monotonicity method applied to the complex ginzburg landau and related equations abstract global existence of unique strong solutions is established for the complex ginzburg landau equation tu i u i u p 1u u 0 where 0 0 r p 1 and 1 2 p p 1 the key is a new inequality in monotonicity methods it is based on the sectorial estimates of in lp 1 and the nonlinear operator u u p 1u appearing in the equation the key inequality also yields the global existence of unique strong solutions of the nonlinear schrodinger type equation with monotone nonlinearity tu i u u p 1u 0 for all p 1

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

some global dynamical properties of the kuramoto sivashinsky equations nonlinear stability and attractors abstract the kuramoto sivashinsky equations model pattern formations on unstable flame fronts and thin hydrodynamic films they are characterized by the coexistence of coherent spatial structures with temporal chaos we investigate some global dynamical properties including nonlinear stability we demonstrate their low modal behavior in terms of determining modes and that the fractal dimension of all attractors is bounded by a universal constant times l 13 8 where l is a dimensionless pattern cell size in the one dimensional case such equations are indeed a paradigm of low dimensional behavior for infinite dimensional systems

optimal two stage algorithms for group testing problems group testing refers to the situation in which one is given a set of objects cal o an unknown subset cal p subseteq cal o and the task of determining cal p by asking queries of the type does cal p intersect cal q where cal q is a subset of cal o group testing is a basic search paradigm that occurs in a variety of situations such as quality control testing searching in storage systems multiple access communications and data compression among others group testing procedures have been recently applied in computational molecular biology where they are used for screening libraries of clones with hybridization probes and sequencing by hybridization motivated by particular features of group testing algorithms used in biological screening we study the efficiency of two stage group testing procedures our main result is the first optimal two stage algorithm that uses a number of tests of the same order as the information theoretic lower bound on the problem we also provide efficient algorithms for the case in which there is a bernoulli probability distribution on the possible sets cal p and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of inhibitory items in cal o our results depend on a combinatorial structure introduced in this paper we believe that it will prove useful in other contexts too

global attractors and convergence to equilibrium for degenerate ginzburg landau and parabolic equations abstract we study the dynamics of a degenerate complex ginzburg landau cgl and a real parabolic equation with a variable generally nonsmooth diffusion coefficient which may vanish at some points or be unbounded for the cgl equation there exists a global attractor in l 2 for the parabolic equation we show the existence of a global branch of nonnegative stationary states the global bifurcation result is used in order to establish in conjunction with the definition of a gradient dynamical system in the natural phase space that any solution with nonnegative initial data tends to the trivial or the nonnegative equilibrium

global attractors for the complex ginzburg landau equation abstract this paper concerns the long time behavior of the following complex ginzburg landau equations u t i u i u p 2 u u 0 without any restriction on p 2 under the assumptions 1 4 we first prove the well posedness of strong solutions for the complex ginzburg landau equations and then the existence of absorbing sets in l 2 h 0 1 l p and h 2 l 2 p 1 respectively for the semigroup s t t 0 generated by 1 1 1 3 is established finally we prove the existence of global attractors in l 2 and h 0 1 for the semigroup s t t 0 generated by 1 1 1 3 by the sobolev compactness embedding theorem and prove the existence of global attractor in l p for the semigroup s t t 0 generated by 1 1 1 3 using interpolation inequality

group testing for image compression this paper presents group testing for wavelets gtw a novel embedded wavelet based image compression algorithm based on the concept of group testing we explain how group testing is a generalization of the zerotree coding technique for wavelet transformed images we also show that golomb coding is equivalent to hwang s group testing algorithm du and hwang 1993 gtw is similar to spiht said and pearlman 1996 but replaces spiht s significance pass with a new group testing based method although no arithmetic coding is implemented gtw performs competitively with spiht s arithmetic coding variant in terms of rate distortion performance

on the principal eigenvalue of a second order linear elliptic problem on considere le probleme de dirichlet 7b lu mu dans u 0 sur dans un domaine borne r n a frontiere lisse 7b l est un operateur differentiel uniformement elliptique sur de la forme 7b lu i n j 1 a ij 2 u x j x i i n 1 a i u x i a 0 u a coefficients a valeurs reels appartenant a c 0 1

elliptic problems involving an indefinite weight we consider a selfadjoint elliptic eigenvalue problem which is derived formally from a variational problem of the form lu a o x u in q b1u 0 on f j 1 m where l is a linear elliptic operator of order 2m defined in a bounded open set q c rn n 2 with boundary f the bj are linear differential operators defined on f and w is a real valued function assuming both positive and negative values for our problem we prove the completeness of the eigenvectors and associated vectors in two function spaces which arise naturally in such an indefinite problem we also establish some results concerning the eigenvalues of the problem which complement the known results and investigate the structure of the principal subspaces

weak and strong solutions of the complex ginzburg landau equation abstract the generalized complex ginzburg landau equation t a ra 1 iv a 1 i a 2 a has been proposed and studied as a model for turbulent dynamics in nonlinear partial differential equations it is a particularly interesting model in this respect because it is a dissipative version of the hamiltonian nonlinear schrodinger equation possessing solutions that form localized singularities in finite time in this paper we investigate existence and regularity of solutions to this equation subject to periodic boundary conditions in various spatial dimensions appropriately defined weak solutions are established globally in time and unique strong solutions are found locally a new collection of a priori estimates are presented and we discuss the relationship of our results for the complex ginzburg landau equation to analogous issues for fluid turbulence described by the incompressible navier stokes equations

uniform hypergraphs containing no grids abstract a hypergraph is called an r r grid if it is isomorphic to a pattern of r horizontal and r vertical lines i e a family of sets a 1 a r b 1 b r such that a i a j b i b j 0 for 1 i j r and a i b j 1 for 1 i j r three sets c 1 c 2 c 3 form a triangle if they pairwise intersect in three distinct singletons c 1 c 2 c 2 c 3 c 3 c 1 1 c 1 c 2 c 1 c 3 a hypergraph is linear if e f 1 holds for every pair of edges e f in this paper we construct large linear r hypergraphs which contain no grids moreover a similar construction gives large linear r hypergraphs which contain neither grids nor triangles for r 4 our constructions are almost optimal these investigations are motivated by coding theory we get new bounds for optimal superimposed codes and designs

induced trajectories and approximate inertial manifolds for the ginzburg landau partial differential equations abstract this paper studies the long time behavior of solutions to the ginzburg landau partial differential equation we explicitly produce four approximate inertial manifolds and associate with each manifold a thin neighborhood into which the orbits enter with an exponential speed and in a finite time these neighborhoods localize the universal attractor we consider the space periodic case however with slight modifications the construction carries over to dirichlet and neumann boundary conditions

constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels in this paper we introduce a parameterized generalization of the well known superimposed codes we give algorithms for their construction and provide non existential results we apply our new combinatorial structures to the efficient solution of new group testing problems and access coordination issues in multiple access channels

on the complexity of neighbourhood learning in radio networks consider a synchronous radio network of n stationary nodes represented by an undirected graph with maximum degree suppose that each node has a unique id from 1 u where un in the neighbourhood learning task each node must produce a list of the ids of its neighbours in the network we prove new lower bounds on the number of slots needed by certain classes of deterministic algorithms that solve this task first we show that o u slot round robin algorithms are optimal for the class of collision free algorithms then we consider algorithms where each node fixes its entire transmission schedule at the start for such algorithms we prove a 2loglogu slot lower bound on schedule length that holds in very general models e g when nodes possess collision detectors messages can be of arbitrary size and nodes know the schedules being followed by all other nodes we also prove a similar result for the sinr model of radio networks to prove these results we consider a generalization of cover free families of sets we also show a separation between the class of fixed schedule algorithms and the class of algorithms where nodes can choose to leave out some transmissions from their schedule

on the eigenvalues of nonselfadjoint problems involving indefinite weights on etudie la distribution asymptotique des valeurs propres de problemes aux valeurs limites elliptiques comprenant des fonctions poids

dimension of the attractors associated to the ginzburg landau partial differential equation abstract we study the long time behavior of solutions to the ginzburg landau partial differential equation it is shown that a finite dimensional attractor captures all the solutions an upper bound on this dimension is given in terms of physical quantities by estimating the lyapunov exponents on the trajectories finally using the well known side band instabilities of an exact time dependent solution stokes solution we derive lower bounds on the dimension of the universal attractor moreover the lower and upper bounds agree

optimal algorithms for two group testing problems and new bounds on generalized superimposed codes two variants of the well known group testing problem are considered in the first variant a finite set of items o and an unknown subset psubeo are given and one wants to identify the set p by asking the least number of questions of the form is qcapp 1 where qsubeo this problem naturally arises in the design of efficient contention resolution algorithms for certain random multiple access communication systems berger et al random multiple access communication and group testing ieee trans commun vol 32 no 7 pp 769 779 1984 in the second variant of the problem the answer to the question is qcapp 1 is correctly yes if qcapp 1 and no if qcapp 0 and it is left to a possibly malicious adversary otherwise this model was introduced in damaschke randomized group testing for mutually obscuring defectives inf process lett vol 67 pp 131 135 1998 in the context of chemical compound testing in this correspondence several algorithms for these group testing problems are presented trying to optimize different measures of performance the overall number of tests performed by the algorithm the number of stages in which tests can be arranged and the decoding complexity of identifying the elements of p from tests outcomes some of the given algorithms are optimal with respect to more than one of the above criteria instrumental to the results presented in the correspondence are new and improved bounds on certain generalization of superimposed codes introduced in dyachkov and rykov a generalization of superimposed codes and its application to the multiple access channel in proc 1984 ieee int symp inf theory pp 62 64 de bonis and vaccaro constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels theoretic comput sci vol 306 no 1 3 pp 223 243 2003 a result that it is believed to be of independent interest

monotonicity method applied to complex ginzburg landau type equations abstract global existence and smoothing effect are established for the complex ginzburg landau type equation in which the real and imaginary parts of the complex coefficient are multiplied by nonlinear terms with different powers the proof is based on monotonicity methods described by subdifferential operators the key lies in two modified inequalities

born again group testing multiaccess communications a brief summary of the basic notions of group testing is presented together with a brief historical account one of the early papers on group testing is shown to include a description of the tree search polling algorithm of hayes the classical group testing problem is formulated including a criterion for optimality of test plans a restricted class of tests called nested testing is described and a complete description for an optimal nested strategy is given for both a finite number and an infinite number of bernoulli distributed random variables a generalization of group testing applicable to the random access communications problem is presented

the cauchy problem in local spaces for the complex ginzburg landau equation i compactness methods we continue the study of the initial value problem for the complex ginzburg landau equation with a 0 b 0 g 0 in initiated in a previous paper i we treat the case where the initial data and the solutions belong to local uniform spaces more precisely to spaces of functions satisfying local regularity conditions and uniform bounds in local norms but no decay conditions or arbitrarily weak decay conditions at infinity in in i we used compactness methods and an extended version of recent local estimates 3 and proved in particular the existence of solutions globally defined in time with local regularity of the initial data corresponding to the spaces l r for r 2 or h 1 here we treat the same problem by contraction methods this allows us in particular to prove that the solutions obtained in i are unique under suitable subcriticality conditions and to obtain for them additional regularity properties and uniform bounds the method extends some of those previously applied to the nonlinear heat equation in global spaces to the framework of local uniform spaces

a simple approach to the cauchy problem for complex ginzburg landau equations by compactness methods abstract this paper is concerned with the cauchy problem cgl in l 2 r n for complex ginzburg landau equations with laplacian and nonlinear term u q 2 u multiplied by the complex coefficients i and i respectively q 2 0 0 r the global existence of strong solutions to cgl is established without any upper restriction on q 2 but with some restriction on and the result corresponds to ginibre and velo 1996 3 proposition 5 1 which is technically proved by combining convolution regularizing methods with compactness localizing methods while our proof here is fairly simplified the key to our proof is the cauchy problem cgl r which is cgl with replaced with v r where v r x x r 2 x r v r x 0 x r the solvability of cgl r is a direct consequence of okazawa and yokota 2002 16 theorem 4 1 taking the limit of global strong solutions to cgl r as r yields a global strong solution to cgl the result gives also an unbounded version of okazawa and yokota 2002 16 theorem 1 1 with p 2 for the initial boundary value problem on bounded domains

the cauchy problem in local spaces for the complex ginzburg landau equation ii contraction methods we continue the study of the initial value problem for the complex ginzburg landau equation with a 0 b 0 g 0 in initiated in a previous paper i we treat the case where the initial data and the solutions belong to local uniform spaces more precisely to spaces of functions satisfying local regularity conditions and uniform bounds in local norms but no decay conditions or arbitrarily weak decay conditions at infinity in in i we used compactness methods and an extended version of recent local estimates 3 and proved in particular the existence of solutions globally defined in time with local regularity of the initial data corresponding to the spaces l r for r 2 or h 1 here we treat the same problem by contraction methods this allows us in particular to prove that the solutions obtained in i are unique under suitable subcriticality conditions and to obtain for them additional regularity properties and uniform bounds the method extends some of those previously applied to the nonlinear heat equation in global spaces to the framework of local uniform spaces

group testing with blockers and synergism discovery and development of a new drug can cost hundreds of millions of dollars pharmaceutical companies have used group testing methodology routinely as one of the efficient high throughput screening techniques to search for lead compounds among collections of hundreds of thousands of chemical compounds the lead compounds can be modified to produce new and effective molecules which eventually may lead to new drugs this article develops models and estimation procedures to obtain quantitative information from data in such applications it investigates group testing procedures and studies cost efficiency when the standard assumption adopted by dorfman that tested items act independently of one another is violated the investigation is focused on but not limited to the square array pooling method and the methodologies developed are illustrated through simulations and a drug discovery dataset from glaxo wellcome inc

on the spectrum of elliptic operators with respect to indefinite weights abstract recent results on linear elliptic eigenvalue problems with respect to indefinite weight functions are recalled and some applications are given