same decay rate of second order evolution equations with or without delay abstract we consider abstract second order evolution equations with unbounded feedback with delay if the delay term is small enough we rigorously prove the fact that the system with delay has the same decay rate than the one without delay some old and new results easily follow

segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

orbits and phase transitions in the multifractal spectrum we consider the one dimensional classical ising model in a symmetric dichotomous random field the problem is reduced to a random iterated function system rifs for an effective field the dq spectrum of the invariant measure of this effective field exhibits a sharp drop of all dq with q 0 at some critical strength of the random field we introduce the concept of orbits which naturally group the points of the support of the invariant measure we then show that the pointwise dimension at all points of an orbit has the same value and calculate it for a class of periodic orbits and their so called offshoots as well as for generic orbits in the non overlapping case the sharp drop in the dq spectrum is analytically explained by a drastic change of the scaling properties of the measure near the points of a certain periodic orbit at a critical strength of the random field which is explicitly given a similar drastic change near the points of a special family of periodic orbits explains a second hitherto unnoticed transition in the dq spectrum as it turns out a decisive role in this mechanism is played by a specific offshoot we furthermore give rigorous upper and or lower bounds on all dq in a wide parameter range in most cases the numerically obtained dq coincide with either the upper or the lower bound the results in this paper are relevant for the understanding of rifss in the case of moderate overlap in which periodic orbits with weak singularity can play a decisive role

two dimensional critical point configuration graphs the configuration of the critical points of a smooth function of two variables is studied under the assumption that the function is morse that is that all of its critical points are nondegenerate a critical point configuration graph cpcg is derived from the critical points ridge lines and course lines of the function then a result from the theory of critical points of morse functions is applied to obtain several constraints on the number and type of critical points that appear on cycles of a cpcg these constraints yield a catalog of equivalent cpcg cycles containing four entries the slope districts induced by a critical point configuration graph appear useful for describing the behavior of smooth functions of two variables such as surfaces images and the radius function of three dimensional symmetric axes

green s matrix for a second order self adjoint matrix differential operator a systematic construction of the green s matrix for a second order self adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out we follow the general approach of extracting the green s matrix from the green s matrix of the corresponding first order system this construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques

on the stabilization of an overhead crane system with dynamic and delayed boundary conditions this article is dedicated to the investigation of long time behavior of an overhead crane with input delays in the boundary control contrary to previous works the compensating terms in the proposed feedback control law are not of the same type as the delayed term next the closed loop system is shown to be well posed in the sense of semigroups theory furthermore the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data is obtained by applying lasalle s invariance principle then the convergence rate is shown to be exponential by means of the frequency domain method the asymptotic distribution of the eigenvalues as well as the eigenfunctions of the system are also provided based on which the differentiability of its semigroup is proved and hence the spectrum determined growth condition holds finally the outcomes are illustrated by a set of numerical simulations

surface curvature as a measure of image texture methods from the theory of surfaces in differential geometry are applied to the gray tone intensity and absorbance surfaces defined by a digital image in particular the first fundamental form the second fundamental form the two principal curvatures the gaussian curvature and mean curvature from classical differential geometry are presented new curvatures are introduced which appear to be more appropriate for the purposes of image texture for each curvature a texture feature is generated these features are applied to biological cell nuclei and it is found that they are useful for purposes of discrimination

stabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedback we consider the stabilization of the wave equation with variable coefficients and a delay in the dissipative boundary feedback by virtue of the riemannian geometry methods the energy perturbed approach and the multiplier skills we establish the uniform stability of the energy of the closed loop system

stabilization of an unstable reaction diffusion pde cascaded with a heat equation abstract we consider a control problem of an unstable reaction diffusion parabolic pde cascaded with a heat equation through a boundary where the heat influx of the heat equation is fed into the temperature of the reaction diffusion equation and the control actuator is designed at the another boundary of the heat equation a backstepping invertible transformation is used to design a suitable boundary feedback control so that the closed loop system is equivalent to a cascade of pde pde system which is shown to be exponentially stable in a suitable hilbert space with the dirichlet boundary input from the heat equation the reaction diffusion pde is shown to be exponentially stable in h 1 0 1 numerical simulations are presented to illustrate the convergence of the state of the reaction diffusion equation

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

two examples of ill posedness with respect to small time delays in stabilized elastic systems two examples of elastic control systems that are uniformly stabilized by feedback controls on their boundaries for which divergence rates can be obtained when small time delays are introduced into their feedbacks are presented

two examples of ill posedness with respect to time delays revisited we revisit two examples of elastic control systems which are stabilized by boundary feedback and then destabilized when time delays occur in the feedback in the first example a wave equation with a feedback gain greater than or equal to one arbitrary divergence rates are obtained for small time delays in the second example a euler bernoulli beam any time delay results in an arbitrary divergence rate

conditions for robustness and nonrobustness of thestability of feedback systems with respect to small delays inthe feedback loop it has been observed that for many stable feedback control systems the introduction of arbitrarily small time delays into the loop causes instability in this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems we consider the class of all matrix valued transfer functions which are bounded on some right half plane and which have a limit at spinfty along the real axis such transfer functions are called regular under the assumption that a regular transfer function is stabilized by unity output feedback we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop these conditions are given in terms of the high frequency behavior of the open loop system moreover we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators in particular we show that if a plant with infinitely many poles in the closed right half plane is stabilized by a controller then the stability is not robust with respect to delays we show that the instability created by small delays is itself robust to small delays three examples are given to illustrate these results

output feedback stabilization of a one dimensional schrodinger equation by boundary observation with time delay in this article we are concerned with the stabilization of a 1 d schrodinger equation with boundary control and observation the boundary observation is suffered from an arbitrary given time delay we first show that the proportional output feedback control that stabilizes exponentially the time delay free system can not stabilize the corresponding time delay system anymore we then use the observer and predictor to solve the stabilization problem of time delay system the state is estimated in the time span where the observation is available and the state is predicted in the time interval when the observation is not available it is shown that the estimated state feedback stabilizes exponentially the time delay system the numerical simulation is presented to illustrate the effect of the stabilizing controller

on the stabilization and stability robustness against small delays of some damped wave equations in this paper we consider a system which can be modeled by two different one dimensional damped wave equations in a bounded domain both parameterized by a nonnegative damping constant we assume that the system is axed at one end and is controlled by a boundary controller at the other end we consider two problems namely the stabilization and the stability robustness of the closed loop system against arbitrary small time delays in the feedback loop we propose a class of dynamic boundary controllers and show that these controllers solve the stabilization problem when the damping coefficient is nonnegative and the stability robustness problem when the damping coefficient is strictly positive

noncommutative torus from fibonacci chains via foliation we classify the fibonacci chains f chains by their index sequences and construct an approximately finite dimensional af c algebra on the space of f chains as connes did on the space of penrose tiling the k theory on this af algebra suggests a connection between the noncommutative torus and the space of f chains a noncommutative torus which can be regarded as the c algebra of a foliation on the torus is explicitly embedded into the af algebra on the space of f chains as a counterpart of that we obtain a relation between the space of f chains and the leaf space of kronecker foliation on the torus using the cut procedure of constructing f chains our embedding of the c algebra of the foliation is consistent with the recent result of landi lizzi and szabo that the c algebra of noncommutative torus can be embedded into an af algebra

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

stability analysis of heat flow with boundary time varying delay effect abstract in this paper we investigate the stabilization of heat flow with boundary time varying delay effect under some assumptions we prove exponential stability of the solution applying variable norm technique and modified lyapunov functional approach

global well posedness and exponential stability for heterogeneous anisotropic maxwell s equations under a nonlinear boundary feedback with delay abstract we consider an initial boundary value problem for the maxwell s system in a bounded domain with a linear nonhomogeneous anisotropic instantaneous material law subject to a nonlinear silver muller type boundary feedback mechanism incorporating both an instantaneous damping and a time localized delay effect by proving the maximal monotonicity property of the underlying nonlinear generator we establish the global well posedness in an appropriate hilbert space further under suitable assumptions and geometric conditions we show the system is exponentially stable

multi focus image fusion based on the neighbor distance the effective measurement of pixel s sharpness is a key factor in multi focus image fusion in this paper a gray image is considered as a two dimensional surface and the neighbor distance deduced from the oriented distance in differential geometry is used as a measure of pixel s sharpness where the smooth image surface is restored by kernel regression based on the deduced neighbor distance filter we construct a multi scale image analysis framework and propose a multi focus image fusion method based on the neighbor distance the experiments demonstrate that the proposed method is superior to the conventional image fusion methods in terms of some objective evaluation indexes such as spatial frequency standard deviation average gradient etc

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

the exponential stability region of timoshenko beam with interior delays and boundary damping abstractin this paper we investigate the exponential stability of a timoshenko beam with interior time delays and boundary damping at first we show that the system is well posed by the semigroup method next we construct an appropriate functional to study the exponential stability we transform the exponential stability into the solvability of inequality equations and then by analysing the relationship between delays parameters 1 2 and damping parameters 1 2 we describe the 1 2 region for which the system is exponentially stable

wave equation stabilization by delays equal to even multiples of the wave propagation time for a string equation with time delays in the output feedback loop we study stability and show that the system is a riesz spectral system and prove that the spectrum determined growth condition holds for all delays when the delay is equal to the even multiples of the wave propagation time we develop the necessary and sufficient conditions for the feedback gain and time delay which guarantee the exponential stability of the closed loop system in particular we show that as the delay of even multiples is increasing to infinity the stability bound on the feedback gain decays to zero we also show that whenever the delay is an odd multiple of the wave propagation time the closed loop system is unstable the lack of robustness to a small perturbation in time delay is specifically discussed for the delay equal to two a numerical simulation for the case of the delay equal to two is presented to illustrate the convergence finally an alternative stability analysis is conducted within the framework of well posed infinite dimensional systems

two questions concerning the boundary control of certain elastic systems abstract we present two questions connected with the stabilization of certain hyperbolic partial differential equations which are controlled on their boundaries the uncontrolled versions of these systems are conservative and therefore represent only approximate realizations of the physical phenomena the first question concerns the qualitative behavior of a given stabilizing feedback for such a system vis a vis that of an appropriately damped realization using the same feedback the second question concerns the robustness of both the original system and a damped version when time delays occur in a given feedback stabilization scheme

strong stability of neutral equations with an arbitrary delay dependency structure the stability theory for linear neutral equations subjected to delay perturbations is addressed it is assumed that the delays cannot necessarily vary independently of each other but depend on a possibly smaller number of independent parameters as a main result necessary and sufficient conditions for strong stability are derived along with bounds on the spectrum which take into account the precise dependency structure of the delays in the derivation of the stability theory results from realization theory and determinantal representations of multivariable polynomials play an important role the observations and results obtained in the paper are first illustrated and validated with a numerical example next the effects of small feedback delays on the stability of a boundary controlled hyperbolic partial differential equation and of a control system involving state derivative feedback are analyzed

a symmetric green function for the non collinear magnetic multilayer symmetry properties of the green function in magnetic multilayers with non collinear magnetization of the layers are investigated on the basis of the transfer matrix method the green function symmetric with respect to permutation of its arguments is constructed it is shown how the boundary conditions can be imposed on this green function

reeb graphs for shape analysis and applications reeb graphs are compact shape descriptors which convey topological information related to the level sets of a function defined on the shape their definition dates back to 1946 and finds its root in morse theory reeb graphs as shape descriptors have been proposed to solve different problems arising in computer graphics and nowadays they play a fundamental role in the field of computational topology for shape analysis this paper provides an overview of the mathematical properties of reeb graphs and reconstructs its history in the computer graphics context with an eye towards directions of future research

sensitivity to infinitesimal delays in neutral equations the stability of a steady state solution of a neutral functional differential equation can be sensitive to infinitesimal changes in the delays this phenomenon is caused by the behavior of the essential spectrum and is determined by the roots of an exponential polynomial avellar and hale j math anal appl 73 1980 pp 434 452 have considered the case of multiple fixed and nonzero delays in the first part of this paper their results are illustrated by means of spectral plots in the second part we extend the theory of avellar and hale to the limit case whereby some of the delays are brought to zero which may lead to characteristic roots with arbitrarily large real part necessary and sufficient conditions are provided using these results we show that the ratio of the delays plays a crucial role when several delays tend to zero simultaneously as an illustration of the theory we analyze the robustness of a boundary controlled pde in the presence of a small feedback delay

a paradigm of ill posedness with respect to time delays the authors present a simple general model of an infinite dimensional control system which is stabilized by a velocity feedback but then destabilized by small or large time delays in the feedback this model is in some sense generic for boundary stabilized conservative hyperbolic linear partial differential equations

singularities of principal direction fields from 3 d images generic singularities can provide position independent information about the qualitative shape of surfaces the authors determine the singularities of the principal direction fields of a surface its umbilic points from a computation of the index of the fields the authors present examples both for 3 d synthetic images to which noise has been added and for clinical magnetic resonance images

a note on stabilization of locally damped wave equations with time delay abstract in this paper we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain r n when the local damping acts on a neighborhood of a suitable part of the boundary of we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small

approximation of granular textures by quadric surfaces abstract the method to compute the best biquadratic form approximating an image on neighbourhoods of sizes 3 3 to 9 9 pixels is given when this quadric surface is an elliptic paraboloid various geometric parameters are expressed in terms of quadric coefficients they are the exact position of the apex the height direction eccentricity projected area and mean and gaussian curvatures two examples of approximation by elliptic paraboloids are then presented on two kinds of images radiographs of metallic pieces and histological sections

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

curvature based normalized 3d component facial image recognition using fuzzy integral the depth information in the face represents personal features in detail in particular the surface curvatures extracted from the face contain the most important personal facial information in this paper we develop a method for recognizing 3d face images by combining face component fisherface method and fuzzy integral for the proposed approach the first step uses face curvatures which present the facial features for 3d face images after normalization using the svd as a result of this process we obtain curvature feature for each component range face pca and fisherface method are then applied to each component range face the reason for adapting pca and fisherface method is that the methods maintain the surface attribute for face curvature even though they can generate reduced image dimension in the last step the aggregation of the individual classifiers using the fuzzy integral is explained for each component the experimental results show that the proposed approach has outstanding classification in comparing with other methods

pointwise stabilisation of a string with time delay in the observation abstractpointwise stabilisation is proposed in this paper for a string equation where the observation signal is subject to a time delay different from the boundary control the feedback stabiliser is acting at the middle joint of the string well posedness of the open loop system and solvability of the observer are shown first an observer system is then designed to estimate the state at the time interval when the observation is available and a predictor system is designed to predict the state at the time interval when the observation is not available pointwise output feedback controller is introduced to make the closed loop system asymptotically stable for the non smooth initial values and exponentially stable for the smooth initial values respectively simulation results demonstrate that the output feedback based on the observer and predictor effectively stabilises the pointwise control system with time delay