global well posedness for a boussinesq navier stokes system with critical dissipation abstract in this paper we study a fractional diffusion boussinesq model which couples a navier stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature we establish global well posedness results with rough initial data

complementarity of suq 3 and uq 2 and q boson realization of the suq 3 irreducible representations the complementarity relationship also termed duality that arises between the irreps of the su 3 and u 2 lie algebras when their direct sum su 3 u 2 is embedded into a larger u 6 algebra and single row irreps of the latter are considered is extended to the corresponding q algebras suq 3 and uq 2 it is demonstrated by explicitly constructing the unique q boson state that is simultaneously maximal in suq 3 and uq 2 for a given u q 2 weight in addition the relations between the suq 3 and uq 2 casimir operators resulting from their complementarity are explicitly found together with the q bargmann representation of q boson operators the complementarity relationship is then used to construct a gel fand tseitlin basis for arbitrary suq 3 irreps in terms of q boson operators

positive representations of general commutation relations allowing wick ordering we consider the problem of representing in hilbert space commutation relations of the form graphics where the tklij are essentially arbitrary scalar coefficients examples comprise the q canonical commutation relations introduced by greenberg bozejko and speicher and the twisted canonical anti commutation relations studied by pusz and woronowicz as well as the quantum group s u 2 using these relations any polynomial in the generators ai and their adjoints can uniquely be written in wick ordered form in which all starred generators are to the left of all unstarred ones in this general framework we define the fock representation as well as coherent representations we develop criteria for the natural scalar product in the associated representation spaces to be positive definite and for the relations to have representations by bounded operators in a hilbert space we characterize the relations between the generators ai not involving a i which are compatible with the basic relations the relations may also be interpreted as defining a non commutative differential calculus for generic coefficients tklij however all differential forms of degree 2 and higher vanish we exhibit conditions for this not to be the case and relate them to the ideal structure of the wick algebra and conditions of positivity we show that the differential calculus is compatible with the involution iff the coefficients t define a representation of the braid group this condition is also shown to imply improved bounds for the positivity of the fock representation finally we study the kms states of the group of gauge transformations defined by aj exp it aj

a new bernstein s inequality and the 2d dissipative quasi geostrophic equation we show a new bernstein s inequality which generalizes the results of cannone planchon danchin and lemarie rieusset as an application of this inequality we prove the global well posedness of the 2d quasi geostrophic equation with the critical and super critical dissipation for the small initial data in the critical besov space and local well posedness for the large initial data

global well posedness issues for the inviscid boussinesq system with yudovich s type data the present paper is dedicated to the study of the global existence for the inviscid two dimensional boussinesq system we focus on finite energy data with bounded vorticity and we find out that under quite a natural additional assumption on the initial temperature there exists a global unique solution no smallness conditions are imposed on the data the global existence issues for infinite energy initial velocity and for the benard system are also discussed

retinal vessel segmentation using multiwavelet kernels and multiscale hierarchical decomposition we propose a comprehensive method for segmenting the retinal vasculature in fundus camera images our method does not require preprocessing and training and can therefore be used directly on different images sets we enhance the vessels using matched filtering with multiwavelet kernels mfmk separating vessels from clutter and bright localized features noise removal and vessel localization are achieved by a multiscale hierarchical decomposition of the normalized enhanced image we show a necessary condition to achieve the optimal decomposition and derive the associated value of the scale parameter controlling the amount of details captured finally we obtain a binary map of the vasculature by locally adaptive thresholding generating a threshold surface based on the vessel edge information extracted by the previous processes we report experimental results on two public retinal data sets drive and stare demonstrating an excellent performance in comparison with retinal vessel segmentation methods reported recently

curvilinear structure analysis by ranking the orientation responses of path operators the analysis of thin curvilinear objects in 3d images is a complex and challenging task in this article we introduce a new non linear operator called rorpo ranking the orientation responses of path operators inspired by the multidirectional paradigm currently used in linear filtering for thin structure analysis rorpo is built upon the notion of path operator from mathematical morphology this operator unlike most operators commonly used for 3d curvilinear structure analysis is discrete non linear and non local from this new operator two main curvilinear structure characteristics can be estimated an intensity feature that can be assimilated to a quantitative measure of curvilinearity and a directional feature providing a quantitative measure of the structure s orientation we provide a full description of the structural and algorithmic details for computing these two features from rorpo and we discuss computational issues we experimentally assess rorpo by comparison with three of the most popular curvilinear structure analysis filters namely frangi vesselness optimally oriented flux and hybrid diffusion with continuous switch in particular we show that our method provides up to 8 percent more true positive and 50 percent less false positives than the next best method on synthetic and real 3d images

remarks on classical invariant theory a uniform formulation applying to all classical groups simultaneously of the first fundamental theory of classical invariant theory is given in terms of the weyl algebra the formulation also allows skew symmetric as well as symmetric variables examples illustrate the scope of this formulation

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

global regularity results for the 2d boussinesq equations and micropolar equations with partial dissipation abstract this paper establishes the global regularity of the two dimensional 2d boussinesq equations and micropolar equations with partial dissipation our first result is the global regularity of the 2d boussinesq equations with fractional vertical dissipation in the horizontal velocity horizontal dissipation in the vertical velocity and zero thermal diffusion which is shown by taking advantage of the nice structure of the 2d boussinesq equations and several refined commutator estimates the second goal of this paper is to consider a system of the 2d incompressible micropolar equations with vertical dissipation in the horizontal velocity equation horizontal dissipation in the vertical velocity equation and the fractional dissipation in the micro rotation velocity in order to overcome the difficulty caused by the lack of full laplacian diffusion in the velocity equations we fully exploit the nice structure of the corresponding equations to show that this equations with arbitrarily small 0 always possesses a unique global classical solution

vessel tree reconstruction in thoracic ct scans with application to nodule detection vessel tree reconstruction in volumetric data is a necessary prerequisite in various medical imaging applications specifically when considering the application of automated lung nodule detection in thoracic computed tomography ct scans vessel trees can be used to resolve local ambiguities based on global considerations and so improve the performance of nodule detection algorithms in this study a novel approach to vessel tree reconstruction and its application to nodule detection in thoracic ct scans was developed by using correlation based enhancement filters and a fuzzy shape representation of the data the proposed correlation based enhancement filters depend on first order partial derivatives and so are less sensitive to noise compared with hessian based filters additionally multiple sets of eigenvalues are used so that a distinction between nodules and vessel junctions becomes possible the proposed fuzzy shape representation is based on regulated morphological operations that are less sensitive to noise consequently the vessel tree reconstruction algorithm can accommodate vessel bifurcation and discontinuities a quantitative performance evaluation of the enhancement filters and of the vessel tree reconstruction algorithm was performed moreover the proposed vessel tree reconstruction algorithm reduced the number of false positives generated by an existing nodule detection algorithm by 38

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

wavelet based approach to character skeleton character skeleton plays a significant role in character recognition the strokes of a character may consist of two regions i e singular and regular regions the intersections and junctions of the strokes belong to singular region while the straight and smooth parts of the strokes are categorized to regular region therefore a skeletonization method requires two different processes to treat the skeletons in theses two different regions all traditional skeletonization algorithms are based on the symmetry analysis technique the major problems of these methods are as follows 1 the computation of the primary skeleton in the regular region is indirect so that its implementation is sophisticated and costly 2 the extracted skeleton cannot be exactly located on the central line of the stroke 3 the captured skeleton in the singular region may be distorted by artifacts and branches to overcome these problems a novel scheme of extracting the skeleton of character based on wavelet transform is presented in this paper this scheme consists of two main steps namely a extraction of primary skeleton in the regular region and b amendment processing of the primary skeletons and connection of them in the singular region a direct technique is used in the first step where a new wavelet based symmetry analysis is developed for finding the central line of the stroke directly a novel method called smooth interpolation is designed in the second step where a smooth operation is applied to the primary skeleton and thereafter the interpolation compensation technique is proposed to link the primary skeleton so that the skeleton in the singular region can be produced experiments are conducted and positive results are achieved which show that the proposed skeletonization scheme is applicable to not only binary image but also gray level image and the skeleton is robust against noise and affine transform

global regularity of 2d leray alpha regularized incompressible magneto micropolar equations abstract in this paper we consider a cauchy problem of the 2d leray regularized incompressible magneto micropolar equations the global smooth solution of the cauchy problem for the equations with zero angular viscosity and zero magnetic diffusion or with only angular viscosity and magnetic diffusion are established

global regularity results for the 2d boussinesq equations with vertical dissipation abstract the two dimensional 2d incompressible boussinesq equations model geophysical fluids and play an important role in the study of the raleigh bernard convection mathematically this 2d system retains some key features of the 3d navier stokes and euler equations such as the vortex stretching mechanism the issue of whether the 2d boussinesq equations always possess global in time classical solutions can be difficult when there is only partial dissipation or no dissipation at all this paper obtains the global regularity for two partial dissipation cases and proves several global a priori bounds for two other prominent partial dissipation cases these results take us one step closer to a complete resolution of the global regularity issue for all the partial dissipation cases involving the 2d boussinesq equations

global existence of three dimensional incompressible magneto micropolar system with mixed partial dissipation magnetic diffusion and angular viscosity abstract the magneto micropolar fluid flows describe the motion of electrically conducting micropolar fluids in the presence of a magnetic field the issue of whether the strong solution of magneto micropolar equations in three dimensional can exist globally in time with large initial data is still unknown in this paper we deal with the cauchy problem of the three dimensional magneto micropolar system with mixed partial dissipation magnetic diffusion and angular viscosity more precisely the global existence of smooth solutions to the three dimensional incompressible magneto micropolar fluid equations with mixed partial dissipation magnetic diffusion and angular viscosity are obtained by energy method under the assumption that h 1 norm of the initial data u 0 b 0 w 0 sufficiently small namely u 0 b 0 0 h 1 r 3 2 e 2 where e is a sufficiently small positive number this work follows the techniques in the paper of cao and wu 2011

global regularity for 2d magneto micropolar equations with only micro rotational velocity dissipation and magnetic diffusion abstract this paper studies the global regularity of classical solutions to 2d magneto micropolar fluid equations with only micro rotational velocity dissipation and magnetic diffusion here the micro rotational velocity dissipation and magnetic diffusion are given by and b making use of several combined quantities maximal regularity of heat operator and littlewood paley decomposition theory we establish a regularity criterion in terms of magnetic field for the case 1 and the global regularity for 1 the regularity criterion given here is also new even for the 2d magnetohydrodynamic equations in addition to prove these two main results as preparation we establish a new global a priori estimate for magnetic field namely b l 0 t l p r 2 with p 2 which also holds for the 2d magnetohydrodynamic equations as a particular case

global well posedness of the 2d boussinesq equations with vertical dissipation we prove the global well posedness of the two dimensional boussinesq equations with only vertical dissipation the initial data u 0 theta 0 are required to be only in the space x f in l 2 mathbb r 2 partial x f in l 2 mathbb r 2 and thus our result generalizes that of cao and wu arch rational mech anal 208 985 1004 2013 where the initial data are assumed to be in h 2 mathbb r 2 the assumption on the initial data is at the minimal level that is required to guarantee the uniqueness of the solutions a logarithmic type limiting sobolev embedding inequality for the l infty mathbb r 2 norm in terms of anisotropic sobolev norms and a logarithmic type gronwall inequality are established to obtain the global in time a priori estimates which guarantee the local solution to be a global one

the dual bootstrap iterative closest point algorithm with application to retinal image registration motivated by the problem of retinal image registration this paper introduces and analyzes a new registration algorithm called dual bootstrap iterative closest point dual bootstrap icp the approach is to start from one or more initial low order estimates that are only accurate in small image regions called bootstrap regions in each bootstrap region the algorithm iteratively 1 refines the transformation estimate using constraints only from within the bootstrap region 2 expands the bootstrap region and 3 tests to see if a higher order transformation model can be used stopping when the region expands to cover the overlap between images steps 1 and 3 the bootstrap steps are governed by the covariance matrix of the estimated transformation estimation refinement step 2 uses a novel robust version of the icp algorithm in registering retinal image pairs dual bootstrap icp is initialized by automatically matching individual vascular landmarks and it aligns images based on detected blood vessel centerlines the resulting quadratic transformations are accurate to less than a pixel on tests involving approximately 6000 image pairs it successfully registered 99 5 of the pairs containing at least one common landmark and 100 of the pairs containing at least one common landmark and at least 35 image overlap

limiting case of the sobolev inequality in bmo with application to the euler equations we shall prove a logarithmic sobolev inequality by means of the bmo norm in the critical exponents as an application we shall establish a blow up criterion of solutions to the euler equations

complex derivative filters steerable filters are a valuable tool for various low level vision tasks in this paper we argue for the use of complex analysis in the context of 2 d steerable filters in particular we recommend the use of complex partial derivatives as a computational basis complex derivatives have a major advantage in comparison to real derivatives they show a canonical rotation behavior namely a rotation affects the derivative just by a multiplication with a complex unit number so the complex derivatives can be steered in a more elegant way and above that they are less expensive to compute we present several analytical formulas for common and new filter kernels in terms of complex derivatives further we relate the complex derivatives of a gaussian with the gauss laguerre transform and show that the gauss laguerre functions provide an optimal signal representation for local and smooth images we discuss various finite difference schemes for the realization of the derivatives and use them in practice in a first experiment we use a newly introduced filter kernel for anisotropic blurring the complex formalism offers an elegant way to locally adapt the shape and orientation of the kernel second we use the proposed filters as matched filters to detect vessels in retinal images

an adaptive morphological filter for image processing novel types of opening operator nop and closing operator ncp are proposed an adaptive morphological filter is then constructed on the basis of the nop and ncp the filter can remove any details consisting of fewer pixels than a given number n while preserving the other details efficient algorithms are also developed for the implementation of the nop and ncp

global regularity for the two dimensional anisotropic boussinesq equations with vertical dissipation this paper establishes the global in time existence of classical solutions to the two dimensional anisotropic boussinesq equations with vertical dissipation when only vertical dissipation is present there is no direct control on the horizontal derivatives and the global regularity problem is very challenging to solve this problem we bound the derivatives in terms of the l infty norm of the vertical velocity v and prove that v l r with 2 leqq r infty does not grow faster than sqrt r log r at any time as r increases a delicate interpolation inequality connecting v l infty and v l r then yields the desired global regularity

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

classification of temporal sequences via prediction using the simple recurrent neural network abstract an approach to classify temporal sequences using the simple recurrent neural network srnn is developed in this paper a classification problem is formulated as a component prediction problem and two training methods are described to train a single srnn to predict the components of temporal sequences belonging to multiple classes issues related to the selection of the dimension of the context vector and the influence of the context vector on classification are identified and investigated the use of a different initial context vector for each class is proposed as a means to improve classification and a classification rule which incorporates the different initial context vectors is formulated a systematic method in which the srnn is trained with noisy exemplars is developed to enhance the classification performance of the network a 4 class localized object classification problem is selected to demonstrate that a a single srnn can be trained to classify real multi class sequences via component prediction b the classification accuracy can be improved by using a distinguishing initial context vector for each class and c the classification accuracy of the srnn can be improved significantly by using the distinguishing initial context vector in conjunction with the systematic re training method it is concluded that through the approach developed in this paper the srnn can robustly classify temporal sequences which may have an unequal number of components

detection of blood vessels in retinal images using two dimensional matched filters blood vessels usually have poor local contrast and the application of existing edge detection algorithms yield results which are not satisfactory an operator for feature extraction based on the optical and spatial properties of objects to be recognized is introduced the gray level profile of the cross section of a blood vessel is approximated by a gaussian shaped curve the concept of matched filter detection of signals is used to detect piecewise linear segments of blood vessels in these images twelve different templates that are used to search for vessel segments along all possible directions are constructed various issues related to the implementation of these matched filters are discussed the results are compared to those obtained with other methods

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

global unique solvability of nonhomogeneous asymmetric fluids a lagrangian approach abstract we show global existence and uniqueness of solutions for the 3d nonhomogeneous asymmetric fluids equations through a lagrangian approach in particular uniqueness of the solution is proved under quite soft assumptions about its regularity which brings the knowledge about nonhomogeneous asymmetric fluids to the same level as for the variable density navier stokes equations

surfaces from stereo integrating feature matching disparity estimation and contour detection an approach is described that integrates the processes of feature matching contour detection and surface interpolation to determine the three dimensional distance or depth of objects from a stereo pair of images integration is necessary to ensure that the detected surfaces are smooth surface interpolation takes into account detected occluding and ridge contours in the scene interpolation is performed within regions enclosed by these contours planar and quadratic patches are used as local models of the surface occluded regions in the image are identified and are not used for matching and interpolation a coarse to fine algorithm is presented that generates a multiresolution hierarchy of surface maps one at each level of resolution experimental results are given for a variety of stereo images

matching of partially occluded planar curves abstract an algorithm for curves partial matching up to a similarity transformation is presented the matching is based on the total curvature graph which is the direction of the first derivative of the curve no higher derivatives are required the algorithm uses dynamic programming it is not dependent on reference or feature points the base step consists of a comparison of the total curvatures of neighborhoods the neighborhoods are dynamically chosen according to local characteristics of the curve in the recursive step ratios of lengths of matched curve segments are compared in order to extend the matches the matching is not sensitive to local deviations of the curves the algorithm is fast and simple its worst case time complexity is o mn where m and n are the number of points in the two digital curves experimental results are presented

regularity criterion for a critical fractional diffusion model of two dimensional micropolar flows abstract this paper is devoted to the beale kato majda bkm regularity criterion of the 2d micropolar equations in the critical fractional diffusion situation 1 for 0 and 0 with the use of the littlewood paley theory the global existence of the unique solution u w to the equations is found to be completely determined by the velocity field u the dynamical behaviour of the scalar angular velocity w is controlled by the velocity u more precisely it is shown that the strong solution u w exists globally if 0 t u l 2 d for any t

transcending classical invariant theory let sp2 r sp2 sp be the real symplectic group of rank n let sp denote the two fold cover of sp there is a unitary representation constructed by shale sh and weil wa of sp that is of considerable interest in the theory of automorphic forms we denote this representation by co and call it the oscillator representation the purpose of this paper is to establish about c a fact that should be useful for clarifying the structure of spaces of automorphic forms constructed using co we begin by formulating the result let e be a reductive subgroup of sp and let e denote the inverse image of e in sp denote by r e the set of infinitesimal equivalence classes of continuous irreducible admissible representations of e on locally convex spaces let co be the smooth representation of sp associated to co let co be realized on a hilbert space and let the subspace of smooth vectors on which space co is defined be written denote by r9 e co the set of elements of e which are realized as quotients by co e invariant closed subspaces of t g consider a reductive dual pair g g c sp h2 it is not hard to show that g and g commute with one another hence we may regard co i g g as a representation of gx g it is well known f that r gx g s9 g xr9 g the identification associates to p e r g and p e i g the tensor product p x p we note that p x p is not defined as a topological vector space nevertheless the infinitesimal equivalence class of p op is well defined select p x p e g x g suppose that in fact p p e 9 g g c then clearly p e r g c and p e 9 g c hence g co defines the graph of a correspondence between certain subsets of r9 g cv and j g co in fact the situation is quite precise

howe duality for the quantum groups uqu m n uqu m a dual pair is defined to be a pair of mutually centralizing subgroups of the real symplectic group let g g be a dual pair of reductive groups in which g is also compact and consider the decomposition of the metaplectic representation of the symplectic group into gg irreducibles each such irreducible is a tensor product of an irreducible of g with one of g and it turns out there is a bijective correspondence between them a particular irreducible of g only occurring with a particular one of g and vice versa this so called howe duality is here generalized to the quantum group case uqu m n uqu m for q not a root of unity a metaplectic representation for this dual pair is given in terms of the q oscillator algebra and a uqu m n uqu m covariant heisenberg weyl algebra is also constructed and realized on fock space the heart of the proof lies in showing that uqu m n and uqu m are essentially mutual commutants on fock space the duality follows using the compactness of uqu m the proof is i

global well posedness to the cauchy problem of 2d density dependent micropolar equations with large initial data and vacuum abstract this paper studies the cauchy problem of the 2d nonhomogeneous incompressible micropolar equations it is shown that the problem admits a unique global strong solution note that the initial data can be arbitrary large and the initial density can contain vacuum states

vanishing viscosity for non homogeneous asymmetric fluids in r3 the l2 case abstract we study the vanishing viscosity problem for the local in time solutions to the equations of non homogeneous viscous incompressible asymmetric fluid in r 3 in the l 2 context we prove that the fluid variables converge uniformly as the viscosities go to zero to a solution of a non homogeneous non viscous incompressible asymmetric fluid governed by an euler like system this completes the previous work 5 where results for l p p 3 where obtained

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

global well posedness and large time decay for the 2d micropolar equations abstract this paper studies the global in time regularity and large time behavior of solutions to the 2d micropolar equations with only angular viscosity dissipation micropolar equations model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium when there is no kinematic viscosity in the momentum equation the global regularity problem is not easy due to the lack of suitable bounds on the derivatives the idea here is to fully exploit the structure of the system and control the vorticity via the evolution equation of a combined quantity of the vorticity and the micro rotation angular velocity to understand the large time behavior we overcome two main difficulties the lack of kinematic viscosity and the presence of linear terms classical tools such as the fourier splitting method of schonbek and kato s approach for the decay of small solutions do not apply here we introduce a diagonalization process to eliminate the linear terms and rely on the uniform bounds for the first derivatives of the solutions to generate suitable decay rates

global well posedness for the 2d boussinesq system with anisotropic viscosity and without heat diffusion abstract we establish global existence and uniqueness theorems for the two dimensional non diffusive boussinesq system with anisotropic viscosity acting only in the horizontal direction which arises in ocean dynamics models global well posedness for this system was proven by danchin and paicu however an additional smoothness assumption on the initial density was needed to prove uniqueness they stated that it is not clear whether uniqueness holds without this additional assumption the present work resolves this question and we establish uniqueness without this additional assumption furthermore the proof provided here is more elementary we use only tools available in the standard theory of sobolev spaces and without resorting to para product calculus we use a new approach by defining an auxiliary stream function associated with the density analogous to the stream function associated with the vorticity in 2d incompressible euler equations then we adapt some of the ideas of yudovich for proving uniqueness for 2d euler equations

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

global well posedness for the micropolar fluid system in critical besov spaces abstract we prove the global well posedness for the 3 d micropolar fluid system in the critical besov spaces by making a suitable transformation of the solutions and using the fourier localization method especially combined with a new l p estimate for the green matrix to the linear system of the transformed equation this result allows to construct global solutions for a class of highly oscillating initial data of cannone s type meanwhile we analyze the long time behavior of the solutions and get some decay estimates

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

global weak solutions for variable density asymmetric incompressible fluids abstract we establish the existence of global in time weak solutions for the equations of asymmetric incompressible fluids with variable density when the initial density is not necessarily strictly positive

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

segmentation of vessel like patterns using mathematical morphology and curvature evaluation this paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel like patterns in a noisy environment such patterns are very common in medical images vessel detection is interesting for the computation of parameters related to blood flow its tree like geometry makes it a usable feature for registration between images that can be of a different nature in order to define vessel like patterns segmentation is performed with respect to a precise model we define a vessel as a bright pattern piece wise connected and locally linear mathematical morphology is very well adapted to this description however other patterns fit such a morphological description in order to differentiate vessels from analogous background patterns a cross curvature evaluation is performed they are separated out as they have a specific gaussian like profile whose curvature varies smoothly along the vessel the detection algorithm that derives directly from this modeling is based on four steps 1 noise reduction 2 linear pattern with gaussian like profile improvement 3 cross curvature evaluation 4 linear filtering we present its theoretical background and illustrate it on real images of various natures then evaluate its robustness and its accuracy with respect to noise

global well posedness of the 2d boussinesq equations with fractional laplacian dissipation abstract as a continuation of the previous work 48 in this paper we focus on the cauchy problem of the two dimensional 2d incompressible boussinesq equations with fractional laplacian dissipation we give an elementary proof of the global regularity of the smooth solutions of the 2d boussinesq equations with a new range of fractional powers of the laplacian the argument is based on the nonlinear lower bounds for the fractional laplacian established in 13 consequently this result significantly improves the recent works 13 45 48

different averages of a fuzzy set with an application to vessel segmentation image segmentation is a major problem in image processing particularly in medical image analysis a great number of segmentation procedures produce intermediate gray scale images that can be understood as fuzzy sets additionally some segmentation procedures tend to leave free tuning parameters very influential in the final binary image for the user these different binary images can be easily aggregated into a fuzzy set by making use of fuzzy set theory in any case a single binary image is required so our interest is to associate a crisp set to a given fuzzy set in an intelligent and unsupervised manner the main idea of this paper is to define the averages of a given fuzzy set by using different definitions of the mean of a random compact set in particular the average distance of baddeley molchanov and the mean of vorob ev have been used a theoretical study of some new definitions of fuzzy set averages has been performed in particular these averages have been obtained for l r fuzzy numbers finally we present a medical image application that of retinal vessel detection some recent segmentation procedures have been revisited and modified using these new averages the experimental results are very promising

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

on the regularity criterion for three dimensional micropolar fluid flows in besov spaces abstract this paper studies the regularity criterion of weak solutions for three dimensional 3d micropolar fluid flows when the velocity field satisfies u l 2 1 r 0 t b r r 3 for 1 r 1 then the weak solution u w is regular on 0 t the methods are mainly based on the fourier localization technique and bony s para product decomposition

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

global regularity for the 2d magneto micropolar equations with partial and fractional dissipation abstract this paper studies two cases of global regularity problems on the 2d magneto micropolar equations with partial magnetic diffusion and fractional dissipation for the first case the velocity field is ideal the micro rotational velocity is with laplacian dissipation and the magnetic field has fractional partial diffusion 22 b 1 11 b 2 with 1 in the second case the velocity has a fractional laplacian dissipation u with any 0 the micro rotational velocity is with laplacian dissipation and the magnetic field has partial diffusion 22 b 1 11 b 2 in two cases the global well posedness of classical solutions is proved in this paper

global well posedness for 2d polymeric fluid models and growth estimate motivated by p constantin n masmoudi global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d comm math phys 278 2008 179 191 f lin ping zhang zhifei zhang on the global existence of smooth solution to the 2 d fene dumbbell model comm math phys 277 2008 531 553 we prove the global existence of smooth solutions to a coupled microscopic macroscopic model for polymeric fluid in 2d under the co rotational assumption furthermore we provide an estimate on the time growth of these solutions our method is general and can be applied to the co rotational fene model and to the rod like model without the co rotational assumption c 2008 elsevier b v all rights reserved

global regularity of the 2d micropolar fluid flows with zero angular viscosity abstract in this paper we prove the global existence and uniqueness of smooth solutions to the 2d micropolar fluid flows with zero angular viscosity

non parametric planar shape representation based on adaptive curvature functions this paper presents a non parametric method to extract a very short feature vector from the curvature function of a planar shape curvature is adaptively calculated using a new procedure that removes noise from the contour without missing relevant points then its fourier transform is projected onto a set of vectors which have been chosen to be as representative as possible to obtain the similarity between the input object and each vector of the set these similarity values are the elements of the feature vector the proposed method is very fast and classification has proven that the representation is good

irreducibility of the three and two and a half dimensional hall magnetohydrodynamics system abstract the hall magnetohydrodynamics system has been considered by many to play an important role in astrophysical plasmas star formation and magnetic re connection the hall term mathematically elevates the magnetohydrodynamics system from a semi linear to a quasi linear type and standard results which are well known for the navier stokes equations and the magnetohydrodynamics system such as the local well posedness in the non diffusive case as well as the uniqueness of the weak solution in case the solution depends only on two spatial variables are completely open for the hall magnetohydrodynamics system because the hall magnetohydrodynamics system is not known to be globally well posed even if the solution depends only on two spatial variables a typical method to prove ergodicity for the two dimensional navier stokes equations such as hairer and mattingly 2006 seems to have no chance in this manuscript we take advantage of the structure of the hall term follow the work of flandoli 1997 and prove its irreducibility property in order to elaborate on the effect of the hall term we also prove analogous results for related systems such as the magnetohydrodynamics system benard problem magnetic benard problem micropolar fluid system as well as the magneto micropolar fluid system at the time of writing this manuscript due to a technical difficulty the strong feller property of the hall magnetohydrodynamics system is an open problem

robust automatic target recognition using a localized boundary representation abstract a localized classification approach which includes a localized target boundary representation a set of local features to characterize parts of a target boundary and a feature matching method is developed to classify highly degraded targets each pixel on the target boundary is represented by the perpendicular euclidean distance between the boundary pixel and the chord connecting the end points of a window centered on the boundary pixel the resulting localized representation is quite robust with respect to noise and missing segments in the targets a local feature is the segment of the localized representation between two points selected on the target boundary the two points on the boundary may be specified or randomly selected the reference features of a hypothesized target class are compared with segments of the localized representation of the test target to determine a dissimilarity measure between the hypothesized target class and the test target segments of the test target may also be matched with the reference localized contour sequences of the targets the test target is assigned to a target class using a minimum mismatch rule results from a series of experiments conducted on three targets show that it is possible to classify targets experiencing high levels of noise and high percentages of missing segments in partial targets

retina verification system based on biometric graph matching this paper presents an automatic retina verification framework based on the biometric graph matching bgm algorithm the retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators then retinal templates are defined as formal spatial graphs derived from the retinal vasculature the bgm algorithm a noisy graph matching algorithm robust to translation non linear distortion and small rotations is used to compare retinal templates the bgm algorithm uses graph topology to define three distance measures between a pair of graphs two of which are new a support vector machine svm classifier is used to distinguish between genuine and imposter comparisons using single as well as multiple graph measures the classifier achieves complete separation on a training set of images from the varia database 60 of the data equaling the state of the art for retina verification because the available data set is small kernel density estimation kde of the genuine and imposter score distributions of the training set are used to measure performance of the bgm algorithm in the one dimensional case the kde model is validated with the testing set a 0 eer on testing shows that the kde model is a good fit for the empirical distribution for the multiple graph measures a novel combination of the svm boundary and the kde model is used to obtain a fair comparison with the kde model for the single measure a clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60 and more than two orders of magnitude

vanishing viscosity for non homogeneous asymmetric fluids in r3 we consider a non homogeneous viscous incompressible asymmetric fluid in r 3 we prove that there exists a small time interval where the fluid variables converge uniformly as the viscosities tend to zero in the limit we find a non homogeneous non viscous incompressible asymmetric fluid governed by an euler like system

on the global well posedness for boussinesq system abstract in this paper we give a global well posedness result for the two dimensional boussinesq system with partial viscosity when the initial data v 0 b 1 1 r 2 l 2 r 2 and 0 b 2 1 0 r 2

fast detection of facial wrinkles based on gabor features using image morphology and geometric constraints facial wrinkles are important features of aging human skin which can be incorporated in several image based applications related to aging facial wrinkles are 3d features of skin and appear as subtle discontinuities or cracks in surrounding skin texture however facial wrinkles can easily be masked by illumination acquisition conditions in 2d images due to the specific nature of skin surface texture and its reflective properties existing approaches to image based analysis of aging skin are based on the analysis of wrinkles as texture and not as curvilinear discontinuity crack features previously we proposed a stochastic approach based on marked point processes mpp to localize facial wrinkles as curves in this paper we present a fast deterministic algorithm based on gabor filters and image morphology to improve localization results we propose image features based on gabor filter bank to highlight the subtle curvilinear discontinuities in skin texture caused by wrinkles then image morphology is used to incorporate geometric constraints to localize curvilinear shapes of wrinkles at image sites of large gabor filter responses experiments are conducted on two sets of low and high resolution images and results are compared with those of mpp modeling experiments show that the proposed algorithm not only is significantly faster than mpp based approach but also provides visually better results highlightsthe algorithm localizes subtle cracks in skin texture caused by wrinkles the algorithm is computationally fast based on the morphology the algorithm localizes wrinkles as curvilinear objects from the results typical challenges in localization of wrinkles are highlighted

weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum abstract we prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain r 3 when the initial vacuum is allowed i e the initial density 0 is not necessarily strictly positive our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense the global in time solutions are obtained under smallness assumptions on the initial data and forcing terms