finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

hukuhara differentiability of interval valued functions and interval differential equations on time scales abstract using the concept of the generalized hukuhara difference in this paper we introduce and study the differentiability and the integrability for the interval valued functions on time scales some illustrative examples to interval differential equations on time scales are presented

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

on nirenberg type conditions for higher order systems on time scales we study the existence of periodic solutions for a nonlinear system of nth order differential equations on time scales assuming a suitable nirenberg type condition we prove the existence of at least one solution of the problem using mawhin s coincidence degree

homoclinic orbits and periodic solutions for a class of hamiltonian systems on time scales abstract in this paper we are concerned with a second order non autonomous hamiltonian system on time scales t u t v u t u t f t t t under certain conditions the existence and multiplicity of periodic solutions are obtained for this hamiltonian system on time scales by using the saddle point theory the least action principle as well as the three critical point theorem in addition the existence of homoclinic orbit is obtained as a limit of 2 k t periodic solutions of a given sequence of hamiltonian system on time scales by means of the mountain pass theorem and the standard minimizing argument

a dynamic matrix exponential via a matrix cylinder transformation abstract in this work we develop a new matrix exponential on time scales via a cylinder transformation with a component wise locally integrable square matrix subscript our resulting matrix function can be written in terms of the matrix exponential of a lebesgue integral added to a logarithmic sum in terms of the gaps of a general time scale under strict commutativity conditions we show our dynamic matrix exponential is equivalent to the one in the standard literature finally we demonstrate that our matrix exponential satisfies a nonlinear dynamic integral equation

integrable equations on time scales integrable systems are usually given in terms of functions of continuous variables on r in terms of functions of discrete variables on z and recently in terms of functions of q variables on kq we formulate the gel fand dikii gd formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations in particular they yield integrable equations over integers difference equations and over q numbers q difference equations we formulate the gd formalism also in terms of shift operators for all regular discrete time scales we give a method allowing to construct the recursion operators for integrable systems on time scales finally we give a trace formula on time scales and then construct infinitely many conserved quantities casimirs of the integrable systems on time scales

domination of blocks fusion systems and hyperfocal subgroups abstract we aim in this paper to investigate the connections between some properties of blocks and of their dominating blocks we find conditions to verify that a block is inertial if and only if its dominating block is inertial in some situations the equality of the factor fusion systems associated with a block and with its brauer correspondent block give information about the hyperfocal subgroups

global stability for nonlinear dynamic equations with variable coefficients we give sufficient conditions under which the trivial solution of a nonlinear dynamic equation with variable coefficients is globally asymptotically stable for arbitrary time scales unbounded above

stability for time varying linear dynamic systems on time scales we study conditions under which the solutions of a time varying linear dynamic system of the form x t a t x t are stable on certain time scales we give sufficient conditions for various types of stability including lyapunov type stability criteria and eigenvalue conditions on slowly varying systems that ensure exponential stability finally perturbations of the unforced system are investigated and an instability criterion is also developed

active contours for tracking distributions a new approach to tracking using active contours is presented the class of objects to be tracked is assumed to be characterized by a probability distribution over some variable such as intensity color or texture the goal of the algorithm is to find the region within the current image such that the sample distribution of the interior of the region most closely matches the model distribution two separate criteria for matching distributions are examined and the curve evolution equations are derived in each case the flows are shown to perform well in experiments

a generic framework for tracking using particle filter with dynamic shape prior tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time tracking algorithms using kalman filters or particle filters pfs have been proposed for tracking such objects but these have limitations due to the lack of dynamic shape information in this paper we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter the pf also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

adaptive sampling control of high gain stabilizable systems it is well known that proportional output feedback control can stabilize any relative degree one minimum phase system if the sign of the feedback is correct and the proportional gain is high enough moreover there exist simple adaptation laws for tuning the proportional gain so called high gain adaptive controllers which do not need to know the system and do not attempt to identify system parameters the authors consider sampled versions of the high gain adaptive controller the motivation for sampling arises from the possibility that the output of a system may not be available continuously but only at sampled times the main point of interest is the need to develop techniques for adapting the sampling rate since the stiffness of the system increases as the proportional gain is increased our main result shows that adaptive sampling stabilization is possible if the product hk of the decreasing sampling interval h and the increasing proportional gain k decreases at a rate proportional to 1 log k

uniform exponential stability of first order dynamic equations with several delays abstract this paper is concerned with the uniform exponential stability of ordinary and delay dynamic equations after revealing the equivalence between various types of uniform exponential stability definitions on time scales with bounded graininess and demonstrating their relation when the graininess is arbitrary we confine our attention to the uniform exponential stability of ordinary dynamic equations we introduce and prove the bohl perron criterion for delay dynamic equations if for any bounded right hand side the solution of the delay dynamic equation with bounded coefficients and delays is bounded then the trivial solution of the equation is uniformly exponentially stable we also obtain some corollaries of this criterion based on these results explicit exponential stability tests are derived for delay dynamic equations with nonnegative coefficients which are illustrated with an example on a nonstandard time scale

stability and instability for dynamic equations on time scales in this paper we examine the stability and instability of the equilibrium solution x 0 to the first order system of dynamic equations x d f t x t t 0 x d r n where t is from a so called time scale t with t 0 tand d is a compact set our methods involve the existence of a positive definite liapunov function v such that its delta derivative v d satisfies certain integral definite or semidefinite sign properties finally we use liapunov functions to develop an invariance principle regarding solutions to the above dynamic equation

higher order self adjoint boundary value problems on time scales in this study higher order self adjoint differential expressions on time scales and their associated self adjoint boundary conditions are discussed the symmetry property of the corresponding green s functions is shown together with specific formulas of green s functions for select time scales

hamiltonian systems on time scales linear and nonlinear hamiltonian systems are studied on time scales t we unify symplectic flow properties of discrete and continuous hamiltonian systems a chain rule which unifies discrete and continuous settings is presented for our so called alpha derivatives on generalized time scales this chain rule allows transformation of linear hamiltonian systems on time scales under simultaneous change of independent and dependent variables thus extending the change of dependent variables recently obtained by dosl and hilscher we also give the legendre transformation for nonlinear euler lagrange equations on time scales to hamiltonian systems on time scales

the laplace transform on time scales revisited abstract in this work we reexamine the time scale laplace transform as defined by bohner and peterson m bohner a peterson dynamic equations on time scales an introduction with applications birkhauser boston 2001 m bohner a peterson laplace transform and z transform unification and extension methods appl anal 9 1 2002 155 162 in particular we give conditions on the class of functions which have a transform develop an inversion formula for the transform and further we provide a convolution for the transform the notion of convolution leads to considering its algebraic structure in particular the existence of an identity element motivating the development of the dirac delta functional on time scales applications and examples of these concepts are given

singular value conditions for stability of dynamic switched systems abstract in this paper the stability of a certain class of time varying systems evolving over nonuniformly spaced discrete domains is analyzed switched systems used here in the context of dynamic equations over time scale domains arise naturally in applications when a continuous time system is discretized via a sample and hold method with multiple sample rates the stability of switched systems is typically deduced by appealing to certain interrelated properties of the subsystems such as pairwise commutativity 24 simultaneous diagonalization 7 simultaneous triangularizability 8 or other lie algebraic conditions 1 which imply the existence of a common quadratic lyapunov function a novel approach is used here to determine the existence of quadratic lyapunov functions which does not rely on how the subsystems interact with each other this new method instead examines the role they each play in the aggregate system by way of singular value conditions results implying switched system stability and instability are developed under the two primary methods of examining such systems how the system behaves during arbitrary switching and how it behaves under the influence of a particular switching signal several examples illuminating the results are provided throughout the text as well as important insight discussing certain bounds on these results as they apply to stability theory in general

uniqueness and existence results for initial value problems on time scales through a reciprocal problem and applications this paper is devoted to deriving the existence uniqueness and approximation of solutions to a first order initial value problem on an interval of an arbitrary time scale taking values in a different time scale we obtain the results considering dynamic equations whose nonlinear part is nonnegative and satisfies a type of inverse caratheodory s conditions and discontinuity several examples are given to illustrate the applicability of these results

sobolev s spaces on time scales and its applications to a class of second order hamiltonian systems on time scales abstract in this paper we study the sobolev s spaces on time scales and their properties as applications we present a recent approach via variational methods and the critical point theory to obtain the existence of solutions for a class of second order hamiltonian systems on time scales by establishing a proper variational setting three existence results for systems under consideration are obtained finally three examples are presented to illustrate the feasibility and effectiveness of the existence results

mac magnetostatic active contour model we propose an active contour model using an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries the major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations weak edges and broken boundaries the proposed method is shown to achieve significant improvements when compared against six well known and state of the art shape recovery methods including the geodesic snake the generalized version of gradient vector flow gvf snake the combined geodesic and gvf snake and the charged particle model

line integrals and green s formula on time scales in this paper we study curves parametrized by a time scale parameter introduce line delta and nabla integrals along time scale curves and obtain an analog of green s formula in the time scale setting

stability criteria for set dynamic equations on time scales very recently a new theory known as set dynamic equations on time scales has been built in this paper notions of stability for the solutions of set dynamic equations on time scales using lyapunov like functions are considered criteria for the equistability equiasymptotic stability uniform and uniform asymptotic stability are developed

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

implicit polynomial representation through a fast fitting error estimation this paper presents a simple distance estimation for implicit polynomial fitting it is computed as the height of a simplex built between the point and the surface i e a triangle in 2 d or a tetrahedron in 3 d which is used as a coarse but reliable estimation of the orthogonal distance the proposed distance can be described as a function of the coefficients of the implicit polynomial moreover it is differentiable and has a smooth behavior hence it can be used in any gradient based optimization in this paper its use in a levenberg marquardt framework is shown which is particularly devoted for nonlinear least squares problems the proposed estimation is a generalization of the gradient based distance estimation which is widely used in the literature experimental results both in 2 d and 3 d data sets are provided comparisons with state of the art techniques are presented showing the advantages of the proposed approach

factorization method on time scales abstract we present an approach to the factorization method for second order difference equations on time scales we construct hilbert spaces of functions on the time scale and show how to construct a chain of intertwined first order difference operators a k in the sense that a k and a k act as ladder operators generating new solutions of eigenproblem of a k a k

stabilization of parametric active contours using a tangential redistribution term depending on implementation active contours have been classified as geometric or parametric active contours parametric contours irrespective of representation are known to suffer from the problem of irregular bunching and spacing out of curve points during the curve evolution in a spline based implementation of active contours this leads to occasional formation of loops locally and subsequently the curve blows up due to instabilities in this paper we analyze the reason for this problem and propose a solution to alleviate the same we propose an ordinary differential equation ode for controlling the curve parametrization during evolution by including a tangential force we show that the solution of the proposed ode is bounded we demonstrate the effectiveness of the proposed method for segmentation and tracking tasks on closed as well as open contours

on stabilisability of nonlinear systems on time scales in this article stabilisability of nonlinear finite dimensional control systems on arbitrary time scales is studied the classical results on stabilisation of nonlinear continuous time and discrete time systems are extended to systems on arbitrary time scales with bounded graininess function it is shown that uniform exponential stability of the linear approximation of a nonlinear system implies uniform exponential stability of the nonlinear system then this result is used to show a similar implication for uniform exponential stabilisability

stability and periodicity in dynamic delay equations let t be an arbitrary time scale that is unbounded above by means of a variation of lyapunov s method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations x d t a t x d t d d t moreover if t is a periodic time scale then necessary conditions are given for the existence of a unique periodic solution of the above mentioned equation

foundations of nabla fractional calculus on time scales and inequalities here we develop the nabla fractional calculus on time scales then we produce related integral inequalities of types poincare sobolev opial ostrowski and hilbert pachpatte finally we give inequality applications on the time scales r z

hyperfocal subalgebras of blocks and computation of characters abstract in terms of puig s theory on blocks it is described how to compute the irreducible characters of any block from the hyperfocal subalgebra of the block and the source algebra and the characters of a block whose hyperfocal subgroup is a direct factor of its defect group are characterized

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

mimetic methods on measure chains we introduce the divergence and the gradient for functions defined on a measure chain and this includes as special cases both continuous derivatives and discrete forward differences it is shown that in one dimension subject to dirichlet boundary conditions the divergence and the gradient are negative adjoints of each other and that the divergence of the gradient is negative semidefinite these are well known results in tile continuous theory and hence mimic those properties also for the case of a general measure chain 2001 elsevier science ltd all rights reserved

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

image segmentation using active contours calculus of variations or shape gradients we consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals we show that one can go from one class to the otherby solving poisson s orhelmholtz s equation with well chosen boundar y conditions using this equivalence we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding euler lagrange equations we revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals we also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding gateaux derivatives and euler lagrange equations finally we apply this new functional to the problem of regions segmentation in sequences of color images we briefly describe our numerical scheme and show some experimental results

a non autonomous hamiltonian system on time scales abstract in this paper we are concerned with a second order non autonomous hamiltonian system on time scales t of the form u 2 t f t u t a e t 0 t t u 0 u t 0 u 0 u t 0 some results on the existence and multiplicity of periodic solutions are obtained for the hamiltonian system by means of the saddle point theorem the least action principle as well as the three critical point theorem

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

l2 spaces and boundary value problems on time scales abstract in this paper we consider a second order sturm liouville type boundary value operator of the form l u p u q u on an arbitrary bounded time scale t for suitable functions p q together with suitable boundary conditions operators of this type on time scales have normally been considered in a setting involving banach spaces of continuous functions on t in this paper we introduce a space l 2 t of square integrable functions on t and sobolev type spaces h n t n 1 consisting of l 2 t functions with nth order generalised l 2 t type derivatives we prove some basic functional analytic results for these spaces and then formulate the operator l in this setting in particular we allow p h 1 t while q l 2 t this generalises the usual conditions that p c rd 1 t q c rd 0 t 2 we give some immediate applications of the functional analytic results to l such as positivity injectivity invertibility and compactness of the inverse we also construct a green s function for l the analogues of these results on real intervals are well known and are fundamental to the usual sturm liouville theory on such intervals

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

efficient energies and algorithms for parametric snakes parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity however they have a few drawbacks which limit their performance in this paper we identify some of these problems and propose efficient solutions to get around them the widely used gradient magnitude based energy is parameter dependent its use will negatively affect the parametrization of the curve and consequently its stiffness hence we introduce a new edge based energy that is independent of the parameterization it is also more robust since it takes into account the gradient direction as well we express this energy term as a surface integral thus unifying it naturally with the region based schemes the unified framework enables the user to tune the image energy to the application at hand we show that parametric snakes can guarantee low curvature curves but only if they are described in the curvilinear abscissa since normal curve evolution do not ensure constant arc length we propose a new internal energy term that will force this configuration the curve evolution can sometimes give rise to closed loops in the contour which will adversely interfere with the optimization algorithm we propose a curve evolution scheme that prevents this condition

geodesic active contours and level sets for the detection and tracking of moving objects this paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model this model is composed of two components namely the static background and the mobile moving objects one both components are zero mean and obey laplacian or gaussian law this statistical framework is used to provide the motion detection boundaries additionally the original frame is used to provide the moving object boundaries then the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function this function is minimized using a gradient descent method a new approach named hermes is proposed which exploits aspects from the well known front propagation algorithms and compares favorably to them very promising experimental results are provided using real video sequences

control of fusion and solubility in fusion systems abstract in this article we consider control of fusion quotients and p soluble fusion systems for control of fusion we prove the three main theorems in the literature in a new largely elementary way significantly shortening their proofs to prove one of these and a theorem of aschbacher that the product of strongly closed subgroups is strongly closed we produce a consolidated treatment of quotients collating and expanding the constructions previously available we include analogues of the isomorphism theorems for fusion systems we move on to p soluble fusion systems and prove that they are constrained allowing us to effectively characterize fusion systems of p soluble groups this leads us to recast thompson factorization for q d p free fusion systems and consider it for more general fusion systems

stability in delay difference equations with nonuniform exponential behavior abstract we study the stability under perturbations for delay difference equations in banach spaces namely we establish the nonuniform stability of linear nonuniform exponential contractions under sufficiently small perturbations we also obtain a stable manifold theorem for perturbations of linear delay difference equations admitting a nonuniform exponential dichotomy and show that the stable manifolds are lipschitz in the perturbation

the concept of spectral dichotomy for linear difference equations abstract this paper is concerned with two notions of dichotomies for linear difference equations in banach spaces we introduce the new concept of spectral dichotomy and relate it to the known notion of exponential dichotomy the equations we consider are in general not supposed to have invertible right hand sides

on gain adaptation in adaptive control the adaptive high gain output feedback strategy u t k t y t d dt k t spl par y t spl par sup 2 is well established in the context of linear minimum phase m input m output systems a b c with the property that spec cb spl sub spl copf sub the strategy applied to any such linear system achieves the performance objectives of 1 global attractivity of the zero state and 2 convergence of the adapting gain to a finite limit here these results are generalized in three aspects first the class of systems is enlarged to a class n sub h spl mu encompassing nonlinear systems modeled by functional differential equations where the parameter h spl ges 0 quantifies system memory and the continuous function spl mu 0 spl infin spl rarr 0 spl infin with spl mu 0 0 relates to the allowable system nonlinearities next the linear control law is replaced by u t k t y t spl mu spl par y t spl par spl par y t spl par y t wherein the additional nonlinear term counteracts the system nonlinearities then the quadratic adaptation law is replaced by the law d dt k t spl psi spl par y t spl par where the continuous function spl psi satisfies certain growth conditions determined by spl mu in particular cases e g linear systems a bounded function spl psi is admissible the above performance objectives 1 and 2 are shown to persist in the generalized framework

generalized gradients priors on minimization flows this paper tackles an important aspect of the variational problem underlying active contours optimization by gradient flows classically the definition of a gradient depends directly on the choice of an inner product structure this consideration is largely absent from the active contours literature most authors explicitely or implicitely assume that the space of admissible deformations is ruled by the canonical l 2 inner product the classical gradient flows reported in the literature are relative to this particular choice here we investigate the relevance of using i other inner products yielding other gradient descents and ii other minimizing flows not deriving from any inner product in particular we show how to induce different degrees of spatial consistency into the minimizing flow in order to decrease the probability of getting trapped into irrelevant local minima we report numerical experiments indicating that the sensitivity of the active contours method to initial conditions which seriously limits its applicability and efficiency is alleviated by our application specific spatially coherent minimizing flows we show that the choice of the inner product can be seen as a prior on the deformation fields and we present an extension of the definition of the gradient toward more general priors

nonlinear integro differential equations and optimal control problems on time scales this paper is mainly concerned with a class of optimal control problems of a system governed by the nonlinear integro differential equation on time scales using the contraction mapping principle the existence and uniqueness of a weak solution of the nonlinear integro differential equation on time scales are proved discussing l t 1 strong weak lower semicontinuity of integral functional on time scales we give sufficient conditions for the existence of optimal control by the virtue of the integration by parts formula on time scales the necessary conditions of optimality are derived

regularized laplacian zero crossings as optimal edge integrators we view the fundamental edge integration problem for object segmentation in a geometric variational framework first we show that the classical zero crossings of the image laplacian edge detector as suggested by marr and hildreth inherently provides optimal edge integration with regard to a very natural geometric functional this functional accumulates the inner product between the normal to the edge and the gray level image gradient along the edge we use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models we also incorporate a 2d geometric variational explanation to the haralick edge detector into the geometric active contour framework

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

representations and ostrowski type inequalities on time scales here we give univariate and multivariate representations of the montgomery type for hybrid functions on time scales based on these we establish univariate and multivariate ostrowski type inequalities on time scales domains these compare the average of a function to its values the estimates involve the higher order delta and nabla derivatives and partial derivatives we finish with applications on the time scales r and z

integration on time scales in this paper we study the process of riemann and lebesgue integration on time scales the relationship of the riemann and lebesgue integrals is considered and a criterion for riemann integrability is established

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

existence uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales abstract in this paper we study the existence and uniqueness of solution and stability results of mixed integral dynamic system with instantaneous and noninstantaneous impulses on time scales by using the fixed point method the main tools to establish our results are the gronwall s inequality on time scales picard operator and abstract gronwall lemma some assumptions are made to overcome the hurdles in achieving our results at the end an example is given that shows the validity of our main results

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

necessary conditions of optimality for a class of optimal control problems on time scales a class of optimal control problems of a system governed by linear dynamic equations on time scales with quadratic cost functional is considered by the lebesgue d integral theory and the sobolev type space h 1 on time scales the weak solution of linear dynamic equations on time scales for both initial value problem and backward problem are introduced therefore the necessary conditions of optimality are presented some typical examples are given for demonstration

on the exponential stability of dynamic equations on time scales in this paper we deal with some theorems on the exponential stability of trivial solution of time varying non regressive dynamic equation on time scales with bounded graininess in particular well known perron s theorem is generalized on time scales under rather restrictive condition that is integral boundedness of coefficient operators we obtain a characterization of the uniformly exponential stability

on a disconjugacy criterion for second order dynamic equations on time scales in this paper a sufficient condition for disconjugacy of second order differential equations on time scales is given for this purpose a mean value result on time scales is employed

stability for first order delay dynamic equations on time scales in this paper we establish some sufficient conditions for the uniform stability and the uniformly asymptotical stability of the first order delay dynamic equation x d t p t x t t t 0 t t where t is a time scale p is rd continuous and positive the delay function t t 0 r our results unify the corresponding ones for differential and difference equations to the best of our knowledge this is the first time to discuss the asymptotical behavior of delay dynamic equations on time scales

the number of irreducible brauer characters in a p block of a finite group with cyclic hyperfocal subgroup abstract we show that a p block b of a finite group g with cyclic hyperfocal subgroup and the inertial index e has exactly e irreducible brauer characters

weak solutions for the dynamic cauchy problem in banach spaces abstract this paper is devoted to unify and extend the results of the existence of the weak solutions of continuous and discrete cauchy problem in banach spaces we offer the existence of the weak solution of dynamic cauchy problem on an infinite time scale the measure of weak noncompactness and the fixed point theorem of kubiaczyk are used to prove the main result

high gain robust adaptive controllers for multivariable systems abstract this paper extends the switching free high gain stabilizing adaptive control rules of byrnes and willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback perturbations

solvability of sturm liouville problems on time scales at resonance under the appropriate growth conditions on the inhomogeneous term we present the existence of the nontrivial solution for sturm liouville boundary value problems on time scales at resonance by making use of coincidence degree theory of mawhin the interesting point is the nonlinearity f which is involved with first order d derivative explicitly

on blocks of finite groups with central hyperfocal subgroups abstract let b be a p block of a finite group g with a defect group p and a hyperfocal subgroup q p let c be a block of n g q associated with b we show that if q z p then the brauer categories of b and c are equal we show that if q is abelian and g is p solvable then b and c are morita equivalent moreover we show that if b is the principal block q is cyclic and q z p then b and c are isotypic

automated b spline curve representation incorporating mdl and error minimizing control point insertion strategies the main issues of developing an automatic and reliable scheme for spline fitting are discussed and addressed in this paper which are not fully covered in previous papers or algorithms the proposed method incorporates b spline active contours the minimum description length mdl principle and a novel control point insertion strategy based on maximizing the potential for energy reduction maximization perm a comparison of test results shows that it outperforms one of the better existing methods

on the connection between the hilger and radon nikodym derivatives abstract we show that the hilger derivative on time scales is a special case of the radon nikodym derivative with respect to the natural measure associated with every time scale moreover we show that the concept of delta absolute continuity agrees with the one from measure theory in this context

on the evolution of curves via a function of curvature i the classical case abstract the problem of curve evolution as a function of its local geometry arises naturally in many physical applications a special case of this problem is the curve shortening problem which has been extensively studied here we consider the general problem and prove an existence theorem for the classical solution the main theorem rests on lemmas that bound the evolution of length curvature and how far the curve can travel

stability analysis of a class of switched linear systems on non uniform time domains abstract this paper deals with the stability analysis of a class of switched linear systems on non uniform time domains the considered class consists of a set of linear continuous time and linear discrete time subsystems first some conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function when the subsystems are exponentially stable these results are extended when considering an unstable discrete time subsystem or an unstable continuous time subsystem some examples illustrate these results

on stability bohl exponent and bohl perron theorem for implicit dynamic equations in this paper we develop a stability theory for implicit dynamic equations which is a general form of differential algebraic equations and implicit difference equations we derive some results abo

on existence of optimal control governed by a class of the first order linear dynamic systems on time scales in this paper by using the approximation of classical solution we introduce the definition of solution and prove the existence and uniqueness of solutions of the first order linear dynamic systems on time scales existence of lagrange optimal control problem governed by the first order linear dynamic systems on time scales is also presented for illustration some examples of optimal control problems on time scales are also discussed

stability by linear approximation for time scale dynamical systems abstract we study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods in this paper we consider linear systems and their small nonlinear perturbations in terms of time scales and of eigenvalues of matrices we formulate conditions sufficient for stability by linear approximation for non periodic time scales we use techniques of central upper lyapunov exponents a common tool of the theory of linear odes to study stability of solutions also time scale versions of the famous chetaev s theorem on conditional instability are proved in a nutshell we have developed a completely new technique in order to demonstrate that methods of non autonomous linear ode theory may work for time scale dynamics

absolute continuity and existence of solutions to dynamic inclusions in time scales we provide some properties for absolutely continuous functions in time scales then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question we also introduce the so called euler solution to dynamical systems in time scales and prove its existence a combination of the existence of euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty compact convex and has closed graph

multiple positive solutions of singular dirichlet problems on time scales via variational methods abstract this paper is devoted to using variational techniques and critical point theory to derive some sufficient conditions for the existence of multiple positive solutions to a singular second order dynamic equation with homogeneous dirichlet boundary conditions

on exponential dichotomy bohl perron type theorems and stability of difference equations abstract for a delay difference equation x n 1 k d n a n k x k f n in a banach space the following result is proved if for any f l p the solution is x l p then the solution of the homogeneous equation f 0 is exponentially stable this result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation