prescribing the center of mass of a multi soliton solution for a perturbed semilinear wave equation abstract we construct a finite time blow up solution for a class of strongly perturbed semilinear wave equation with an isolated characteristic point in one space dimension given any integer k 2 and 0 r we construct a blow up solution with a characteristic point a such that the asymptotic behavior of the solution near a t a shows a decoupled sum of k solitons with alternate signs whose centers in the hyperbolic geometry have 0 as a center of mass for all times although the result is similar to the unperturbed case in its statement our method is new indeed our perturbed equation is not invariant under the lorentz transform and this requires new ideas in fact the main difficulty in this paper is to prescribe the center of mass 0 r we would like to mention that our method is valid also in the unperturbed case and simplifies the original proof by cote and zaag 9 as far as the center of mass prescription is concerned

a fast algorithm for subspace state space system identification via exploitation of the displacement structure two recent approaches van overschee de moor n4sid automatica 30 1 1994 75 verhaegen int j control 58 3 1993 555 in subspace identification problems require the computation of the r factor of the qr factorization of a block hankel matrix h which in general has a huge number of rows since the data are perturbed by noise the involved matrix h is in general full rank it is well known that from a theoretical point of view the r factor of the pr factorization of h is equivalent to the cholesky factor of the correlation matrix hth apart from a multiplication by a sign matrix in sima proceedings second niconet workshop paris versailles december 3 1999 p 75 a fast cholesky factorization of the correlation matrix exploiting the block hankel structure of h is described in this paper we consider a fast algorithm to compute the r factor based on the generalized schur algorithm the proposed algorithm allows to handle the rank deficient case c 2001 elsevier science b v all rights reserved

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

a weaker regularity condition for subdifferential calculus and fenchel duality in infinite dimensional spaces abstract in this paper we present a new regularity condition for the subdifferential sum formula of a convex function with the precomposition of another convex function with a continuous linear mapping this condition is formulated by using the epigraphs of the conjugates of the functions involved and turns out to be weaker than the generalized interior point regularity conditions given so far in the literature moreover it provides a weak sufficient condition for fenchel duality regarding convex optimization problems in infinite dimensional spaces as an application we discuss the strong conical hull intersection property chip for a finite family of closed convex sets

fast subspace based system identification recently developed subspace based system identification 4sid techniques have opened new routes to the identification of multi input multi output systems the 4sid techniques guarantee convergence and run faster than the statistically efficient prediction error methods without much performance loss the resulting computational load of the 4sid techniques is o nm2 where n is the data length and m is the sliding window size however the computational burden o nm2 can become prohibitively large as n and m grow large noting that the major bottleneck comes from the qr factorization of an m i n data matrix and that the existing 4sid techniques do not exploit the structure of the matrices arising in the identification procedure we propose a new implementation of the existing 4sid which reduces the computational burden to o nm by exploiting the displacement and low rank structure of the matrices

fast identification of state space models via exploitation of displacement structure the computational burden of state space model identification has prevented its real time application although it offers some important advantages over other methods based on input output transfer functions a recently proposed state space identification method uses ideas from sensor array signal processing to somewhat reduce the computational burden the major costs still remain because of the need for the singular value or sometimes qr decomposition which requires o mn sup 2 hops and o n sup 2 storage when the data matrix has size m spl times n n m it turns out that proper exploitation using results from the theory of displacement structure of the toeplitz like nature of several matrices arising in the procedure reduces the computational effort to o mn flops with o m sup 2 n storage further computational gains are made by using the recently developed fast subspace decomposition methods results of the study of an actual system are described

construction of a multisoliton blowup solution to the semilinear wave equation in one space dimension we consider the semilinear wave equation with power nonlinearity in one space dimension given a blow up solution with a characteristic point we refine the blow up behavior first derived by merle and zaag we also refine the geometry of the blow up set near a charac teristic point and show that except may be for one exceptional situation it is never symmetric with the respect to the characteristic point then we show that all blow up modalities predicted by those authors do occur more precisely given any integer k 2 and 0 we construct a blow up solution with a characteristic point a such that the asymptotic behavior of the solution near a t a shows a decoupled sum of k solitons with alternate signs whose centers in the hyperbolic geometry have 0 as a center of mass for all times

construction of type ii blowup solutions for the 1 corotational energy supercritical wave maps abstract we consider the energy supercritical wave maps from r d into the d sphere s d with d 7 under an additional assumption of 1 corotational symmetry the problem reduces to the one dimensional semilinear wave equation t 2 u r 2 u d 1 r r u d 1 2 r 2 sin 2 u we construct for this equation a family of c solutions which blow up in finite time via concentration of the universal profile u r t q r t where q is the stationary solution of the equation and the speed is given by the quantized rates t c u t t l l n l d 1 2 the construction relies on two arguments the reduction of the problem to a finite dimensional one thanks to a robust universal energy method and modulation techniques developed by merle raphael and rodnianski 49 for the energy supercritical nonlinear schrodinger equation then we proceed by contradiction to solve the finite dimensional problem and conclude using the brouwer fixed point theorem

openness of the set of non characteristic points and regularity of the blow up curve for the 1 d semilinear wave equation we consider here the 1 d semilinear wave equation with a power nonlinearity and with no restriction on initial data we first prove a liouville theorem for that equation then we consider a blow up solution its blow up curve x mapsto t x and i 0 subset mathbb r the set of non characteristic points we show that i0 is open and that t x is c1 on i0 all these results fundamentally use our previous result in 19 showing the convergence in selfsimilar variables for x in i 0

farkas lemma in random locally convex modules and minkowski weyl type results in l0 f rn abstract in this paper we investigate the structure of a finitely generated l 0 positively homogeneous and l 0 convex cone in a random locally convex module first we establish a farkas type characterization for such a kind of cone then we can further give some minkowski weyl type results for the specific case when the random locally convex module is the space l 0 f r n of equivalence classes of r n valued random variables

construction of solutions with exactly k blow up points for the schrodinger equation with critical nonlinearity we consider the nonlinear schrodinger equation i partial u mathord left vphantom i partial u partial t right kern nulldelimiterspace partial t delta u left u right 4 mathord left vphantom 4 n right kern nulldelimiterspace n uandu left 0 right varphi left right 1 whereu 0 t n for any given pointsx1 x2 x k in n we construct a solution of eq 1 u t which blows up in a finite timet at exactlyx1 x2 x k in addition we describe the precise behavior of the solutionu t whent t at the blow up points x1 x2 x k and in n x1 x2 x k

blowup dynamics for smooth data equivariant solutions to the critical schrodinger map problem we consider the energy critical schrodinger map problem with the 2 sphere target for equivariant initial data of homotopy index k 1 we show the existence of a codimension one set of smooth well localized initial data arbitrarily close to the ground state harmonic map in the energy critical norm which generates finite time blowup solutions we give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy

construction of solutions to the subcritical gkdv equations with a given asymptotical behavior we consider the subcritical generalized korteweg de vries equation ut uxx u4 x 0 t x r let rj t x qcj x xj cjt j 1 n be n soliton solutions to this equation denote u t the kdv linear group and let v be in an adequate weighted sobolev space we construct a solution u t to the generalized korteweg de vries equation such that limt u t u t v j 1nrj t h1 0

farkas type results with conjugate functions we present some new farkas type results for inequality systems involving a finite as well as an infinite number of convex constraints for this we use two kinds of conjugate dual problems namely an extended fenchel type dual problem and the recently introduced fenchel lagrange dual problem for the latter which is a combination of the classical fenchel and lagrange duals the strong duality is established

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

fast recursive identification of state space models via exploitation of displacement structure abstract the seemingly computational burden of state space model identification has limited its real time application though it offers some important advantages over methods based on input output transfer functions it has been shown recently that ideas from the theory of displacement structure can be used in state space identification to reduce the computational burden of batch processing from o mn 2 to o mn flops when the data matrix is of size m n where n m however in many on line identification scenarios with slowly time varying systems it is desirable to update the model as time goes on with the minimal computational burden in this paper we extend our results of the batch processing algorithm to allow updating of the identified state space model with o m 2 flops again the theories of displacement structure and of the fast subspace decomposition fsd technique play crucial roles in the realization of the fast updating algorithm some computer simulation results are also presented

hyperbolic householder transformations a class of transformation matrices analogous to the householder matrices is developed with a nonorthogonal property designed to permit the efficient deletion of data from least squares problems these matrices which we term hyperbolic householder are shown to effect deletion or simultaneous addition and deletion of data with much less sensitivity to rounding errors than for techniques based on normal equations when the addition deletion sets are large this numerical robustness is obtained at the expense of only a modest increase in computations and when only a relatively small fraction of the data set is modified there is a decrease in required computations two applications to signal processing problems are considered first these transformations are used to obtain a square root algorithm for windowed recursive least squares filtering second the transformations are employed to implement the rejection of spurious data from the weight vector estimator in an adaptive array

stable blow up patterns abstract for the semilinear heat equation ut u eu in a convex domain r n given any b we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u t x 2 ln x b ln ln x b ln 8 t being the blow up time using a suitable set of rescaled coordinates this asymptotic behavior is proved to be stable with respect to small perturbations of the initial conditions

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

inequality systems and optimization abstract in this paper new versions of solvability theorems are given for general inequality systems involving nonconvex functions and noncompact sets the results are applied to constrained optimization problems with an infinite number of constraints and to minimax problems on noncompact sets

farkas type results for inequality systems with composed convex functions via conjugate duality we present some farkas type results for inequality systems involving finitely many functions therefore we use a conjugate duality approach applied to an optimization problem with a composed convex objective function and convex inequality constraints some recently obtained results are rediscovered as special cases of our main result

constraint qualifications for extended farkas s lemmas and lagrangian dualities in convex infinite programming for an inequality system defined by a possibly infinite family of proper functions not necessarily lower semicontinuous we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions under the new constraint qualifications we obtain characterizations of those reverse convex inequalities which are a consequence of the constrained system and we provide necessary and or sufficient conditions for a stable farkas lemma to hold similarly we provide characterizations for constrained minimization problems to have the strong or strong stable lagrangian dualities several known results in the conic programming problem are extended and improved

blowup solutions for a reaction diffusion system with exponential nonlinearities abstract we consider the following parabolic system whose nonlinearity has no gradient structure t u u e p v t v v e q u u 0 u 0 v 0 v 0 p q 0 in the whole space r n we show the existence of a stable blowup solution and obtain a complete description of its singularity formation the construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude in particular our analysis uses neither the maximum principle nor the classical methods based on energy type estimates which are not supported in this system the stability is a consequence of the existence proof through a geometrical interpretation of the quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem

existence and classification of characteristic points at blow up for a semilinear wave equation in one space dimension we consider the semilinear wave equation with power nonlinearity in one space dimension we first show the existence of a blow up solution with a characteristic point then we consider an arbitrary blow up solution u x t the graph x mapsto t x of its blow up points and scr s subset bbb r the set of all characteristic points and show that scr s has an empty interior finally given x 0 in scr s we show that in selfsimilar variables the solution decomposes into a decoupled sum of at least two solitons with alternate signs and that t x forms a corner of angle pi over 2 at x 0

blow up profile for the complex ginzburg landau equation abstract we construct a solution to the complex ginzburg landau equation which blows up in finite time t only at one blow up point we also give a sharp description of its blow up profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude two major difficulties arise in the proof the linearized operator around the profile is not self adjoint and it has a second neutral mode in the last section the interpretation of the parameters of the finite dimensional problem in terms of the blow up time and the blow up point gives the stability of the constructed solution with respect to perturbations in the initial data

brief paper convergence analysis of instrumental variable recursive subspace identification algorithms the convergence properties of recently developed recursive subspace identification methods are investigated in this paper the algorithms operate on the basis of instrumental variable iv versions of the propagator method for signal subspace estimation it is proved that under suitable conditions on the input signal and the system the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and by extension to the state space system matrices

farkas type results for fractional programming problems abstract considering a constrained fractional programming problem within the present paper we present some necessary and sufficient conditions which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant the desired results are obtained using the fenchel lagrange duality approach applied to an optimization problem with convex or difference of convex dc objective functions and finitely many convex constraints these are obtained from the initial fractional programming problem using an idea due to dinkelbach we also show that our general results encompass as special cases some recently obtained farkas type results

blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term abstract we consider the following exponential reaction diffusion equation involving a nonlinear gradient term t u u u 2 e u x t r n 0 t 1 we construct for this equation a solution which blows up in finite time t 0 and satisfies some prescribed asymptotic behavior we also show that the constructed solution and its gradient blow up in finite time t simultaneously at the origin and find precisely a description of its final blowup profile it happens that the quadratic gradient term is critical in some sense resulting in the change of the final blowup profile in comparison with the case 0 the proof of the construction is inspired by the method of merle and zaag in 1997 it relies on the reduction of the problem to a finite dimensional one and uses the index theory to conclude one of the major difficulties arising in the proof is that outside the blowup region the spectrum of the linearized operator around the profile can never be made negative truly new ideas are needed to achieve the control of the outer part of the solution thanks to a geometrical interpretation of the parameters of the finite dimensional problem in terms of the blowup time and the blowup point we obtain the stability of the constructed solution with respect to perturbations in the initial data

hierarchical gradient based identification of multivariable discrete time systems in this paper we use a hierarchical identification principle to study identification problems for multivariable discrete time systems we propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation the proposed algorithms can be applied to identification of systems involving non stationary signals and have significant computational advantage over existing identification algorithms finally we test the proposed algorithms by simulation and show their effectiveness

inequality systems and global optimization abstract solvability results for infinite inequality systems involving convex and difference of convex dc functions are given generalizations of farkas lemma are obtained these results are presented in terms of epigraphs of conjugate functions applications are given for characterizing global optimality and optimality of difference of convex dc optimization problems with convex inequality constraints solvability results for cone convex inequality systems are also given

complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions necessary and sufficient global optimality conditions are presented for certain non convex minimization problems subject to inequality constraints that are expressed as the pointwise minimum of sublinear msl functions a generalized farkas lemma for inequality systems with msl functions plays a crucial role in presenting the conditions in dual forms applications to certain multiplicative sublinear programming problems and fractional programming problems are also given

nonlinear extensions of farkas lemma with applications to global optimization and least squares a nonlinear extension of farkas lemma for systems involving the difference of sublinear functions is presented this extension of farkas lemma is applied to give a complete characterization of global optimality for constrained global optimization problems in which the objective function is the difference of a convex and sublinear function and the constraints are systems of difference sublinear functions an application to certain fractional programming problems is also given these results are achieved with merely a stronger consistency condition which reduces to the usual feasibility requirement for problems with sublinear constraints further generalizations of farkas lemma for systems involving convex and difference sublinear functions are also presented moreover a generalized farkas lemma for certain specially structural convex inequality systems is shown to be related to the solution of appropriate constrained least squares problems

brief recursive 4sid algorithms using gradient type subspace tracking sometimes we obtain some prior information about a system to be identified e g the order model structure etc in this paper we consider the case where the order of a mimo system to be identified is a priori known recursive subspace state space system identification algorithms presented here are based on the gradient type subspace tracking method used in the array signal processing the algorithms enable us to estimate directly the subspace spanned by the column vectors of the extended observability matrix of the system to be identified without performing the singular value decomposition also a new convergence proof of the gradient type subspace tracking is given in this paper under the condition of a step size between 0 and 1 we prove the convergence property of the recursive equation of the gradient type subspace tracking a numerical example illustrates that our algorithm is more robust with respect to the choice of the initial values than the corresponding past one

characterizing set containments involving infinite convex constraints and reverse convex constraints dual characterizations of the containment of a closed convex set defined by infinite convex constraints in an arbitrary polyhedral set in a reverse convex set defined by convex constraints and in another convex set defined by finite convex constraints are given a special case of these dual characterizations has played a key role in generating knowledge based support vector machine classifiers which are powerful tools in data classification and mining the conditions in these dual characterizations reduce to simple nonasymptotic conditions under slater s constraint qualification

asymptotic n soliton like solutions of the subcritical and critical generalized korteweg de vries equations we consider the generalized korteweg de vries equations ut uxx upx 0t x r inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i in the subcritical and critical cases p 2 3 4 or 5 let r j t x qc j x c j t x j where j 1 n be n soliton solutions of this equation with corresponding speeds 0 c 1 c 2 c n in this paper we construct a solution u t of the generalized korteweg de vries equation such that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i this solution behaves asymptotically as t as the sum of n solitons without loss of mass by dispersion this is an exceptional behavior indeed being given the parameters c j 1 j n x j 1 j n we prove uniqueness of such a solution in the integrable cases p 2 and 3 such solutions are explicitly known and their properties were extensively studied in the literature they are called n soliton solutions therefore the existence result is new only for the nonintegrable cases the uniqueness result is new for all cases

a farkas lemma for difference sublinear systems and quasidifferentiable programming a new generalized farkas theorem of the alternative is presented for systems involving functions which can be expressed as the difference of sublinear functions various other forms of theorems of the alternative are also given using quasidifferential calculus comprehensive optimality conditions are then developed for broad classes of infinite dimensional quasidifferentiable programming problems applications to difference convex programming and infinitely constrained concave minimization problems are also discussed

from the farkas lemma to the hahn banach theorem this paper provides new versions of the farkas lemma characterizing those inequalities of the form f x geq 0 which are consequences of a composite convex inequality s circ g x leq 0 on a closed convex subset of a given locally convex topological vector space x where f is a proper lower semicontinuous convex function defined on x s is an extended sublinear function and g is a vector valued s convex function in parallel associated versions of a stable farkas lemma considering arbitrary linear perturbations of f are also given these new versions of the farkas lemma and their corresponding stable forms are established under the weakest constraint qualification conditions the so called closedness conditions and they are actually equivalent to each other as well as equivalent to an extended version of the so called hahn banach lagrange theorem and its stable version correspondingly it is shown that any of them implies analytic and algebraic versions of the hahn banach t

construction of a blow up solution for the complex ginzburg landau equation in a critical case we construct a solution for the complex ginzburg landau equation in some critical case which blows up in finite time t only at one blow up point we also give a sharp description of its profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude the interpretation of the parameters of the finite dimension problem in terms of the blow up point and time allows to prove the stability of the constructed solution

subspace model identification part 1 the output error state space model identification class of algorithms in this paper we present two novel algorithms to realize a finite dimensional linear time invariant state space model from input output data the algorithms have a number of common features they are classified as one of the subspace model identification schemes in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input output data this structure is then exploited in the calculation of a realization another common feature is their algorithmic organization an rq factorization followed by a singular value decomposition and the solution of an overdetermined set or sets of equations the schemes assume that the underlying system has an output error structure and that a measurable input sequence is available the latter characteristic indicates that both schemes are versions of the mimo output error state space model identification moesp approach the first algorithm is denoted in particular as the elementary moesp scheme

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

a class of subspace model identification algorithms to identify periodically and arbitrarily time varying systems abstract subspace model identification algorithms that allow the identification of a linear time varying ltv state space model from an ensemble set of input output measurements are presented in this paper each pair of input and output sequences in this ensemble is recorded when the underlying system to be identified undergoes the same time varying behavior the algorithms operate directly on the available ensemble of input output data and are a generalization of the recently proposed multivariable output error state space moesp class of algorithms to this ensemble type of identification problems a special case is considered in this paper where the repetition of this time varying behavior is intrinsic namely in periodically time varying systems an example of identifying a multirate sampled data system from a recorded input and output sequence demonstrates some of the capabilities of the presented subspace model identification algorithms

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

on the stability of critical chemotactic aggregation we consider the two dimensional parabolic elliptic keller segel model of chemotactic aggregation for radially symmetric initial data we show the existence of a stable mechanism of singularity formation and obtain a complete description of the associated aggregation process

construction of a stable periodic solution to a semilinear heat equation with a prescribed profile we construct a periodic solution to the semilinear heat equation with power nonlinearity in one space dimension which blows up in finite time t only at one blow up point we also give a sharp description of its blow up profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude thanks to the geometrical interpretation of the finite dimensional parameters in terms of the blow up time and blow up point we derive the stability of the constructed solution with respect to initial data

construction of solutions to the l 2 critical kdv equation with a given asymptotic behaviour we consider the critical korteweg de vries equation ut uxx u x 0 t x r let rj t x qcj x xj cjt j 1 n be n soliton solutions to this equation denote u t the kdv linear group and let v h be with sufficient decay on the right that is 1 x0 v l for some 0 0 we construct a solution u t to the critical korteweg de vries equation such that lim t u t u t v n x j 1 rj t h1 0

existence and universality of the blow up profile for the semilinear wave equation in one space dimension in this paper we consider the semilinear wave equation with a power nonlinearity in one space dimension we exhibit a universal one parameter family of functions which stand for the blow up profile in self similar variables at a non characteristic point for general initial data the proof is done in self similar variables we first characterize all the solutions of the associated stationary problem as a one parameter family then we use energy arguments coupled with dispersive estimates to show that the solution approaches this family in the energy norm in the non characteristic case and to a finite decoupled sum of such a solution in the characteristic case finally in the case where this sum is reduced to one element which is the case for noncharacteristic points we use modulation theory coupled with a nonlinear argument to show the exponential convergence in the self similar time variable of the various parameters and conclude the proof this step provides us with a result of independent interest the trapping of the solution in self similar variables near the set of stationary solutions valid also for non characteristic points the proof of these results is based on a new analysis in the self similar variable 2007 elsevier inc all rights reserved

high performance numerical algorithms and software for subspace based linear multivariable system identification basic algorithmic and numerical issues involved in subspace based linear multivariable discrete time system identification are described a new identification toolbox slident has been developed and incorporated in the freely available subroutine library in control theory slicot reliability efficiency and ability to solve industrial identification problems received a special consideration two algorithmic subspace based approaches moesp and n4sid and their combination and both standard and fast techniques for data compression are provided structure exploiting algorithms and dedicated linear algebra tools enhance the computational efficiency and reliability extensive comparisons with the available computational tools based on subspace techniques show the better efficiency of the slident toolbox at comparable numerical accuracy and its capabilities to solve identification problems with many thousands of samples and hundreds of parameters

type ii blow up for the four dimensional energy critical semi linear heat equation abstract we consider the energy critical four dimensional semi linear heat equation t u u u 3 0 we show the existence of type ii finite time blow up solutions and give a sharp description of the corresponding singularity formation these solutions concentrate a universal bubble of energy in the critical topology u t r 1 q r t u in h 1 where the blow up profile is given by the talenti aubin soliton q r 1 1 r 2 8 and with speed t t t log t t 2 as t t our approach uses a robust energy method approach developed for the study of geometrical dispersive problems raphael and rodnianski 2012 18 merle et al 2011 15 and lies in the continuation of the study of the energy critical harmonic heat flow raphael and schweyer 2011 19 and the energy critical four dimensional wave equation hillaret and raphael 2010 5

complete characterizations of stable farkas lemma and cone convex programming duality we establish necessary and sufficient conditions for a stable farkas lemma we then derive necessary and sufficient conditions for a stable duality of a cone convex optimization problem where strong duality holds for each linear perturbation of a given convex objective function as an application we obtain stable duality results for convex semi definite programs and convex second order cone programs

solution of a nonlinear heat equation with arbitrarily given blow up points we consider the equation where i u is scalar valued and p 1 it has been proven that if u t blows up at time t the blow up points are finite in number and located in i our aim is to prove that this result is optimal that is for any given points x1 xk in i there is a solution u such that its blow up points are exactly x1 xk