free vibrations of rectangular cantilever plates part 1 out of plane motion an analysis of the free in plane vibrations of a cantilevered rectangular plate is performed by means of a variational approximation procedure the problem is treated by first obtaining the exact solution for waves in the plate satisfying the equations of plane stress including in plane inertia with two opposite edges traction free the solution results in a set of dispersion curves a number of the resulting waves are used in what remains of the variational equation in which all conditions occur as natural conditions roots of the resulting transcendental equation are calculated which yield the eigensolutions and associated eigenfrequencies the results are compared with results obtained using fem and good agreement is shown

attractors for the semilinear reaction diffusion equation with distribution derivatives in unbounded domains abstract in this paper we prove the existence of global attractors for a nonlinear reaction diffusion equation with a nonlinearity having a polynomial growth of arbitrary order p 1 p 2 and with distribution derivatives in the inhomogeneous term the global attractors are obtained in l 2 r n and l p r n respectively a new a priori estimate method has been used since the solutions of the equation have no higher regularity and the semigroup associated with the solutions is not continuous in l p r n the results are new and appear to be optimal

entangled three qubit states without concurrence and three tangle we provide a complete analysis of mixed three qubit states composed of a greenberger horne zeilinger state and a w state orthogonal to the former we present optimal decompositions and convex roofs for the three tangle further we provide an analytical method to decide whether or not an arbitrary rank 2 state of three qubits has vanishing three tangle these results highlight intriguing differences compared to the properties of two qubit mixed states and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states by studying the coffman kundu wootters inequality we find that while the amounts of inequivalent entanglement types strictly add up for pure states this monogamy can be lifted for mixed states by virtue of vanishing tangle measures

vibration analysis of a continuous system subject to generic forms of actuation forces and sensing devices this work provides a general formulation to solve vibration problems for continuous systems with damping effects including modal transient harmonic and spectrum response analyses in modal analysis the system eigenvalues and corresponding eigenfunctions can be determined the orthogonal relations of eigenfunctions are shown for transient harmonic and spectrum analyses the generic force actuator functions and response sensing operators are introduced respectively and used to derive the system response the time domain response is obtained for transient analysis the frequency response function is derived for harmonic analysis and statistical quantities of response variables due to random excitation are determined in spectrum analysis the solution for each type of analysis can be formulated and expressed in a concise format in terms of generic force actuator and response sensor mode shape functions in particular one dimensional beam and two dimensional plate vibration analyses are illustrated by following the developed generic formulation this work provides the complete analytical solutions of four types of vibration analyses for continuous systems and can be applied to other engineering structures as well

the attractor for a nonlinear reaction diffusion system in an unbounded domain in this paper the quasi linear second order parabolic systems of reaction diffusion type in an unbounded domain are considered our aim is to study the long time behavior of parabolic systems for which the nonlinearity depends explicitly on the gradient of the unknown functions to this end we give a systematic study of given parabolic systems and their attractors in weighted sobolev spaces dependence of the hausdorff dimension of attractors on the weight of the sobolev spaces is considered 2001 john wiley sons inc

the existence of global attractors for the norm to weak continuous semigroup and application to the nonlinear reaction diffusion equations abstract in this paper first we introduce a new concept called the norm to weak continuous semigroup in a banach space and give a technical theorem to verify this notion of continuity then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup as an application we obtain the existence of the global attractor for a nonlinear reaction diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term the global attractors are obtained in l p h 0 1 and h 2 h 0 1 respectively a new a priori estimate method called asymptotic a priori estimate has been introduced since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in l p h 0 1 and h 2 h 0 1 the results in this part are new and appear to be optimal

strongly damped wave equation in uniform spaces abstract the cauchy problem for a semilinear strongly damped wave equation is considered in the whole of r n under suitable conditions imposed on nonlinear term which are much like for equations in bounded domains a dissipative semigroup t t of global solutions to this problem is constructed in a reach phase space being the product of the locally uniform spaces existence of an attractor for t t is then established

attractors for reaction diffusion equations in unbounded domains abstract in this paper we study the asymptotic behaviour of solutions for parabolic non linear evolution equations in r n we prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in l 2 r n

accurate free vibration analysis of the orthotropic cantilever plate abstract utilizing the superposition method an accurate analytical type solution is described for resolving the problem of free vibration of cantilever plates with rectangular orthotropy a number of verification checks performed to verify the mathematical procedure are described convergence is found to be rapid and eigenvalues are tabulated for a wide range of plate aspect ratios and a number of combinations of values of orthotropic parameters full delineation is made between symmetric and antisymmetric modes it is believed the tabulated results will prove useful to designers and provide a reference against which other researchers can compare their results

pullback attractors for the non autonomous reaction diffusion equations in rn in this paper we prove the existence of the pullback attractors in l2 rn lp rn and h1 rn for a nonlinear reaction diffusion equation in unbounded domains in which the nonlinearity f satisfies the polynomial growth of arbitrary order p 1 p 2 and the external forcing g lloc2 r l2 rn only subjects to the weaker integrability condition te s g s 22ds in this paper we prove the existence of the pullback attractors in l2 rn lp rn and h1 rn for a nonlinear reaction diffusion equation in unbounded domains in which the nonlinearity f satisfies the polynomial growth of arbitrary order p 1 p 2 and the external forcing g lloc2 r l2 rn only subjects to the weaker integrability condition te s g s 22ds

global attractor for plate equation with nonlinear damping abstract in this paper we study the long time behavior of plate equation with nonlinear damping and critical nonlinearity we prove the existence of a global attractor in the space h 0 2 l 2

global attractors for degenerate parabolic equations on unbounded domains we consider a nonlinear degenerate parabolic equation and show existence of the maximal compact attractor in weighted spacesl1 rn x dx with weight l1 rn going to zero at infinity

global attractors for von karman equations with nonlinear interior dissipation abstract in this paper we study the asymptotic behavior of weak solutions for von karman equations with nonlinear interior dissipation we prove the existence of a global attractor in the space w 2 2 l 2

quantification of gaussian quantum steering einstein podolsky rosen steering incarnates a useful nonclassical correlation which sits between entanglement and bell nonlocality while a number of qualitative steering criteria exist very little has been achieved for what concerns quantifying steerability we introduce a computable measure of steering for arbitrary bipartite gaussian states of continuous variable systems for two mode gaussian states the measure reduces to a form of coherent information which is proven never to exceed entanglement and to reduce to it on pure states we provide an operational connection between our measure and the key rate in one sided device independent quantum key distribution we further prove that peres conjecture holds in its stronger form within the fully gaussian regime namely steering bound entangled gaussian states by gaussian measurements is impossible

attractors of partial differential evolution equations in an unbounded domain there is a large number of papers in which attractors of parabolic reaction diffusion equations in bounded domains are investigated in this paper these equations are considered in the whole unbounded space and a theory of attractors of such equations is built while investigating these equations specific difficulties arise connected with the noncompactness of operators with the continuity of their spectra etc therefore some new conditions on nonlinear terms arise in this paper weighted spaces are widely applied an important feature of this problem is worth mentioning namely properties of semigroups corresponding to equations with solutions in spaces of growing and of decreasing functions essentially differ

strong monogamy conjecture for multiqubit entanglement the four qubit case we investigate the distribution of bipartite and multipartite entanglement in multiqubit states in particular we define a set of monogamy inequalities sharpening the conventional coffman kundu wootters constraints and we provide analytical proofs of their validity for relevant classes of states we present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits

asymptotic behavior and attractors for reaction diffusion equations in unbounded domains abstract in this paper we give general and flexible conditions for a reaction diffusion equation to be dissipative in an unbounded domain the functional setting is based on standard lebesgue and sobolev lebesgue spaces we show how the reaction and diffusion mechanisms have to work together to obtain the asymptotic compactness of solutions and therefore the existence of the compact attractor in particular cases our results allow us to improve some previous known results

continuity and pullback attractors for a non autonomous reaction diffusion equation in r n in this paper we study the dynamics of a non autonomous reaction diffusion equation in r n with the nonlinearity f satisfying the polynomial growth of arbitrary order p 1 p 2 firstly we prove the existence of the pullback d attractor in l 2 r n secondly we use a scheme to establish some new estimates higher order integrability of the difference of the solutions near the initial time instead of using the usual estimates about higher regularities and higher order integrability of solutions thirdly we verify that the usual l 2 r n l 2 r n pullback d attractor indeed can pullback attract the d class in l 2 norm for any 0 and h 1 norm and the solutions of the equation in h 1 r n are continuous with respect to initial data finally we obtain the pullback d attractor in l p r n and h 1 r n as an application of the higher order integrability and the continuity respectively

reaction diffusion equations with non autonomous force in h 1 and delays under measurability conditions on the driving delay term abstract in this paper we analyze the existence of solutions for a reaction diffusion problem with hereditary effects and a time dependent force term with values in h 1 the main novelty is that the delay term may be driven by a function under very minimal assumptions namely just measurability this is due to the fact that we only deal with a phase space of functions continuous in time allowing this general setting which might be more useful when less regularity is known in the hereditary mechanism after that we obtain uniform estimates and asymptotic compactness properties via an energy method that allow us to ensure the existence of pullback attractors for the associated process to the problem actually we obtain two different families of minimal pullback attractors namely those of fixed bounded sets but also for a class of time dependent families universe given by a tempered condition finally from comparison results we establish relations among them and under suitable additional assumptions we conclude that these families of attractors are in fact the same object

the existence of uniform attractors for non autonomous reaction diffusion equations on the whole space in this paper we introduce a new class of functions satisfying spacial absolutely continuous see definition 3 1 denoted by lsac2 r rn which are translation bounded but not normal see s s lu h q wu and c k zhong attractors for non autonomous 2d navier stokes equations with normal external forces discrete contin dyn syst a 13 3 701 719 2005 10 3934 dcds 2005 13 701 and definition 3 1 in lloc2 r rn then the asymptotic a priori estimate is applied to some nonlinear reaction diffusion equations with external forces g x s lsac2 r rn we obtain the existence of uniform attractor together with its structure in the bi spaces l2 rn l2 rn and l2 rn lp rn p 2 without any restriction on the growing order of the nonlinear term

dynamics of strongly damped wave equations in locally uniform spaces attractors and asymptotic regularity this paper is dedicated to analyzing the dynamical behavior of strongly damped wave equations with critical nonlinearity in locally uniform spaces after proving the global well posedness we first establish the asymptotic regularity of the solutions which appears to be optimal and the existence of a bounded in h 2 lu r n x h 1 lu r n subset which attracts exponentially every initial h 1 lu r n x l 2 lu r n bounded set with respect to the h 1 lu r n x l 2 lu r n norm then we show there is a h 1 lu r n x l 2 lu r n h 1 r n x h 1 r n global attractor which reflects the strongly damped property of u t to some extent

attractors for partly dissipative reaction diffusion systems in rn in this paper we study the asymptotic behavior of solutions for the partly dissipative reaction diffusion equations in n we prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in 2 n 2 n l l 2000 academic press

random attractors for the stochastic fitzhugh nagumo system on unbounded domains abstract the existence of a random attractor for the stochastic fitzhugh nagumo system defined on an unbounded domain is established the pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables these estimates are obtained by a cut off technique

monogamy inequality for distributed gaussian entanglement we show that for all n mode gaussian states of continuous variable systems the entanglement shared among n parties exhibits the fundamental monogamy property the monogamy inequality is proven by introducing the gaussian tangle an entanglement monotone under gaussian local operations and classical communication which is defined in terms of the squared negativity in complete analogy with the case of n qubit systems our results elucidate the structure of quantum correlations in many body harmonic lattice systems

strong monogamy of bipartite and genuine multipartite entanglement the gaussian case we demonstrate the existence of general constraints on distributed quantum correlations which impose a trade off on bipartite and multipartite entanglement at once for all n mode gaussian states under permutation invariance we establish exactly a monogamy inequality stronger than the traditional one that by recursion defines a proper measure of genuine n partite entanglement strong monogamy holds as well for subsystems of arbitrary size and the emerging multipartite entanglement measure is found to be scale invariant we unveil its operational connection with the optimal fidelity of continuous variable teleportation networks

l2 lp random attractors for stochastic reaction diffusion equation on unbounded domains abstract in this paper the existence of l 2 l p random attractor is established for a stochastic reaction diffusion equation on the whole space r n this random attractor is a compact and invariant tempered set which attracts every tempered random subset of l 2 in the topology of l p the nonlinearity f is supposed to satisfy some growth of arbitrary order p 1 where p 2 the l 2 l p asymptotic compactness of the random dynamical system is proved by an asymptotic a priori estimate of the unbounded part of solutions

the global attractor for the 2d navier stokes flow on some unbounded domains we extend previous results on the existence of the global attractor for the 2d navier stokes equations on some unbounded domains in the sense that the forcing term need not lie in any weighted space nor is the boundary of the domain required to be smooth the existence of the global attractor is obtained on arbitrary open sets such that the poincare inequality holds and for forces in the natural dual space v the proof is based on the energy equation and the concept of asymptotic compactness an estimate of the hausdorff and fractal dimensions of the attractor is also given

on the symplectic superposition method for new analytic free vibration solutions of side cracked rectangular thin plates abstract in this study a first attempt is made to develop an up to date symplectic superposition method for some new analytic free vibration solutions of side cracked rectangular thin plates that were not obtained by conventional semi inverse methods in contrast with the classical lagrangian system and euclidean space the present method is implemented within the hamiltonian system framework and symplectic space the solution procedure involves expressing the problems in the hamiltonian system and dividing a side cracked plate into several sub plates that are analytically solved by the symplectic superposition method where the imposed quantities are determined by the plate boundary conditions free edge conditions along the crack and interfacial continuity conditions between the sub plates in the analytic solution of a sub plate specifically the symplectic eigenvalue problems are formulated followed by the symplectic eigen expansion the integration of the solutions of the sub plates yields the final solution of a side cracked plate the rigorous mathematical techniques without predetermination of solution forms qualify the present method as an unusual approach for exploring more analytic solutions comprehensive natural frequency and mode shape solutions of the side cracked plates under three representative boundary constraints are provided and well validated by other methods the new analytic solutions obtained may serve as benchmarks for other potential solution methods