strongest strong cycles and theta fuzzy graphs in this paper new concepts are introduced to enhance the process of block identification in fuzzy graphs since reduction in the strength of the connectedness between two nodes occurs more frequently than total disconnection of a network block identification in fuzzy graph networks is very important a special type of cycle which is called a strongest strong cycle and a new connectivity parameter which is called cycle connectivity are introduced in fuzzy graphs a subclass of fuzzy graphs known as fuzzy graphs is identified in which all the existing characterizations of blocks in graphs are true a set of necessary conditions is obtained for a fuzzy graph to be a block as well as a set of necessary and sufficient conditions for a fuzzy graph to be a block

on a class of degenerate parabolic equations with dynamic boundary conditions we consider a quasi linear parabolic possibly degenerate equation with nonlinear dynamic boundary conditions the corresponding class of initial and boundary value problems has already been studied previously proving well posedness of weak solutions and the existence of the global attractor assuming that the nonlinearities are subcritical to a given exponent the goal of this article is to show that the previous analysis can be redone for supercritical nonlinearities by proving an additional l estimate on the solutions in particular we derive new conditions which reflect an exact balance between the internal and the boundary mechanisms involved even when both the nonlinear sources contribute in opposite directions then we show how to construct a trajectory attractor for the weak solutions of the associated parabolic system and prove that any solution belonging to the attractor is bounded which implies uniqueness finally we also prove for the semilinear reaction diffusion equation with nonlinear dynamic boundary conditions that the fractal dimension of the global attractor is of the order n 1 as diffusion 0 in any space dimension n 2 improving some recent results in gal 2012 23

the existence of multiple equilibrium points in a global attractor for some p laplacian equation abstract in this paper we are mainly concerned with some properties of the global attractor for some p laplacian equation with a lyapunov function in a banach space under some suitable assumptions we prove the existence of multiple equilibrium points in a global attractor for some p laplacian equation

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

global attractors for p laplacian equation abstract the existence of a l 2 w 0 1 p l q global attractor is proved for the p laplacian equation u t div u p 2 u f u g on a bounded domain r n n 3 with dirichlet boundary condition where p 2 the nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c 1 u q k f u u c 2 u q k and f u l where q 2 is arbitrary there is no other restriction on p and q the asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method called asymptotic a priori estimate

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

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

asymptotic behaviour of non linear parabolic equations with monotone principal part abstract we consider non linear parabolic equations with subdifferential principal part and give conditions under which they posses global attractors in spite of considering non lipschitz perturbations the case of globally lipschitz perturbations of a maximal monotone operator has been addressed in boll un mat ital b 8 2 2000 693 706 in the case of perturbations which are not globally lipschitz the main difficulty is the lack of uniqueness of solutions which at first does not even allow us to define attractors we overcome this difficulty for problems enjoying certain regularity and absorption properties that allow uniqueness of solutions after some time has been elapsed the results developed here are applied to the case when the subdifferential operator is the p laplacian to obtain existence of attractors and the existence of periodic solutions

time series modeling by a second order hammerstein system in this paper we discuss the modeling of an observed time series as the output of a second order hammerstein model driven by an independent and identically distributed i i d gaussian noise the modeling is discussed from the point of view of the hypothesis testing ht of statistical indexes derived from higher order statistics hos three points of view can be adopted in ht the more general approach is to not make any assumption on the index statistics notably on the variance and thus to use the t 2 hotelling test the second point of view involves calculating a theoretical variance in order to define normalized variables whose statistics are known the last approach is a mixed version of the others two these three approaches are applied to statistical indexes derived from linear combination of slices of spectra from the third order up the fifth order some subcases need to use the derivatives of the polyspectra since general relationships are null and cannot be used for the ht the second part of this paper is devoted to linear and quadratic kernel identification using the relationship defined for ht definition as for the ht several subcases have to be discussed using either the polyspectra or the derivatives of polyspectra

fuzzy location problems on networks location problems concern a wide set of fields where it is usually assumed that exact data are known however in real applications the location of the facility considered can be full of linguistic vagueness that can be appropriately modelled using networks with fuzzy values thus fuzzy location problems on networks arise this paper deals with their general formulation and the description of the ways to solve them namely we show the variety of problems that can be considered in this context and for some of them we propose the most operative approaches for their solution

on the z2 index of the global attractor for a class of p laplacian equations by means of the z 2 index we study the geometrical property of the global attractor for a class of symmetric p laplacian equations u t div vertical bar del u vertical bar p 2 del u vertical bar u vertical bar r 2 u lambda vertical bar u vertical bar s 2 u f x u 0 where lambda 0 2 s p r we first provide under suitable assumptions the existence result for the symmetric global attractor a then when 2 s p r we prove that the z 2 index of the global attractor is infinite as a corollary we obtain that the fractal dimension of the global attractor is infinite for when 2 s p r we provide the lower bound of the z 2 index of the global attractor c 2010 elsevier ltd all rights reserved

global attractors for one dimensional p laplacian equation abstract we study the existence of the l 2 r w 1 p r global attractor for an evolution p laplacian equation under additional restrictions on force and source terms we improve the result of a kh khanmamedov existence of a global attractor for the parabolic equation with nonlinear laplacian principal part in an unbounded domain j math anal appl 316 2006 601 615 and correct the result of m yang c sun c zhong existence of a global attractor for a p laplacian equation in r n nonlinear anal 66 2007 1 13 in the one dimensional case

output dead beat control for a class of planar polynomial systems output dead beat control for a class of nonlinear discrete time systems which are described by a single input output i o polynomial difference equation is considered the class of systems considered is restricted to systems with a two dimensional state space description it is assumed that the highest degree with which the present input appears in the equation is odd necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented we also design a minimum time output dead beat control algorithm feedback controller which yields stable zero dynamics whenever this is feasible a number of interesting phenomena are discussed and illustrated with examples

dynamics for a class of non autonomous degenerate p laplacian equations abstract in this paper we investigate a class of non autonomous degenerate p laplacian equations t u div a x u p 2 u u f u g x t in where a x is allowed to vanish on a nonempty closed subset with lebesgue measure zero g x t l l o c p r d 1 p a and an unbounded domain in r n we first establish the well posedness of these equations by constructing a compact embedding then we show the existence of the minimal pullback d attractor and prove that it indeed attracts the d class in l 2 norm for any 0 our results extend some known ones in previously published papers

global attractors for nonlinear parabolic equations with nonstandard growth and irregular data abstract we investigate the large time behavior of solutions to the following nonlinear parabolic equations u t div u p x 2 u f x u g in r u 0 on r u x 0 u 0 x in where u 0 g l 1 we first provide the existence and uniqueness of an entropy solution for the problem then through some delicate analysis we establish some regularity results on the solution by which we prove the existence of a global attractor for the solution semigroup

comparison results for nonlinear parabolic equations with monotone principal part in this work we prove an abstract comparison principle for abstract quasi linear parabolic problems with monotone principal part this result is applied to parabolic problems having the p laplacian as principal part and with non lipschitz perturbations

h1 random attractors for stochastic reaction diffusion equations with additive noise abstract in this paper a new theorem obtained by li and guo y li b guo random attractors for quasi continuous random dynamical systems and applications to stochastic reaction diffusion equations j differential equations 245 7 2008 1775 1800 is employed to some reaction diffusion equations with additive noise we prove the unique existence of d random attractors in h 0 1 for the corresponding random dynamical system we also obtain the existence of a unique random equilibrium for the generated random dynamical system under some restrictive assumption on the coefficients

on the connectedness and asymptotic behaviour of solutions of reaction diffusion systems abstract in this paper we consider reaction diffusion systems in which the conditions imposed on the nonlinearity provide global existence of solutions of the cauchy problem but not uniqueness we prove first that for the set of all weak solutions the kneser property holds that is that the set of values attained by the solutions at every moment of time is compact and connected further we prove the existence and connectedness of a global attractor in both the autonomous and nonautonomous cases the obtained results are applied to several models of physical or chemical interest a model of fractional order chemical autocatalysis with decay the fitz hugh nagumo equation and the ginzburg landau equation

global attractors for degenerate semilinear parabolic equations abstract let be a smooth bounded domain in r n n 2 we consider the long time behavior of solutions to the following problem u t div x u f u g in r u 0 on r u x 0 u 0 x in where u 0 g l 1 the diffusion coefficient x is measurable nonnegative and is allowed to have a finite number of zeroes at some points we provide the existence and uniqueness results for the problem then we establish some asymptotic regularity results on the solution and consider its long time behavior the existence of a global attractor is obtained in the proper space

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

long time random dynamics of stochastic parabolic p laplacian equations on rn abstract in this article we study the long time random dynamics of non autonomous stochastic parabolic p laplacian equations driven by a wiener type multiplicative noise by a new asymptotic a priori estimate method not involving the plus or minus sign of the nonlinearity the omega limit compact of solutions in l p r n l q r n is proved for any p q 2 and n 1 where q is the polynomial growth exponent of the nonlinearity if 2 p n by a boot strap technique we obtain the higher order integrability of difference of solutions near the initial time as an application we show that the obtained l 2 random attractor is attracting in the topology of l 2 r n for any 0

stabilizability and dead beat controllers for two classes of wiener hammerstein models two classes of block oriented models of the wiener hammerstein type are considered we prove that a generic condition is sufficient for a null controllable discrete time system of this form to have a stabilizing minimum time dead beat controller when the condition is violated we show how to design a nonminimum time stabilizing dynamic dead beat controller the result is used to obtain stabilizability conditions for these systems

fuzzy graphs in the evaluation and optimization of networks abstract referring to some predecessing models the paper introduces the concept of fuzzy vertex graphs a way is shown for modeling various quantitatively featurable functional capabilities of computer communication and similar networks it is shown that functional capability of distributed hierarchical multicomponent systems networks can be described by the directed rooted tree model according to the above fuzzy graph idea the problem of optimizing the overall functional capability with given component vertex set is introduced the fuzzy formulae based on the algebraic connectives which are to be optimized are constructed in the main part of the paper a series of results are presented concerning some special however important cases also the hypotheses founded on some computer experiments are formulated finally the application of these results and hypotheses are shown by the example of a distributed communication switching system family being in development in hungary

global attractors for weighted p laplacian equations with boundary degeneracy using a new a priori estimate method which is introduced by zhong et al j differ equations 223 2 367 2006 10 1016 j jde 2005 06 008 we establish the existence of a global attractor in l2 and lq q 2 respectively for weighted p laplacian equations with boundary degeneracy and without any restriction on the growing order of the nonlinearity

long time behavior for a nonlinear parabolic problem with variable exponents abstract this paper addresses the question of the asymptotic behavior of solutions to the p x laplacian problem u t div u p x 2 u f x u g with general assumptions on f x u and the exponent p x we prove the existence of global attractors in proper spaces then we consider the fractal dimension of global attractors for the problem under suitable conditions we show that the problem admits an infinite dimensional global attractor

on fuzzy tree definition abstract the connectedness and acyclicity levels are presented for a fuzzy graph several fuzzy tree definitions are given too and their relations with previous studies on the matter are analyzed

fuzzy optimal flow on imprecise structures abstract the main aim of this paper is to study the maximum flow problem when the underlying associated structure is not well defined and must be modeled as a fuzzy graph however to deal with the problem it is necessary to develop several well known concepts from classical theory in the fuzzy graph context such as flow network and admissible flow the above maximum flow problem is formulated and solved by using algorithms previously developed by the authors

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

controllability for a class of simple wiener hammerstein systems abstract controllability for a class of simple wiener hammerstein systems is considered necessary and sufficient conditions for dead beat and complete controllability for these systems are presented the controllability tests consist of two easy to check tests for the subsystems

existence and continuity of bi spatial random attractors and application to stochastic semilinear laplacian equations abstract a concept of a bi spatial random attractor for a random dynamical system is introduced a unified result about existence and upper semi continuity for a family of bi spatial random attractors is obtained if a family of random systems is convergent uniformly absorbing in an initial space and uniformly omega compact in both initial and terminate spaces the upper semi continuity result improves all existing results even for single spatial attractors as an application of the abstract result it is shown that every semilinear laplacian equation on the entire space perturbed by a multiplicative and stochastic noise possesses an l 2 l q random attractor with q 2 moreover it is proved that the family of obtained attractors is upper semi continuous at any density of noises and the family of attractors for the corresponding compact systems is both upper and lower semi continuous at infinity under the topology of both spaces

global attractors for the p laplacian equations with nonregular data abstract let be a smooth bounded domain in r n n 3 we consider the long time behavior of solutions to the p laplacian equation u t p u f u g where 2 p n p div u p 2 u is the p laplace operator assume that g and the initial condition u 0 lie in l 1 f r r is of class c 1 and satisfies proper growth conditions firstly we prove the uniqueness of the entropy solution and establish some regularity results then we show the existence of a global attractor a in l r 1 w 0 1 s with s max n p 1 n 1 p r 1 r to obtain the results a decomposition method and a bootstrap technique are used

state deadbeat control of nonlinear systems construction via sets a geometric generalization of the discrete time linear deadbeat control problem is studied the proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of the deadbeat feedback law and tracker dynamics are provided for an example system based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given

asymptotic behavior of a class of non autonomous degenerate parabolic equations abstract we investigate the asymptotic behavior of solutions of a class of non autonomous degenerate parabolic equations on r n with unbounded external forcing terms the existence of a pullback global attractor is proved in l 2 r n l p r n w 1 r r n for any p r 2

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

a note on dead beat controllability of generalised hammerstein systems necessary and sufficient conditions for dead beat and complete controllability for a class of generalised hammerstein systems are presented since the system s structure is very close to linear only linear algebra is used for the controllability test the test is very simple and easy to use a closed loop minimum time dead beat controller can be designed for a subclass of generalised hammerstein systems using the grobner basis method

asymptotic regularity for p laplacian equation this paper is devoted to proving some asymptotic regularity of the solutions of the p laplacian equation ut div u p 2 u f u g x p 2 n considered on a bounded domain rn n 3 the nonlinear term f satisfies the polynomial growth condition of arbitrary order c1 u q k f u u c2 u q k where q 2 is arbitrary as an application of the asymptotic regularity results we not only can obtain the existence of a l2 w01 p lq global attractor a immediately but also can show further that a attracts every bounded subsets of l2 under the w01 p lq norm for any 0 furthermore the fractal dimension of a is finite in lq for any 0

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

long time behavior for quasilinear parabolic equations involving weighted p laplacian operators abstract in this paper we study the first initial boundary value problem for a class of quasilinear degenerate parabolic equations involving weighted p laplacian operators the long time behavior of solutions to that problem is considered via the concept of global attractors for multi valued semiflows

attractors for parabolic equations with dynamic boundary conditions abstract in this paper we prove existence of global solutions and l 2 l 2 h 1 l p l p global attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains with a smooth boundary where there is no other restriction on p 2

asymptotic regularity for some dissipative equations abstract this paper is devoted to proving some asymptotic regularity for both reaction diffusion equation with a polynomially growing nonlinearity of arbitrary order and strongly damped wave equation with critical nonlinearity which excel the sharp regularity allowed by the corresponding stationary equations equilibrium points based on this regularity the existence of the finite dimensional global and exponential attractors can be obtained easily