrum besides expressing the hamiltonian in terms of coordinate and momentum we determine the potential and inertia functions coordinate dependent mass and analyse their behaviour by varying the parameters

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

double squeezing in generalized q coherent states using a generalization of the q commutation relations we develop a formalism in which we define generalized q bosonic operators this formalism includes both types of the usual q deformed bosons as special cases the coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components unlike the conventional case in which squeezing is permitted in only one component this also contrasts with the usual quantum group deformation which also only permits one component squeezing

a simple and efficient method for modeling constant mean curvature surfaces a constant mean curvature cmc surface is a critical point of surface area with respect to variations that preserve the volume bounded by the surface we present a simple and elegant method for constructing a triangle mesh approximation to a cmc surface by minimizing the discretized surface area subject to a fixed volume and other constraints such as fixed boundary curves the key idea is an optimization procedure in which the surface area functional is replaced by a least squares energy functional that is easier to minimize and whose critical points are uniformly parameterized surfaces or more generally surfaces parameterized in accord with an arbitrary density function a good initial solution estimate is not required in fact the input mesh quality may be almost arbitrarily poor the user specified volume is taken to be a shape control parameter and since the volume constraint need not be satisfied precisely it is simply treated as an additional equation in the least squares system the nonlinear

multi mode q coherent states we show how to construct a multi mode operator which satisfies the quantum heisenberg weyl algebra h wq algebra we use this operator to create new two mode realizations of the suq 2 and suq 1 1 quantum algebra we also investigate the corresponding coherent states

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

the discrete plateau problem convergence results we solve the problem of nding and justifying an optimal fully discrete nite element procedure for approximating minimal including unsta ble surfaces in a previous paper we introduced the general framework and some preliminary estimates developed the algorithm and give the numerical results in this paper we prove the convergence estimate

synchronization analysis of linearly coupled systems described by differential equations with a coupling delay when a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations lcodes both synchronization and the final synchronized state will vary in this paper mathematical analysis is presented on the synchronization phenomena of lcodes with a single coupling delay criteria are derived for both local and global synchronization it is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration the coupling strength and the coupling delay also play key roles on the stability of synchronization both theoretical and numerical analysis indicate that under some conditions if the coupling strength is large enough the coupled system can be completely synchronized for any coupling delay on the other hand in some cases the coupled system can be synchronized if the coupling delay is small enough

synchronization in complex delayed dynamical networks with nonsymmetric coupling abstract a new general complex delayed dynamical network model with nonsymmetric coupling is introduced and then we investigate its synchronization phenomena several synchronization criteria for delay independent and delay dependent synchronization are provided which generalize some previous results the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues especially we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real furthermore the effects of time delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures the results are illustrated by delayed networks in which each node is a two dimensional limit cycle oscillator system consisting of a two cell cellular neural network numerical simulations show that these networks can realize synchronization with smaller time delay and will lose synchronization when the time delay increase larger than a threshold

a characterization of functional realizations of three dimensional quantum groups the authors study in an exhaustive and systematic way the functional realizations of quantum and classical algebras related with su 2 su 1 1 and the oscillator group os 1 in order to achieve this purpose they have adopted a mapping that is a generalization of an algebra expansion procedure they have not transformed the algebras themselves but their representations this method enables them not only to relate classical algebras and their q analogues but also different type algebras whether they are quantum or not they have obtained and classified all possible q realizations including as particular cases all those already known in the literature

unified approach to the analogues of single photon and multiphoton coherent states for generalized bosonic oscillators a large class of bosonic coherent states known in the literature have been constructed in a unified way by shanta et al 1994 it is shown that this method can be easily extended to generalized bosonic oscillator systems

a fully consistent lie algebraic representation of quantum phase and number operators a fully consistent realization of the quantum operators corresponding to the canonically conjugate phase and number variables is proposed resorting to the 1 positive discrete series of the irreducible unitary representation of the lie algebra su 1 1 of the double covering group of so 1 2 t he realization holds in subspace f 0 the system fock space minus the vacuum state a possible way to extend it to the full space of states based on recourse to a dilated extension of hilbert space is discussed

an iterative method for elliptic problems on regions partitioned into substructures some new preconditioners for discretizations of elliptic boundary problems are studied with these preconditioners the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains analytic estimates are given which guarantee that under appropriate hypotheses the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns numerical examples are presented which illustrate the theoretically predicted iterative convergence rates

a holstein primakoff and a dyson realization for the quantum algebra the known holstein primakoff and dyson realizations of the lie algebra in terms of bose operators are generalized to the class of the quantum algebras for any n it is shown how the elements of can be expressed via n pairs of bose creation and annihilation operators

algebraic treatment of some systems with spin like interactions with applications in quantum optics and vibronic spectroscopy a unified scheme based on algebraic techniques is proposed to solve the eigenvalue equation for a class of systems involving spin like interactions from general assumptions hamiltonian models are built from selected elements in the enveloping algebra of the harmonic oscillator su 2 and su 1 1 algebras our method is next illustrated through examples taken in the areas of quantum optics and dynamical jahn teller systems in orbital doublets

observer based synchronization in complex dynamical networks with nonsymmetric coupling abstract based on a general complex dynamical network model with nonsymmetric coupling some criteria for synchronization are proposed based on the approach of state observer design unlike the nonobserver based dynamical networks where the coupling between two connected nodes is defined by an inner coupling matrix and full state coupling is typically needed in this paper smaller amount of coupling variables or even only a scalar output signal of each node is needed to synchronize the network unlike the commonly researched complex network model where the coupling between nodes is symmetric here in our network model the coupling configuration matrix is not assumed to be symmetric and may have complex eigenvalues the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix is not required to be diagonalizable especially the proposed step by step approach is simpler in computation than the existent ones which usually rely heavily on numerical toolbox and may be done by hand completely an example is given to illustrate the step by step approach in which each node is a two dimensional dynamical limit cycle oscillator system consisting of a two cell cellular neural network and numerical simulations are also done to verify the results of design

generalized q fermion oscillators and q coherent states the algebra of q fermion operators developed earlier by two of the present authors is re examined it is shown that these operators represent particles that are distinct from usual spacetime fermions except in the limit q 1 it is shown that it is possible to introduce generalized q oscillators defined for infinity q or 1 in the range infinity q 0 these coincide with the q boson operators and for 0 q or 1 they coincide with q fermions the ordinary bosons and fermions may be identified with the limits q 1 and 1 respectively generalized q fermion coherent states are constructed by utilizing a nonlinear shift automorphism of the algebra of q fermion operators these are compared with the coherent states defined as eigenstates of annihilation operator matrix elements of the shift operator in the fock space basis are evaluated

chaos synchronization of general complex dynamical networks recently it has been demonstrated that many large scale complex dynamical networks display a collective synchronization motion here we introduce a time varying complex dynamical network model and further investigate its synchronization phenomenon based on this new complex network model two network chaos synchronization theorems are proved we show that the chaos synchronization of a time varying complex network is determined by means of the inner coupled link matrix the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network especially we do not assume that the coupled configuration matrix is symmetric and its off diagonal elements are nonnegative which in a way generalizes the related results existing in the literature

an algorithm for prescribed mean curvature using isogeometric methods we present a newton type algorithm to find parametric surfaces of prescribed mean curvature with a fixed given boundary in particular it applies to the problem of minimal surfaces the algorithm relies on some global regularity of the spaces where it is posed which is naturally fitted for discretization with isogeometric type of spaces we introduce a discretization of the continuous algorithm and present a simple implementation using the recently released isogeometric software library igatools finally we show several numerical experiments which highlight the convergence properties of the scheme

the q boson realizations of the quantum groups uq dn we give explicit realization for the quantum enveloping algebras uq dn to obtain recurrence formulae we simply extend the algebra uq dn to uq n for which uq dn is a subalgebra in these formulae the generators of the algebra are expressed by means of 2n 2 canonical q boson pairs and one auxiliary representation of uq n 1

a q analogue of the campbell baker hausdorff expansion the authors describe a q analogue of the campbell baker hausdorff formula and give an explicit expansion to fourth order

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

finite element approximations to surfaces of prescribed variable mean curvature we give an algorithm for finding finite element approximations to surfaces of prescribed variable mean curvature which span a given boundary curve we work in the parametric setting and prove optimal estimates in the h 1 norm the estimates are verified computationally

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

holder continuity of three types of generalized synchronization manifolds of non autonomous systems abstract this paper studies the existence of holder continuity of the generalized synchronization gs manifold when the modified response system has an asymptotically stable equilibrium periodic or quasi periodic orbit and chaotic attractor gs is classified into four types accordingly the first three types of gs are considered and based on the schauder fixed point theorem sufficient conditions for holder continuous gs in the coupled non autonomous systems are derived and theoretically proved

a q deformed osp 1 2 superalgebra and its two component coherent state representations a q deformed osp 1 2 superalgebra is defined by the use of a pair of q boson annihilation and creation operators a kind of two component coherent state representation of the q deformed superalgebra is found and a q differential realization of the q deformed osp 1 2 superalgebra is obtained

the quantum mechanical schrodinger picture of a q oscillator a q deformed version of standard quantum mechanics in the coordinate schrodinger picture is obtained by replacing the ordinary coordinate derivative by the so called q discrete derivative as the representative of the momentum operator the chosen q discrete derivative is symmetric with respect to the exchange of q and q 1 under the usually adopted assumptions a q deformed schrodinger equation is derived for a harmonic oscillator the complete set of eigenfunctions can be explicitly constructed as special q functions and the corresponding energy eigenvalues are identical to those obtained by biedenharn in his pioneering work 1989 this q deformed oscillator exhibits a rich novel structure including dynamical symmetry and in the limit q to 1 it reveals some hitherto unknown features of the harmonic oscillator eigenfunctions

generally deformed oscillator isospectral oscillator system and hermitian phase operator the generally deformed oscillator gdo and its multiphoton realization as well as the coherent and squeezed vacuum states are studied we discuss in particular the gdo depending on a complex parameter q therefore we call it q gdo together with the finite dimensional cyclic representations as a realistic physical system of a gdo the isospectral oscillator system is studied and it is found that its coherent and squeezed vacuum states are closely related to those of the oscillator it is pointed out that starting from the q gdo with q root of unity one can define the hermitian phase operators in quantum optics consistently and algebraically the new creation and annihilation operators of the pegg barnett type phase operator theory are defined by using the cyclic representations and these operators degenerate to those of the ordinary oscillator in the classical limit

even and odd q coherent states and their optical statistics properties the authors construct explicitly even and odd q coherent states qcss which are proved to form a representation of the quantum heisenberg weyl algebra and study their properties it is shown that optical statistics properties of the even and odd qcss are very different they find that an even qcs exhibits squeezing but no antibunching effect and an odd qcs has antibunching effect but no squeezing for all finite q values

multilevel solvers for unstructured surface meshes parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing such parameterization approaches give rise to large and exceedingly ill conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies since the underlying meshes are very fine to begin with such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy in this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature we introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner