optimal disturbance rejection and performance robustness in linear systems abstract in this paper a method is proposed for the optimal design of regulators and observers from the disturbance rejection and robust performance points of view for a given set of system parameters we obtain a measure of the disturbance rejection capacity of the system or observer optimization routines need to be employed to select control or observer gains which maximize the disturbance rejection capacity the general case of time varying linear systems is considered and time domain techniques are employed also the problem of achieving maximum performance as well as required robustness in the presence of parameter uncertainties is considered an expression is derived for the variation of performance with parameter changes the methodology has connections to the h methods in the case of time invariant systems an application to an aircraft wing leveler system is given to illustrate the methodology

the h infty calculus and sums of closed operators we develop a very general operator valued functional calculus for operators with an h infty calculus we then apply this to the joint functional calculus of two sectorial operators when one has an h infty calculus using this we prove theorem of dore venni type on sums of sectorial operators and apply our results to the problem of l p maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of banach spaces are essential here in the final section we exploit the special banach space structure of l 1 spaces and c k spaces to obtain some more detailed results in this setting

the h calculus and sums of closed operators we develop a very general operator valued functional calcu lus for operators with an h 1 calculus we then apply this to the joint functional calculus of two commuting sectorial operators when one has an h 1 calculus using this we prove theorem of dore venni type on sums of commuting sectorial operators and apply our results to the problem of lp maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of ba nach spaces are essential here in the final section we exploit the special banach space structure of l1 spaces and c k spaces to obtain some more detailed results in this setting

strong convergence to global solutions for multidimensional flows of compressible viscous fluids with polytropic equations of state and discontinuous initial data we extend to general polytropic pressures p k 1 the existence theory of 8 for isothermal 1 flows of navier stokes fluids in two and three space dimensions with fairly general initial data specifically we require that the initial density be close to a constant in l2 and l and that the initial velocity be small in l2 and bounded in l2n in two dimensions the l2 norms must be weighted slightly solutions are obtained as limits of approximate solutions corresponding to mollified initial data the key point is that the approximate densities are shown to converge strongly so that nonlinear pressures can be accommodated even in the absence of any uniform regularity information for the approximate densities

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

on spherically symmetric solutions of the compressible isentropic navier stokes equations we prove the global existence of weak solutions to the cauchy problem for the compressible isentropic navier stokes equations in n n 2 3 when the cauchy data are spherically symmetric the proof is based on the exploitation of the one dimensional feature of symmetric solutions and use of a new multidimensional property induced by the viscous flux the present paper extends lions existence theorem 15 to the case 1 n for spherically symmetric initial data where is the specific heat ratio in the pressure n 3 2 for n 2 and n 9 5 for n 3 dedicated to professor rolf leis on the occasion of his 70th birthday

a new method of feature fusion and its application in image recognition a new method of feature extraction based on feature fusion is proposed in this paper according to the idea of canonical correlation analysis cca at first the theory framework of cca used in pattern recognition and its reasonable description are discussed the process can be explained as follows extract two groups of feature vectors with the same pattern establish the correlation criterion function between the two groups of feature vectors and extract their canonical correlation features to form effective discriminant vector for recognition then the problem of canonical projection vectors is solved when two total scatter matrixes are singular such that it fits for the case of high dimensional space and small sample size in this sense the applicable range of cca is extended at last the inherent essence of this method used in recognition is analyzed further in theory experimental results on concordia university cenparmi database of handwritten arabic numerals and yale face database show that recognition rate is far higher than that of the algorithm adopting single feature or the existing fusion algorithm

a compressible mixture model with phase transition abstract we introduce a new thermodynamically consistent diffuse interface model of allen cahn navier stokes type for multi component flows with phase transitions and chemical reactions for the introduced diffuse interface model we investigate physically admissible sharp interface limits by matched asymptotic techniques we consider two scaling regimes i e a non dissipative and a dissipative regime where we recover in the sharp interface limit a generalized allen cahn euler system for mixtures with chemical reactions in the bulk phases equipped with admissible interfacial conditions the interfacial conditions satisfy for instance a young laplace and a stefan type law

a note on the orthonormal discriminant vector method for feature extraction abstract we propose a new feature extraction method based on the modified plus e take away f algorithm and discuss an aspect of the optimization method used in sequential feature extraction by comparing the proposed method with the orthonormal discriminant vector odv method which belongs to a class of sequential feature extraction it is shown from experimental results that the proposed method is superior to the odv method in terms of the error probability

on the maximal lp lq regularity for a compressible fluid model of korteweg type on general domains abstract the aim of this paper is to show the maximal l p l q regularity for a compressible fluid model of korteweg type on general domains of the n dimensional euclidean space for n 2 e g bounded domains exterior domains half spaces layers tubes and their perturbed domains our approach is based on the theory of the r boundedness for a generalized resolvent problem associated with the korteweg type model

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

uncorrelated multilinear discriminant analysis with regularization and aggregation for tensor object recognition this paper proposes an uncorrelated multilinear discriminant analysis umlda framework for the recognition of multidimensional objects known as tensor objects uncorrelated features are desirable in recognition tasks since they contain minimum redundancy and ensure independence of features the umlda aims to extract uncorrelated discriminative features directly from tensorial data through solving a tensor to vector projection the solution consists of sequential iterative processes based on the alternating projection method and an adaptive regularization procedure is incorporated to enhance the performance in the small sample size sss scenario a simple nearest neighbor classifier is employed for classification furthermore exploiting the complementary information from differently initialized and regularized umlda recognizers an aggregation scheme is adopted to combine them at the matching score level resulting in enhanced generalization performance while alleviating the regularization parameter selection problem the umlda based recognition algorithm is then empirically shown on face and gait recognition tasks to outperform four multilinear subspace solutions mpca dater gtda tr1da and four linear subspace solutions bayesian lda ulda r jd lda

existence of weak solutions to steady navier stokes allen cahn system abstract the boundary value problem for the three dimensional steady viscous compressible navier stokes allen cahn nsac system is considered we establish the existence of a weak solution for the adiabatic index 2 with the phase function belonging to 1 1 moreover we give further analysis on the weak solution more specifically we prove that the steady nsac system degenerates into navier stokes system if the phase function is positive negative on

a new and fast implementation for null space based linear discriminant analysis in this paper we present a new implementation for the null space based linear discriminant analysis the main features of our implementation include i the optimal transformation matrix is obtained easily by only orthogonal transformations without computing any eigendecomposition and singular value decomposition svd consequently our new implementation is eigendecomposition free and svd free ii its main computational complexity is from a economic qr factorization of the data matrix and a economic qr factorization of a nxn matrix with column pivoting here n is the sample size thus our new implementation is a fast one the effectiveness of our new implementation is demonstrated by some real world data sets

uncorrelated linear discriminant analysis based on weighted pairwise fisher criterion in this paper we propose a novel uncorrelated weighted linear discriminant analysis uwlda method for feature extraction and recognition the uwlda first introduces a weighting function to restrain the dominant role of the classes with larger distance and then searches the optimal discriminant vectors under the conjugative orthogonal constrains in the null space of the within class scatter matrix and its conjugative orthogonal complement space respectively as a result the proposed technique not only derive the optimal and lossless discriminative information but also guarantee that all extracted features are statistically uncorrelated experiments on feret face database and ar face database are performed to test and evaluate the proposed algorithm the results demonstrate the effectiveness of uwlda

an optimal transformation for discriminant and principal component analysis a general method is proposed to describe multivariate data sets using discriminant analysis and principal component analysis first the problem of finding k discriminant vectors in an l class data set is solved and compared to the solution proposed in the literature for two class problems and the classical solution for l class data sets it is shown that the method proposed is better than the classical method for l classes and is a generalization of the optimal set of discriminant vectors proposed for two class problems then the method is combined with a generalized principal component analysis to permit the user to define the properties of each successive computed vector all the methods were tested using measurements made on various kinds of flowers iris data

vanishing viscosity limit for a coupled navier stokes allen cahn system abstract in this paper we study the vanishing viscosity limit for a coupled navier stokes allen cahn system in a bounded domain we first show the local existence of smooth solutions of the euler allen cahn equations by modified galerkin method then using the boundary layer function to deal with the mismatch of the boundary conditions between navier stokes and euler equations and assuming that the energy dissipation for navier stokes equation in the boundary layer goes to zero as the viscosity tends to zero we prove that the solutions of the navier stokes allen cahn system converge to that of the euler allen cahn system in a proper small time interval in addition for strong solutions of the navier stokes allen cahn system in 2d the convergence rate is c 1 2

on extensions to fisher s linear discriminant function this correspondence describes extensions to fisher s linear discriminant function which allow both differences in class means and covariances to be systematically included in a process for feature reduction it is shown how the fukunaga koontz transform can be combined with fisher s method to allow a reduction of feature space from many dimensions to two performance is seen to be superior in general to the foley sammon method the technique is developed to show how a new radius vector or pair of radius vectors can be combined with fisher s vector to produce a classifier with even more power of discrimination illustrations of the technique show that good discrimination can be obtained even if there is considerable overlap of classes in any one projection

face recognition based on the uncorrelated discriminant transformation abstract the extraction of discriminant features is the most fundamental and important problem in face recognition this paper presents a method to extract optimal discriminant features for face images by using the uncorrelated discriminant transformation and kl expansion experiments on the orl database and the nust603 database have been performed experimental results show that the uncorrelated discriminant transformation is superior to the foley sammon discriminant transformation and the new method to extract uncorrelated discriminant features for face images is very effective an error rate of 2 5 is obtained with the experiments on the orl database an average error rate of 1 2 is obtained with the experiments on the nust603 database experiments show that by extracting uncorrelated discriminant features face recognition could be performed with higher accuracy on lower than 16 16 resolution mosaic images it is suggested that for the uncorrelated discriminant transformation the optimal face image resolution can be regarded as the resolution m n which makes the dimensionality n mn of the original image vector space be larger and closer to the number of known face classes

quasi incompressible cahn hilliard fluids and topological transitions one of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect it is well known that classical methods involving sharp interfaces fail to describe this type of phenomena following some previous work in this area we suggest a physically motivated regularization of the euler equations which allows topological transitions to occur smoothly in this model the sharp interface is replaced by a narrow transition layer across which the fluids may mix the model describes a flow of a binary mixture and the internal structure of the interface is determined by both diffusion and motion an advantage of our regularization is that it automatically yields a continuous description of surface tension which can play an important role in topological transitions an additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the euler or navier stokes and the cahn hilliard equations the model takes into account weak non locality dispersion associated with an internal length scale and localized dissipation due to mixing the non locality introduces a dimensional surface energy dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes in particular we study a non trivial limit when both components are incompressible the pressure is kinematic but the velocity field is non solenoidal quasi incompressibility to demonstrate the effects of quasi incompressibility we analyse the linear stage of spinodal decomposition in one dimension we show that when the densities of the fluids are not perfectly matched the evolution of the concentration field causes fluid motion even if the fluids are inviscid in the limit of infinitely thin and well separated interfacial layers an appropriately scaled quasi incompressible euler cahn hilliard system converges to the classical sharp interface model in order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity

what s wrong with fisher criterion in this paper a seemingly contradictory experimental result concerning fisher criterion is first exhibited then we analyze this result from the statistical correlation point of view and give a reasonable explanation more importantly we emphasize that fisher criterion is not an absolute criterion and it should be associated with the statistical correlation together to assess the discrimination of a set of discriminant vectors

synthesis of suboptimal h controllers over a finite horizon in this paper a finite horizon h optimal control problem is posed and solved it is shown by way of examples that the finite horizon performance is useful for the fast computation of the infimal h norm in the infinite interval case also a differential equation is derived for the measure of performance a general suboptimal control problem is then posed and an expression for a suboptimal controller is derived solving the saddle point conditions an expression for a feedback controller can be derived by solving a dynamic riccati equation in the time invariant case the finite horizon controller converges to a static controller as the final time becomes large examples are given to illustrate the usefulness of the theory

a survey of multilinear subspace learning for tensor data increasingly large amount of multidimensional data are being generated on a daily basis in many applications this leads to a strong demand for learning algorithms to extract useful information from these massive data this paper surveys the field of multilinear subspace learning msl for dimensionality reduction of multidimensional data directly from their tensorial representations it discusses the central issues of msl including establishing the foundations of the field via multilinear projections formulating a unifying msl framework for systematic treatment of the problem examining the algorithmic aspects of typical msl solutions and categorizing both unsupervised and supervised msl algorithms into taxonomies lastly the paper summarizes a wide range of msl applications and concludes with perspectives on future research directions

regularized discriminant entropy analysis in this paper we propose the regularized discriminant entropy rde which considers both class information and scatter information on original data based on the results of maximizing the rde we develop a supervised feature extraction algorithm called regularized discriminant entropy analysis rdea rdea is quite simple and requires no approximation in theoretical derivation the experiments with several publicly available data sets show the feasibility and effectiveness of the proposed algorithm with encouraging results we propose the regularized discriminant entropy rde the rde is based on the within class entropy and robust estimation we design a supervised algorithm regularized discriminant entropy analysis rdea rdea can be regarded as a framework for supervised feature extraction

on the fokker planck boltzmann equation we consider the boltzmann equation perturbed by fokker planck type operator to overcome the lack of strong a priori estimates and to define a meaningful collision operator we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the cauchy problem with large data the proof of stability and existence combines renormalization with an analysis of a defect measure

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

an optimal orthonormal system for discriminant analysis abstract this paper proposes a new discriminant analysis with orthonormal coordinate axes of the feature space in general the number of coordinate axes of the feature space in the traditional discriminant analysis depends on the number of pattern classes therefore the discriminatory capability of the feature space is limited considerably the new discriminant analysis solves this problem completely in addition it is more powerful than the traditional one in so far as the discriminatory power and the mean error probability for coordinate axes are concerned this is also shown by a numerical example

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

global existence of weak solution to compressible navier stokes allen cahn system in three dimensions abstract in this paper we construct a global weak solution to the compressible navier stokes allen cahn system with possibly large initial data the result holds in three dimensions subject to the conditions that the initial energy is finite and that the adiabatic constant 2

a theorem on the uncorrelated optimal discriminant vectors this paper proposes a theorem on the uncorrelated optimal discriminant vectors uodvs it is proved that the classical optimal discriminant vectors are equivalent to uodv which can be used to extract l 1 uncorrelated discriminant features for l class problems without losing any discriminant information in the meaning of fisher discriminant criterion function experiments on concordia university cenparmi handwritten numeral database indicate that uodvs are much more powerful than the foley sammon optimal discriminant vectors it is believed that when the number of training samples is large the conjugate orthogonal set of discriminant vectors can be much more powerful than the orthogonal set of discriminant vectors

efficient linear discriminant analysis with locality preserving for face recognition linear discriminant analysis lda is one of the most popular techniques for extracting features in face recognition lda captures the global geometric structure however local geometric structure has recently been shown to be effective for face recognition in this paper we propose a novel feature extraction algorithm which integrates both global and local geometric structures we first cast lda as a least square problem based on the spectral regression then regularization technique is used to model the global and local geometric structures furthermore we impose penalty on parameters to tackle the singularity problem and design an efficient model selection algorithm to choose the optimal tuning parameter which balances the tradeoff between the global and local structures experimental results on four well known face data sets show that the proposed integration framework is competitive with traditional face recognition algorithms which use either global or local structure only

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

strong solutions of the navier stokes equations for a compressible fluid of allen cahn type in this work we study the navier stokes allen cahn system a combination of the compressible navier stokes equations with an allen cahn phase field description this model describes two phase patterns in a flowing liquid including phase transformations our purpose is to show the existence and uniqueness of local strong solutions for arbitrary initial data part of the proof is based on methods used in a companion paper which investigated the compressible navier stokes equations

characterization of a family of algorithms for generalized discriminant analysis on undersampled problems a generalized discriminant analysis based on a new optimization criterion is presented the criterion extends the optimization criteria of the classical linear discriminant analysis lda when the scatter matrices are singular an efficient algorithm for the new optimization problem is presented the solutions to the proposed criterion form a family of algorithms for generalized lda which can be characterized in a closed form we study two specific algorithms namely uncorrelated lda ulda and orthogonal lda olda ulda was previously proposed for feature extraction and dimension reduction whereas olda is a novel algorithm proposed in this paper the features in the reduced space of ulda are uncorrelated while the discriminant vectors of olda are orthogonal to each other we have conducted a comparative study on a variety of real world data sets to evaluate ulda and olda in terms of classification accuracy

improvements on the uncorrelated optimal discriminant vectors the algorithm and the theorem of uncorrelated optimal discriminant vectors uodv were proposed by jin in this paper we present new improvements to jin s method which include an improved approach for the original algorithm and a generalized theorem for uodv experimental results prove that our approach is superior to the original in the recognition rate

regularized orthogonal linear discriminant analysis in this paper the regularized orthogonal linear discriminant analysis rolda is studied the major issue of the regularized linear discriminant analysis is to choose an appropriate regularization parameter in existing regularized linear discriminant analysis methods they all select the best regularization parameter from a given parameter candidate set by using cross validation for classification an obvious limitation of such regularized linear discriminant analysis methods is that it is not clear how to choose an appropriate candidate set therefore up to now there is no concrete mathematical theory available in selecting an appropriate regularization parameter in practical applications of the regularized linear discriminant analysis the present work is to fill this gap here we derive the mathematical relationship between orthogonal linear discriminant analysis and the regularized orthogonal linear discriminant analysis first and then by means of this relationship we find a mathematical criterion for selecting the regularization parameter in rolda and consequently we develop a new regularized orthogonal linear discriminant analysis method in which no candidate set of regularization parameter is needed the effectiveness of our proposed regularized orthogonal linear discriminant analysis is illustrated by some real world data sets

asymptotic stability of superposition of stationary solutions and rarefaction waves for 1d navier stokes allen cahn system abstract in this paper we investigate the large time behavior of the solutions to the inflow problem for the one dimensional navier stokes allen cahn system in the half space first we assume that the space asymptotic states u and the boundary data b u b b satisfy some conditions so that the time asymptotic state of solutions for the inflow problem is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave then we show the existence of the stationary solution by the center manifold theorem finally we prove that the nonlinear wave is asymptotically stable when the initial data is a small perturbation of the nonlinear wave the proof is mainly based on the energy method by taking into account the effect of the concentration and the complexity of nonlinear wave

rapid and brief communication uncorrelated heteroscedastic lda based on the weighted pairwise chernoff criterion we propose an uncorrelated heteroscedastic lda uhlda technique which extends the uncorrelated lda ulda technique by integrating the weighted pairwise chernoff criterion the uhlda can extract discriminatory information present in both the differences between per class means and the differences between per class covariance matrices meanwhile the extracted feature components are statistically uncorrelated the maximum number of which exceeds the limitation of the ulda experimental results demonstrate the promising performance of our proposed technique compared with the ulda

phase field and korteweg type models for the time dependent flow of compressible two phase fluids various versions of the navier stokes allen cahn nsac the navier stokes cahn hilliard nsch and the navier stokes korteweg nsk equations have been used in the literature to model the dynamics of two phase fluids one main purpose of this paper consists in re deriving nsac nsch and nsk from first principles in the spirit of rational mechanics for fluids of very general constitutive laws for nsac this deduction confirms and extends a proposal of blesgen regarding nsch it continues work of lowengrub and truskinovsky and provides the apparently first justified formulation in the non isothermal case for nsk it yields a most natural correction to the formulation by dunn and serrin the paper uniformly recovers as examples various classes of fluids distinguished according to whether none one or both of the phases are compressible and according to the nature of their co existence the latter is captured not only by the mixing energy but also by a mixing rule a constitutive law that characterizes the type of the mixing a second main purpose of the paper is to communicate the apparently new observation that in the case of two immiscible incompressible phases of different temperature independent specific volumes nsac reduces literally to nsk this finding may be considered as an independent justification of nsk an analogous fact is shown for nsch which under the same assumption reduces to a new non local version of nsk

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

dynamical stability of non constant equilibria for the compressible navier stokes equations in eulerian coordinates in this paper we establish global existence and uniqueness of strong solutions to the non isothermal compressible navier stokes equations in bounded domains the initial data have to be near equilibria that may be non constant due to considering large external forces we are able to show exponential stability of equilibria in the phase space and above all to study the problem in eulerian coordinates the latter seems to be a novelty since in works by other authors global strong lp solutions have been investigated only in lagrangian coordinates eulerian coordinates are even declared as impossible to deal with the proof is based on a careful derivation and study of the associated linear problem

orthogonal moment features for use with parametric and non parametric classifiers this research examines a variety of approaches for using two dimensional orthogonal polynomials for the recognition of handwritten arabic numerals it also makes use of parametric and non parametric statistical and neural network classifiers polynomials including legendre zernike and pseudo zernike are used to generate moment based features which are invariant to location size and optionally rotation an efficient method for computing the moments via geometric moments is presented a side effect of this method also yields scale invariance a new approach to location invariance using a minimum bounding circle is presented and a detailed analysis of the rotational properties of the moments is given data partitioning tests are performed to evaluate the various feature types and classifiers for rotational invariant character recognition the highest percentage of correctly classified characters was 91 7 and for non rotational invariant recognition it was 97 6 this compares with a previous effort using the same data and test conditions of 94 8 the techniques developed here should also be applicable to other areas of shape recognition

global weak solutions of vlasov maxwell systems we study here the vlasov maxwell system in its classical and relativistic form we prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data the main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work

a generalized optimal set of discriminant vectors abstract a generalized optimal set of discriminant vectors for linear feature extraction is presented first the criteria of selecting the generalized optimal discriminant vectors are introduced and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples the experimental results show that the present method is superior to the foley sammon method foley and sammon ieee trans comput 24 281 289 1975 the positive pseudoinverse method tian et al opt engng 25 7 834 839 1986 the perturbation method hong and yang pattern recognition 24 317 324 1991 and the matrix rank decomposition method cheng et al pattern recognition 25 101 111 1992 in terms of correct classification rate

a uniqueness criterion for unbounded solutions to the vlasov poisson system we prove uniqueness for the vlasov poisson system in two and three dimensions under the condition that the l p norms of the macroscopic density grow at most linearly with respect to p this allows for solutions with logarithmic singularities we provide explicit examples of initial data that fulfill the uniqueness condition and that exhibit a logarithmic blow up in the gravitational two dimensional case such states are intimately related to radially symmetric steady solutions of the system our method relies on the lagrangian formulation for the solutions exploiting the second order structure of the corresponding ode