comments on nonparametric segmentation of curves into various representations with reply the author points out the existence of a theoretical difficulty that underlies the curve segmentation problem studied in the work of rosin and west ibid vol 17 no 12 p 1140 53 1995 and present a possible solution to it the problem arises because curves are segmented into low and high order features and the former are a subset of the latter in reply rosin and west discuss the advantages and disadvantages of two approaches to model selection their original heuristic sequential method and the information theoretic method suggested by kanatani and others

lyapunov based boundary feedback design for parabolic pdes this paper presents a methodology for the construction of simple control lyapunov functionals clfs for boundary controlled parabolic partial differential equations pdes the proposed methodolog

fredholm transform and local rapid stabilization for a kuramoto sivashinsky equation this paper is devoted to the study of the local rapid exponential stabilization problem for a controlled kuramoto sivashinsky equation on a bounded interval we build a feedback control law to force the solution of the closed loop system to decay exponentially to zero with arbitrarily prescribed decay rates provided that the initial datum is small enough our approach uses a method we introduced for the rapid stabilization of a korteweg de vries equation it relies on the construction of a suitable integral transform and can be applied to many other equations

local exact controllability to the trajectories of the 1 d kuramoto sivashinsky equation abstract we are concerned with the boundary controllability to the trajectories of the kuramoto sivashinsky equation by using a carleman estimate we obtain the null controllability of the linearized equation around a given solution from a local inversion theorem we get the local controllability to the trajectories of the nonlinear system

breakpoint detection using covariance propagation presents a statistical approach for detecting breakpoints from chain encoded digital arcs an arc point is declared as a breakpoint if the estimated orientations of the two fitted lines of the two arc segments immediately to the right and left of the arc point are significantly statistically different the major contributions of this research include developing a method for analytically estimating the covariance matrix of the fitted line parameters and proposing a perturbation model to characterize the perturbation associated with each arc point

boundary control of viscosity degasperis procesi equation abstract this paper investigates the boundary control problem of the viscosity degasperis procesi equation in 0 1 results of the existence of a solution to the viscosity degasperis procesi equation in a short time interval under the boundary condition are given in the paper it proves the global exponential stability under the given boundary condition in l 2 h 1 h 2 h 3 space

on the orders of primitive groups with restricted nonabelian composition factors we prove that given c0 there exists c such that the following holds if g is a primitive permutation group of degree n no composition factor of which is an alternating group of degree greater than c0 or a classical group of dimension greater than c0 then g nc in particular if the nonabelian composition factors of g have bounded order then g is polynomially bounded

stability of cellular states of the kuramoto sivashinsky equation this paper is concerned with the instability property of a particular type of solution to the kuramoto sivashinsky equation namely the symmetric time independent cellular states attention is focused on the dimension of their unstable manifolds we show that as a control parameter varies the dimension changes in an ordered way governed by certain properties of an associated ordinary differential equation further change in dimension is shown to be related to hopf bifurcations from the cellular states an asymptotic analysis explains the onset of these bifurcations and predicts approximate parameter values at which they occur

linearized stability of partial differential equations with application to stabilization of the kuramoto sivashinsky equation linearization is a useful tool for analyzing the stability of nonlinear differential equations unfortunately the proof of the validity of this approach for ordinary differential equations does not generalize to all nonlinear partial differential equations general results giving conditions for when stability or instability of the linearized equation implies the same for the nonlinear equation are given here these results are applied to stability and stabilization of the kuramoto sivashinsky equation a nonlinear partial differential equation that models reaction diffusion systems the stability of the equilibrium solutions depends on the value of a positive parameter nu it is shown that if nu 1 then the set of constant equilibrium solutions is globally asymptotically stable if nu 1 then the equilibria are unstable it is also shown that stabilizing the linearized equation implies local exponential stability of the equation stabilization of the kuramoto sivashinsky equation using a sin

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

adaptive output feedback stabilization of non local hyperbolic pdes we address the problem of adaptive output feedback stabilization of general first order hyperbolic partial integro differential equations pide such systems are also referred to as pdes with non local in space terms we apply control at one boundary take measurements on the other boundary and allow the system s functional coefficients to be unknown to deal with the absence of both full state measurement and parameter knowledge we introduce a pre transformation which happens to be based on backstepping of the system into an observer canonical form in that form the problem of adaptive observer design becomes tractable both the parameter estimator and the control law employ only the input and output signals and their histories over one unit of time prior to presenting the adaptive design we present the non adaptive baseline controller which is novel in its own right and facilitates the understanding of the more complex adaptive system the parameter estimator is of the gradient type based on a parametric model in the form of an integral equation relating delayed values of the input and output for the closed loop system we establish boundedness of all signals pointwise in space and time and convergence of the pde state to zero pointwise in space we illustrate our result with a simulation

bases for primitive permutation groups and a conjecture of babai abstract a base of a permutation group g is a sequence b of points from the permutation domain such that only the identity of g fixes b pointwise we show that primitive permutation groups with no alternating composition factors of degree greater than d and no classical composition factors of rank greater than d have a base of size bounded above by a function of d this confirms a conjecture of babai

segmentation of two dimensional curve contours abstract segmentation of digitized planar curves is one of the most important elements in early image processing because a segmented image can describe the object profile in a compact form to facilitate higher level vision processing in many applications it is necessary to decompose an object boundary contour into several primitives such as segments and curves in this paper a two stage hybrid technique for the segmentation of two dimensional 2d curves is presented in which the number of segments is assumed to be known first the boundary is iteratively approximated using a split and merge method next an end point adjustment procedure is applied to reach the best fitting polygonal approximation a computational comparison with two existing methods shows that the proposed technique is fast and accurate an application of the new segmentation technique to industrial part inspection is also provided

global stabilization of a class of nonlinear reaction diffusion partial differential equations by boundary feedback this paper provides global exponential stabilization results by means of boundary feedback control for one dimensional nonlinear unstable reaction diffusion partial differential equations pdes wi

word maps word maps with constants and representation varieties of one relator groups abstract we consider word maps and word maps with constants on a simple algebraic group g we present results on the images of such maps in particular we prove a theorem on the dominance of general word maps with constants which can be viewed as an analogue of a well known theorem of borel on the dominance of genuine word maps besides we establish a relationship between the existence of unipotents in the image of the map induced by w f m and the structure of the representation variety r w g of the group w f m w

nonparametric segmentation of curves into various representations this paper describes and demonstrates the operation and performance of an algorithm for segmenting connected points into a combination of representations such as lines circular elliptical and superelliptical arcs and polynomials the algorithm has a number of interesting properties including being scale invariant nonparametric general purpose and efficient

optimization models for shape matching of nonconvex polygons abstract the shape matching problem is concerned with fitting an input shape represented by a set of discrete boundary data to a defect free reference shape two aspects of the problem must be considered 1 shape modeling and 2 matching algorithm in this paper two shape modeling schemes are proposed to represent the reference shape by a set of primitives in which the object geometric configuration is encoded the primitives uniquely define the pose and dimension of a given polygonal object based on these models optimization matching procedures that use the least squares criterion to find the best fitting between the set of scene data and the reference shape are developed the complexity analysis and computational results show our shape matching approaches to be extremely fast

pro finite p adic lie algebras abstract let p be a prime number a finite nilpotent lie ring of characteristic a power of p is called finite p a pro p lie ring is an inverse limit of finite p lie rings pro p lie rings play a role in lie theory similar to that played by pro p groups in group theory every pro p lie ring admits the structure of a lie algebra over the p adic integers furthermore every p adic lie algebra of finite rank as a p adic module has an open pro p subalgebra we make a detailed study of pro p lie rings in terms of various properties including their topology prufer rank subring growth and p adic module structure in particular we prove the equivalence of the following conditions for a finitely generated pro p lie ring l l has finite prufer rank l is isomorphic to a closed subring of gl v for some p adic module v of finite rank and for sufficiently large n the lie f p subalgebra w n e 12 t e 22 gl 2 f p t t n is not an open section of l by reducing to the pro p lie ring case we also prove that all engelian pro finite lie rings are locally nilpotent this is a lie theoretic analogue of zelmanov s theorem which states that every periodic pro p group is locally finite

reduced resolution and scale space for dominant feature detection in contours abstract analysis of contours or curves at various scales or levels of smoothing scale space is an important tool in curve segmentation and feature detection in this paper we propose the application of the hierarchical discrete correlation algorithm for efficiently calculating and creating a scale space of curves in conjunction with this procedure we also investigate the use of the reduced resolution or gaussian pyramid representation of the set of smoothed curves as the basis for initially localizing and detecting features we also create an approximation to the above algorithms that is computationally less expensive finally we propose a new inter scale method for curve segmentation and feature detection based on the motion of a curve through scale space

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

approximate inertial manifolds for the kuramoto sivashinsky equation analysis and computations abstract we evaluate several alternative methods for the approximation of inertial manifolds for the one dimensional kuramoto sivashinsky equation kse a method motivated by the dynamics originally developed for the navier stokes equation is adapted for the kse rigorous error estimates are obtained and compared to those of other methods introduced in the literature formal relationships between these other methods and the one introduced here are established numerical bifurcation diagrams of the various approximate inertial forms for the kse are presented we discuss the correspondence between the rigorous error estimates and the accuracy of the computational results these methods can be adapted to other dissipative partial differential equations

measures of acutance and shape for classification of breast tumors most benign breast tumors possess well defined sharp boundaries that delineate them from surrounding tissues as opposed to malignant tumors computer techniques proposed to date for tumor analysis have concentrated on shape factors of tumor regions and texture measures while shape measures based on contours of tumor regions can indicate differences in shape complexities between circumscribed and spiculated tumors they are not designed to characterize the density variations across the boundary of a tumor here the authors propose a region based measure of image edge profile acutance which characterizes the transition in density of a region of interest roi along normals to the roi at every boundary pixel the authors investigate the potential of acutance in quantifying the sharpness of the boundaries of tumors and propose its application to discriminate between benign and malignant mammographic tumors in addition they study the complementary use of various shape factors based upon the shape of the roi such as compactness fourier descriptors moments and chord length statistics to distinguish between circumscribed and spiculated tumors thirty nine images from the mammographic image analysis society mias database and an additional set of 15 local cases were selected for this study the cases included 16 circumscribed benign 7 circumscribed malignant 12 spiculated benign and 19 spiculated malignant lesions all diagnoses were proven by pathologic examinations of resected tissue the contours of the lesions were first marked by an expert radiologist using x paint and x windows on a sun sparcstation 2 workstation for computation of acutance the roi boundaries were iteratively approximated using a split merge and end point adjustment technique to obtain the best fitting polygonal approximation the jackknife method using the mahalanobis distance measure in the bmdp biomedical programs package was used for classification of the lesions using acutance and the shape factors as features in various combinations acutance alone resulted in a benign malignant classification accuracy of 95 the mias cases compactness alone gave a circumscribed spiculated classification rate of 92 3 with the mias cases acutance in combination with a moment based shape measure and a fourier descriptor based measure gave four group classification rate of 95 with the mias cases the results indicate the importance of including lesion edge definition with shape information for classification of tumors and that the proposed measure of acutance fills this need

a new global carleman estimate for the one dimensional kuramoto sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem abstract in this paper we establish a new global carleman estimate for the linearized kuramoto sivashinsky equation which is a one parameter carleman estimate based on this estimate we can obtain the local exact controllability to the trajectories and lipschitz stability in an inverse problem for the kuramoto sivashinsky equation

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

fuchsian groups finite simple groups and representation varieties let be a fuchsian group of genus at least 2 at least 3 if is non oriented we study the spaces of homomorphisms from to finite simple groups g and derive a number of applications concerning random generation and representation varieties precise asymptotic estimates for hom g are given implying in particular that as the rank of g tends to infinity this is of the form g 1 o 1 where is the measure of we then prove that a randomly chosen homomorphism from to g is surjective with probability tending to 1 as g combining our results with lang weil estimates from algebraic geometry we obtain the dimensions of the representation varieties text hom gamma bar g where bar g is gl n k or a simple algebraic group over k an algebraically closed field of arbitrary characteristic a key ingredient of our approach is character theory involving the study of the zeta function g s 1 s where the sum is over all irreducible complex characters of g

the signature of a plane curve the signature of a plane curve gamma associated with every point p of gamma the length of gamma to the left of or on the line tangent to gamma at p the signature has properties that make it a useful tool for pattern recognition it discards the location orientation and scale and slant in special cases but preserves symmetries its integral is a measure of convexity this paper explores the theoretical properties of this concept it is shown that in the special case of closed rectilinear curves the signature retains enough information to permit exact reconstruction of the curve computing the signature and reconstructing curves from their signatures are interesting computational problems time complexity bounds on these problems are presented several challenging open questions are posed

an adaptive reduction procedure for the piecewise linear approximation of digitized curves a new algorithm is presented for the piecewise linear approximation of two dimensional digitized curves against a square grid the algorithm utilizes an adaptive reduction procedure in two approximation phases to select the critical points of a digitized curve such that the deviation from the digitized curve to its final approximated curve is bounded by a uniform error tolerance the time complexity of this algorithm is o m sup 2 rather than o n sup 2 on the theoretical plane in the experiments of fixing the initial and the final processing points the performance of the algorithm has been compared to those of three prominent other algorithms regarding the required number of critical points and the total execution time of the program of the four algorithms compared the present algorithm consistently has the shortest execution time of the program and it tends most to require as few critical points as the optimum algorithm that was tested

new method to find corner and tangent vertices in sketches using parametric cubic curves approximation some recent approaches have been presented as simple and highly accurate corner finders in the sketches including curves which is useful to support natural human computer interaction but these in most cases do not consider tangent vertices smooth points between two geometric entities present in engineering models what implies an important drawback in the field of design in this article we present a robust approach based on the approximation to parametric cubic curves of the stroke for further radius function calculation in order to detect corner and tangent vertices we have called our approach tangent and corner vertices detection tcvd and it works in the following way first corner vertices are obtained as minimum radius peaks in the discrete radius function where radius is obtained from differences second approximated piecewise parametric curves on the stroke are obtained and the analytic radius function is calculated then curves are obtained from stretches of the stroke that have a small radius finally the tangent vertices are found between straight lines and curves or between curves where no corner vertices are previously located the radius function to obtain curves is calculated from approximated piecewise curves which is much more noise free than discrete radius calculation several tests have been carried out to compare our approach to that of the current best benchmarked and the obtained results show that our approach achieves a significant accuracy even better finding corner vertices and moreover tangent vertices are detected with an accuracy near to 92 and a false positive rate near to 2

drag reduction in transitional linearized channelow using distributed control this work focuses on feedback control of incompressible transitional newtonian channel flow described by the twodimensional linearized navier stokes equations the control objective is to use distributed feedback to achieve stabilization of the parabolic velocity profile for values of the reynolds number for which this profile is unstable and therefore to reduce the frictional drag exerted on the lower channel wall compared to the open loop values the control system uses measurements of shear stresses on the lower channel wall and the control actuation is assumed to be in the form of electromagnetic lorentz forces applied to the flow near the bottom wall galerkin s method is initially used to derive a high order discretization of the linearized flow field that captures the flow instability and accounts for the effect of control actuation on all the modes then a low order approximation of the linearized flow field is derived and used for the synthesis of a linear output feedback controller that enfor

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

ordered structural shape matching with primitive extraction by mathematical morphology abstract structural shape matching procedures begin by decomposing the shapes to be matched into primitive parts and extracting the properties of and relationships among these primitives the resultant structural descriptions are matched to structural models usually via a tree search whose time is exponential in the number of primitives in this paper we introduce a new fast method of structural shape matching called ordered structural matching which has polynomial time complexity instead of exponential the approach presented also uses mathematical morphology to rapidly decompose the shapes into primitives to be used in the matching the primitives so produced are pieces of the original shape but not necessarily those pieces that a human would select the method has been tested on the toy task of determining which plastic shapes match the shapes of the holes in a child s six sided toy box it is also directly applicable to the inspection and manipulation of certain airplane parts

kuramoto sivashinsky dynamics on the center unstable manifold this paper studies the dynamical behavior of solutions of the kuramoto sivashinsky partial differential equation with periodic boundary conditions on a spatial interval 0 h the length h is the bifurcation parameter and reduction is made to a two complex dimensional system on a local center unstable manifold near the second bifurcation point h 2 from the trivial solution the resulting o 2 equivariant system displays all the behavior found in high precision simulations of the partial differential equation near this bifurcation point in particular bifurcation sequences to stable traveling waves unstable modulated traveling waves and attracting heteroclinic cycles are reproduced qualitatively and quantitatively within 1 in the parameter range h 2 pm 20 a clear understanding of the global dynamical behavior in this region is thus obtained

witt burnside ring and burnside ring over a special λ ring abstract given an arbitrary group g we construct a covariant functor f g from the category of special rings to that of commutative rings with unity when g is a strongly complete profinite group it will be used to reconstruct the functor n r g which was first introduced in y t oh r analogue of the burnside ring of profinite groups and free lie algebras adv math 190 2005 1 46 to investigate the structure of witt burnside rings over special rings more precisely given a special ring r we show that n r g r is functorially isomorphic to f g r j g r for some ideal j g r of f g r the connection to the functor f g due to j j graham generalized witt vectors adv math 99 1993 248 263 will also be demonstrated

on traveling wave solutions of the kuramoto sivashinsky equation abstract previous numerical results indicate that the kuramoto sivashinsky equation admits three classes of non periodic traveling wave solutions namely regular shocks oscillatory shocks and solitary waves however it has been shown that regular monotonic shocks cease to exist in the weak shock limit due to the radiation of oscillatory waves of exponentially small with respect to the shock strength but growing in space amplitude here oscillatory shocks and solitary waves are constructed by asymptotic analysis it thus transpires that in the weak shock limit oscillatory shocks can only be antisymmetric otherwise oscillatory and monotonic waves of exponentially small but growing in space amplitude would inevitably be excited under certain conditions however the growing waves can link a nearly antisymmetric oscillatory shock with a radiating regular shock to form a solitary wave the predictions of the asymptotic theory are supported by numerical results

gradient and texture analysis for the classification of mammographic masses computer aided classification of benign and malignant masses on mammograms is attempted in this study by computing gradient based and texture based features features computed based on gray level co occurrence matrices gcms are used to evaluate the effectiveness of textural information possessed by mass regions in comparison with the textural information present in mass margins a method involving polygonal modeling of boundaries is proposed for the extraction of a ribbon of pixels across mass margins two gradient based features are developed to estimate the sharpness of mass boundaries in the ribbons of pixels extracted from their margins a total of 54 images 28 benign and 26 malignant containing 39 images from the mammographic image analysis society mias database and 15 images from a local database are analyzed the best benign versus malignant classification of 82 1 with an area a sub z of 0 85 under the receiver operating characteristics roc curve was obtained with the images from the mias database by using gcm based texture features computed from mass margins the classification method used is based on posterior probabilities computed from mahalanobis distances the corresponding accuracy using jack knife classification was observed to be 74 4 with a sub x 0 67 gradient based features achieved a sub x 0 6 on the mias database and a sub z 0 76 on the combined database the corresponding values obtained using jack knife classification were observed to be 0 52 and 0 73 for the mias and combined databases respectively

diameters of finite simple groups sharp bounds and applications let g be a finite simple group and let s be a normal subset of g we determine the diameter of the cayley graph r g s associated with g and s up to a multiplicative constant many applications follow for example we deduce that there is a constant c such that every element of g is a product of c involutions and we generalize this to elements of arbitrary order we also show that for any word w w xl xd there is a constant c c w such that for any simple group g on which w does not vanish every element of g is a product of c values of w from this we deduce that every verbal subgroup of a semisimple profinite group is closed other applications concern covering numbers expanders and random walks on finite simple groups

bounded normal generation and invariant automatic continuity abstract we study the question of how quickly products of a fixed conjugacy class in the projective unitary group of a ii1 factor von neumann algebra cover the entire group our result is that the number of factors that are needed is essentially as small as permitted by the 1 norm in analogy to results of liebeck and shalev for non abelian finite simple groups as an application of the techniques we prove that every homomorphism from the projective unitary group of a finite factor to a polish sin group is continuous a result which is even new for pu n moreover we show that the projective unitary group of a ii1 factor carries a unique polish group topology

wavelet projections of the kuramoto sivashinsky equation i heteroclinic cycles and modulated traveling waves for short systems abstract we study fairly low dimensional projections of the kuramoto sivashinsky partial differential equation with periodic boundary conditions on a short interval onto bases spanned by periodic wavelets such projections break the translation reflection symmetry o 2 replacing it by a finite dihedral group dk however we show that for the perrier basdevant wavelets used here the loss of symmetry is sufficiently mild that key global features of the dynamics are preserved in particular we observe heteroclinic cycles and modulated travelling waves arising from interactions of unstable modes on a four dimensional subspace spanned by appropriate combinations of wavelets we use invariant manifold reductions in our analysis and pay particular attention to symmetries and the relation between periodic wavelets and fourier modes which preserve full o 2 symmetry and are also optimal in that fourier truncations maximise the energy l2 norm among all finite dimensional models this study provides a foundation for current and future work in which we use wavelet bases to extract local models of evolution equations in large space domains

on bounded conciseness of words in residually finite groups abstract we conjecture that any group word that is concise in the class of residually finite groups is in fact boundedly concise we show that this is true for the word w q where w is a multilinear commutator word and q is a prime power

word maps conjugacy classes and a noncommutative waring type theorem let w w x xd 1 be a nontrivial group word we show that if g is a sufficiently large finite simple group then every element g e g can be expressed as a product of three values of w in g this improves many known results for powers commutators as well as a theorem on general words obtained in 19 the proof relies on probabilistic ideas algebraic geometry and character theory our methods which apply the zeta function g s x eirrg xo s giye rise to various additional results of independent interest including applications to conjectures of ore and thompson

local dissipativity and attractors for the kuramoto sivashinsky equation in thin 2d domains here 0 e 5 1 is assumed to be sufficiently small so that the basic periodicity cell sz 0 2n x 0 2ne is a thin domain we shall also mention other types of boundary conditions for which the same methods are applicable the dissipativity of the general two and higher dimensional problem has been open for some time the essential difficulty being the lack of a proof of the existence of an absorbing set in fact if such a set exists then there exists a global attractor and one can prove very precise regularity results excellent references for these as well as many refined results on the geometry of the attractor are the paper by nicolaenko et af l il yashenko 2 and the books by ttmam 3 and constantin et al 4 the approach we shall adopt is based on the intuitive idea that l 1 3 should be close to one dimensional and is close to the methods introduced by hale and raugel 5 61 and raugel and sell 7 there are many nontrivial results available for the periodic one dimensional problem the odd periodic case was studied by l 81 the same authors g treat a neumann type of problem without symmetry and the rigid dirichlet problem is studied by 9 again without any symmetry assumptions the general periodic one dimensional problem has only recently been proved to be dissipative 2 our main result is the following theorem

null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time varying feedback laws to this end on the one hand we provide a new proof of the well posedness and the optimal bound with respect to damping constants for the solutions of the kernel equations this allows one to deal with variable coefficients even with a weak regularity of these coefficients on the other hand we establish the well posedness and estimates for the heat equations with a nonlocal boundary condition at one side

techniques for assessing polygonal approximations of curves given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines instead we suggest assessing an algorithm s results relative to an optimal polygon and describe a measure which combines the relative fidelity and efficiency of a curve segmentation we use this measure to compare the application of 23 algorithms to a curve first used by teh and chin 1989 their integral square errors ises are assessed relative to the optimal ise in addition using an example of pose estimation it is shown how goal directed evaluation can be used to select an appropriate assessment criterion

fast polygonal approximation of digital curves using relaxed straightness properties several existing digital straight line segment dss recognition algorithms can be used to determine the digital straightness of a given one pixel thick digital curve because of the inherent geometric constraints of digital straightness these algorithms often produce a large number of segments to cover a given digital curve representing a real life object image thus a curve segment which is not exactly digitally straight but appears to be visually straight is fragmented into multiple dss when these algorithms are run in this paper a new concept of approximate straightness is introduced by relaxing certain conditions of dss and an algorithm is described to extract those segments from a digital curve the number of such segments required to cover the curve is found to be significantly fewer than that of the exact dss cover as a result the data set required for representing a curve also reduces to a large extent the extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance the proposed algorithm involves only primitive integer operations and thus runs very fast compared to those based on exact dss the overall time complexity becomes linear in the number of points present in the representative set experimental results on several digital curves demonstrate the speed elegance and efficacy of the proposed method

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

bounds on the number and sizes of conjugacy classes in finite chevalley groups with applications to derangements we present explicit upper bounds for the number and size of conjugacy classes in finite chevalley groups and their variations these results have been used by many authors to study zeta functions associated to representations of finite simple groups random walks on chevalley groups the final solution to the ore conjecture about commutators in finite simple groups and other similar problems in this paper we solve a strong version of the boston shalev conjecture on derangements in simple groups for most of the families of primitive permutation group representations of finite simple groups the remaining cases are settled in two other papers of the authors and applications are given in a third

dissipation inequalities for the analysis of a class of pdes in this paper we develop dissipation inequalities for a class of well posed systems described by partial differential equations pdes we study passivity reachability induced input output norm boundedness and input to state stability iss we consider both cases of in domain and boundary inputs and outputs we study the interconnection of pde pde systems and formulate small gain conditions for stability for pdes polynomial in dependent and independent variables we demonstrate that sum of squares sos programming can be used to compute certificates for each property therefore the solution to the proposed dissipation inequalities can be obtained via semi definite programming the results are illustrated with examples

contour sequence moments for the classification of closed planar shapes abstract a technique for classifying closed planar shapes is described in which a shape is characterized by a one dimensional sequence that represents the euclidean distance between the centroid and all contour pixels of the shape contour sequences obtained from shapes belonging to the same class are similar and are considered to be different realizations of a stochastic process statistical moment functions derived from contour sequences are used to characterize the process and hence the shapes it is shown that these moment functions are invariant to shape translation rotation and scale transformations examples are presented to illustrate the performance of these moment functions in the classification of noisy shapes

optimum uniform piecewise linear approximation of planar curves two dimensional digital curves are often uniformly approximated by polygons or piecewise linear curves several algorithms have been proposed in the literature to find such curves we present an algorithm that finds a piecewise linear curve with the minimal number of segments required to approximate a curve within a uniform error with fixed initial and final points we compare our optimal algorithm to several suboptimal algorithms with respect to the number of linear segments required in the approximation and the execution time of the algorithm

segmentation of two dimensional boundaries using the chain code abstract we divide the boundary of a two dimensional object into segments each of which is either straight or a circular arc associated with the segment end points are angle measures that can be used to match an object with a transformed rotated scaled version of itself the chain code easily extracted from the boundary pixels is the basis of this division the approach avoids problems common to many of the existing methods for identification of curvature extrema sensitivity to noise and dependence on parameters that are chosen empirically to each section of the boundary we assign a code that represents the change in slope between it and the previous section this set of codes is integrated and thus provides a measure of the total directional change relative to the first section for a closed object the sequence of these sums is periodic and one cycle can be plotted as a function of arc length s such a plot can be shown to contain only straight lines those that are not parallel to the s axis representing circular arcs on the original boundary of the object and those that are representing straight sections on the boundary this paper describes a recursive procedure for dividing the digital version of the curve described above into its linear segments each segment represents an arc that is the best fit to a portion of the original boundary the angle which is defined by the arc is identical to the angle change of the edge in the same section and the length of the arc is identical to that of the edge the recursive procedure measures the error for each value of arc length between a proposed fitting line and the actual value of cumulative angle where the error is maximum and above a threshold the line is segmented the procedure is repeated until the error is sufficiently small the breakpoints thus indicate the location and value of points of greatest curvature change a formal definition of the procedure is given and it is shown to perform well for rotated scaled and noisy objects

closed subgroups of profinite groups theorem 1 asserts that emph in a finitely generated prosoluble group every subgroup of finite index is open this generalises an old result of serre about pro p groups it follows by a standard argument from theorem 2 emph in a d generator finite soluble group every element of the derived group is equal to a product of 72d 2 46d commutators this result about finite soluble groups is proved by induction on the order of the group and is elementary though rather intricate the essence of the proof lies in reducing the problem to one about the number of solutions of quadratic equations over a finite field corollaries include the following emph let gamma be a finitely generated prosoluble group then each term of the lower central series of gamma and each power subgroup gamma n is closed 1991 mathematics subject classification 20e18 20d10

nonlinear stabilization of shock like unstable equilibria in the viscous burgers pde we stabilize the unstable ldquoshock likerdquo equilibrium profiles of the viscous burgers equation using control at the boundaries these equilibria are not stabilizable even locally using the standard ldquoradiation feedback boundary conditions rdquo using a nonlinear spatially scaled transformation that employs three ingredients of which one is the hopf cole nonlinear integral transformation and linear backstepping we design an explicit nonlinear full state control law that achieves exponential stability with a region of attraction for which we give an estimate the region of attraction is not the entire state space since the burgers pde is known not to be globally controllable

global stabilization of the kuramoto sivashinsky equation via distributed output feedback control abstract this work addresses the problem of global exponential stabilization of the kuramoto sivashinsky equation kse subject to periodic boundary conditions via distributed static output feedback control under the assumption that the number of measurements is equal to the total number of unstable and critically stable eigenvalues of the kse and a necessary and sufficient stability condition is satisfied linear static output feedback controllers are designed that globally exponentially stabilize the zero solution of the kse the controllers are designed on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the theoretical results are confirmed by computer simulations of the closed loop system

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

on finitely generated profinite groups ii products in quasisimple groups we prove two results 1 there is an absolute constant d such that for any finite quasisimple group s given 2d arbitrary automorphisms of s every element of s is equal to a product of d twisted commutators defined by the given automorphisms 2 given a natural number q there exist c c q and m m q such that if s is a finite quasisimple group with s z s c j j 1 m are any automorphisms of s and qj j 1 m are any divisors of q then there exist inner automorphisms j of s such that s m s j j q j these results which rely on the classification of finite simple groups are needed to complete the proofs of the main theorems of part i

on line segmentation of freehand sketches by knowledge based nonlinear thresholding operations this paper describes an on line procedure for segmenting freehand sketches into 2d primitives and smooth curves by knowledge based nonlinear thresholding operations drawing position direction speed and acceleration information is used for establishing fuzzy knowledge and inferring user s intention the procedure can be divided into three stages 1 obtaining corner points based on the fuzzy knowledge and adaptive thresholds which includes detecting obtuse and acute corner points 2 finding smooth join points during which stage we use both curve linearity and curvature and 3 classifying the sketches into the corresponding curves according to curve linearity and changes of curve convexity the method is illustrated and tested with a number of sketches

generators and commutators in finite groups abstract quotients of compact groups the first part of the paper establishes results about products of commutators in a d generator finite group g for example if h g g1 gr then every element of the subgroup h g is a product of f r factors of the form h 1 g 1 h 1 prime g 1 1 ldots lbrack h r g r h r prime g r 1 with h 1 h 1 prime ldots allowbreak h r h r prime in h under certain conditions on h a similar conclusion holds with the significantly weaker hypothesis that g h g1 gr where f r is replaced by f1 d r the results are applied in the second part of the paper to the study of normal subgroups in finitely generated profinite groups and in more general compact groups results include the characterization of topologically finitely generated compact groups which have a countably infinite image and of those which have a virtually dense normal subgroup of infinite index as a corollary it is deduced that a compact group cannot have a finitely generated infinite abstract quotient

commutator maps measure preservation and t systems let g be a finite simple group we show that the commutator map g g g is almost equidistributed as g 1 this somewhat surprising result has many applications it shows that a for a subset x g we have 1 x g 2 x g o 1 namely is almost measure preserving from this we deduce that almost all elements g 2 g can be expressed as commutators g x y where x y generate g this enables us to solve some open problems regarding t systems and the product replacement algorithm pra graph we show that the number of t systems in g with two generators tends to infinity as g 1 this settles a conjecture of guralnick and pak a similar result follows for the number of connected components of the pra graph of g with two generators some of our results apply for more general finite groups and more general word maps our methods are based on representation theory combining classical character theory with recent results on character degrees and values in finite simple groups in particular the so called witten zeta function g s p 2irr g 1 s plays a key role in the proofs

word maps and waring type problems waring s problem asks whether every natural number is a sum of g k fcth powers where g is a suitable function this was solved affirmatively by hubert in 1909 optimizing g k has been a central problem in additive number theory ever since see na for more detail and background recently there has been considerable interest in group theoretic analogues of this phenomenon where the aim is to present group elements as short products of certain special elements these special elements can be powers or commutators or values of a general word w or elements of a special conjugacy class in the group the motivation for this is sometimes topological let g be a topologically finitely generated pro p group using expressions of elements of the commutator subgroup g1 as bounded products of commutators serre showed that g is closed and deduced that every finite index subgroup of g is open a recent deep result of nikolov and segal nsi ns2 shows that this holds for every finitely generated profinite group again the core of the proof is presenting group elements as short products of values of certain words

a global attracting set for the kuramoto sivashinsky equation new bounds are given for the l2 norm of the solution of the kuramoto sivashinsky equation partial t u x t partial x 2 partial x 4 u x t u x t partial x u x t for initial data which are periodic with periodl there is no requirement on the antisymmetry of the initial data the result is mathop lim sup limits t to infty left u cdot t right 2 leqslant const l 8 5

a method for shift rotation and scale invariant pattern recognition using the form and arrangement of pattern specific features abstract a new computer based method for visual pattern recognition is described the process extracts shape features from binary edge images represented in either real valued or discrete coordinates both separate and overlapping features are extracted maximizing their completeness and continuity without using templates or mathematical feature descriptions these features and their arrangement are encoded in a shift rotation and scale invariant manner and used to recognize incoming patterns from a set of previously encoded patterns stored in memory new patterns may be automatically classified and stored in memory allowing the system to learn and generalize without operator intervention testing shows the system to be completely shift rotation and scale invariant and insensitive to local image distortion

on finitely generated profinite groups i strong completeness and uniform bounds we prove that in every finitely generated profinite group every subgroup of finite index is open this implies that the topology on such groups is determined by the algebraic structure this is deduced from the main result about finite groups let w be a locally finite group word and d n then there exists f f w d such that in every d generator finite group g every element of the verbal subgroup w g is equal to a product of f w values an analogous theorem is proved for commutators this implies that in every finitely generated profinite group each term of the lower central series is closed the proofs rely on some properties of the finite simple groups to be established in part ii

on the lattice of normal subgroups in ultraproducts of compact simple groups we prove that the lattice of normal subgroups of ultraproducts of compact simple non abelian groups is distributive in the case of ultraproducts of finite simple groups or compact connected simple lie groups of bounded rank the set of normal subgroups is shown to be linearly ordered by inclusion 2010 mathematics subject classification 03c20 20d30 primary 20f69 20d06 22e46 secondary

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

stability enhancement by boundary control in the kuramoto sivashinsky equation where we refer to 0 as the anti di ussion parameter note that a more general form ut 1uxxxx 2uxx 3uux 0 can always be reduced to 1 1 by appropriate rescaling of t x and u eq 1 1 was derived independently by kuramoto et al 20 22 as a model for phase turbulence in reaction di usion systems and by sivashinsky 33 as a model for plane ame propagation describing the combined in uence of di usion and thermal conduction of the gas on stability of a plane ame front so far it has been well understood that the ks equation can also serve as a mathematical model for cellular instabilities in a variety of situations the ow of thin liquid lms on inclined planes 30 in the limit of large surface tension dendritic fronts in dilute binary alloys 31 and alfven drift waves in plasmas 23 as a nonlinear saturation mechanism of the dissipative trapped ion modes

dynamics of a nonlocal kuramoto sivashinsky equation abstract in this paper we study the effects of a nonlocal term on the global dynamics of the kuramoto sivashinsky equation we show that the equation possesses a family of maximal attractors parameterized by the mean value of the initial data the dimension of the attractor is estimated as a function of the coefficient of the nonlocal term and the width of the periodic domain

the existence of steady solutions of the kuramoto sivashinsky equation abstract we investigate the existence of steady solutions of the kuramoto sivashinsky equation for wave speed c 1 we show that there are two periodic solutions and two heteroclinic orbits for the resultant third order ordinary differential equation a discussion is given concerning the possibility of using these solutions to obtain the existence of more complicated patterns