hessian estimates in orlicz spaces for fourth order parabolic systems in non smooth domains abstract we establish the global hessian estimate in orlicz spaces for a fourth order parabolic system with discontinuous tensor coefficients in a non smooth domain under the assumptions that the coefficients have small weak bmo semi norms the boundary of a domain is reifenberg flat for 0 small and the given young function satisfies some moderate growth condition as a corollary we obtain an optimal global w 2 p regularity for such a system

robust partial shape classification using invariant breakpoints and dynamic alignment abstract a system for classifying partially occluded noisy shapes in varying positions orientations and dimensions is described an iterative algorithm derived from the colinearity principle is developed to locate invariant breakpoints on a shape contour the set of invariant breakpoints partitions the contour into a sequence of contour segments each contour segment is described by an ordered sequence that represents the euclidean distance between the pixels in the contour segment and the centroid of the region formed by connecting the end points of the contour segment by a straight line two stages of dynamic alignment with the appropriate constraints are formulated to determine shape similarity the first stage gives a distance measure of contour segment similarity and in the second stage the intersegment distances are used to optimally align contour segments so that a final measure of shape similarity is obtained the performance of the system is demonstrated by considering the classification of aircraft shapes belonging to four classes and classification results are presented as functions of noise and occlusion levels the results indicate that reasonable classification is obtained for noisy shapes with 0 to 30 occlusion

non linear alignment of neural net outputs for partial shape classification abstract a neural network approach to the partial shape classification problem is derived although neural networks are generally robust static pattern classifiers they are not effective in classifying patterns with inherent temporal variations in order to compensate for temporal variations resulting from random partial occlusion a multi neural network system which includes a dynamic alignment procedure at the neural net outputs is proposed in formulating the dynamic alignment stage a similarity measure between an input and the neural net outputs is defined combining the robustness of neural networks with the non linear alignment capability of dynamic alignment results in a classifier which can tolerate high degrees of random noise and random occlusion in shapes

multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions abstract in this paper we study the existence of multiple solutions for the integral boundary value problems of fractional differential equations by the method of upper and lower solutions and leray schauder degree theory the sufficient conditions about the existence of at least three solutions are obtained moreover it is proved that the integral boundary value problem has at least three positive solutions under the conditions of m 0 and f is nonnegative by given two upper and lower solutions which can be easily obtained through our methods we can present the existence theorem of at least three solutions two examples are also included to illustrate the effectiveness of the proposed results

higher integrability result for nonlinear elliptic systems with conormal boundary conditions abstract we prove a boundary higher integrability result for nonlinear elliptic systems with conormal boundary conditions in locally uniform domains to do it we derive a boundary version of gehring giaquinta modica lemma and sobolev poincare type inequality in locally uniform domains our result plays a key role for handling the coefficients when obtaining caldero n zygmund type estimates with conormal boundary conditions in nonsmooth domains

uniqueness and existence results for a third order nonlinear multi point boundary value problem this paper provides sufficient conditions for the existence and uniqueness of solutions to a nonlinear multi point boundary value problem for third order differentia equation the nonlinear term f in the differential equation under consideration may depend on second order derivative the emphasis here is the boundary conditions are nonlinear and this is where the main novelty of this work lies by applying the upper and lower solutions method as well as degree theory the existence and uniqueness results of the problem are established some examples are given to demonstrate the main results

gradient estimates for higher order elliptic equations on nonsmooth domains abstract we establish optimal gradient estimates in orlicz space for a nonhomogeneous elliptic equation of higher order with discontinuous coefficients on a nonsmooth domain our assumption is that for each point and for each sufficiently small scale the coefficients have small mean oscillation and the boundary of the domain is sufficiently close to a hyperplane as a consequence we prove the classical w m p m 1 2 1 p estimates for such a higher order equation our results easily extend to higher order elliptic and parabolic systems

neuro fuzzy reasoning for occluded object recognition abstract to tackle the problem of occluded object recognition first we give a new interpretation to the multidimensional fuzzy reasoning and then realize that new interpretation through backpropagation type neural network at the learning stage of the neural network fuzzy linguistic statements are used once learned the nonfuzzy features of an occluded object can be classified at the time of classification of the nonfuzzy features of an occluded object we use the concept of fuzzy singleton an effective approach to recognize an unknown scene which consists of a set of occluded objects is to detect a number of significant local features on the boundary of the unknown scene thus the major problems fall into the selection of the appropriate set of features local for representing the object in the training stage as well as in the detection of these features in the recognition process the features should be invariant to scale orientation and minor distortions in boundary shape the performance of the proposed scheme is tested through several examples

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

elliptic equations with bmo coefficients in reifenberg domains the inhomogeneous dirichlet problems concerning divergence form elliptic equations are studied optimal regularity requirements on the coefficients and domains for the w1 p theory 1 p are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms the domain is a reifenberg domain these conditions for the w1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains in fact these domains might have fractal dimensions 2004 wiley periodicals inc

monotone iterative method for the second order three point boundary value problem with upper and lower solutions in the reversed order abstract this article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order the sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method meantime the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given some results of previous literature are extended and improved a numerical example is also included to illustrate the effectiveness of the proposed results

elliptic equations with singular bmo coefficients in reifenberg domains abstract w 1 p estimate for the solutions of elliptic equations whose coefficient matrix can have large jump along the boundary of subdomains is obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms and the domain and subdomains are reifenberg flat domains moreover it has been shown that the estimates are uniform with respect to the distance between the subdomains

existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order abstract this paper studies the existence and uniqueness of solutions of second order three point boundary value problems with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution

multiplicity of solutions to two point boundary value problems for second order impulsive differential equations abstract in this paper we obtain some sufficient condition for the existence of at least three solutions to two point boundary value problems for second order impulsive differential equations by using leray schauder degree theory we assume the existence of two pairs of strict lower and upper solutions and the nonlinear term f satisfies a nagumo s growth condition with respect to the first order derivative

existence result for impulsive third order periodic boundary value problems this paper is devoted to the study of periodic boundary value problems for nonlinear third order differential equations subjected to impulsive effects we provide sufficient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one periodic solution our approach is based on a priori estimates the method of upper and lower solutions combined with an iterative technique which need not be monotone

finding contour based abstractions of planar patterns abstract an algorithm is described to detect a number of points on the contour of a planar shape which constitute the vertices of a schematic polygonal representation of the shape itself a set of points initially extracted from the chain coded representation of the contour is iteratively examined while removing some points and inserting new ones the number of selected points decreases in size from iteration to iteration and the selection process converges towards an expected perceptually significant set of points the polygon obtained by linking successive points approximates the contour in an intuitive way it is not constrained within a given tolerance and is likely to locally change from a coarse to a more faithful approximating shape in correspondence with contour regions increasing in details

existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions abstract this paper is concerned with the existence and approximation of solutions for a class of first order functional differential equations with periodic boundary conditions we present a new comparison result and extend previous results

monotone method for the neumann problem with lower and upper solutions in the reverse order this work is devoted to the study of the existence and approximation of solutions of the problem u f t u u u a u b 0 in the presence of lower and upper solutions in the reverse order to this end we prove anti maximum principles for the nonlinear operator u 2k u email protected

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

boundary value problems involving upper and lower solutions in reverse order in this paper we discuss the existence of extreme solutions of the boundary value problem for a class of first order functional equations with a nonlinear boundary condition in the presence of a lower solution a and an upper solution b with email protected email protected we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique

remarks on periodic boundary value problems for functional differential equations we extend some results on existence and approximation of solution for a class of first order functional differential equations with periodic boundary conditions we show the validity of the monotone iterative technique under weaker hypotheses and present some examples

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

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

an end point orlicz type estimate for nonlinear elliptic equations abstract we study nonlinear elliptic equations of p laplacian type in divergence form to establish a natural calderon zygmund type theory of an orlicz space type where the lebesgue space is the special case with t t q p f p l 1 q 2 r d u p l 1 q r in the previous results the estimates obtained were strictly above the natural exponents and the function such as t t log 1 t was ruled out for the candidate of but with our approach can be selected up to the end point case of the estimates and the functions t t and t t log 1 t can be additionally selected for

positive solutions for some second order four point boundary value problems abstract in this paper the second order four point boundary value problem x t h t f t x t 0 0 t 1 x 0 a x x 1 b x is studied where 0 1 0 a b 1 and h 0 1 0 f 0 1 0 0 are nonnegative continuous functions by the use of the property of the corresponding green s function fixed point index theory leray schauder degree and upper and lower solution method some existence nonexistence and multiplicity results of positive solutions are acquired

periodic boundary value problems for the second order functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problems for second order functional differential equations a new concept of lower and upper solutions is introduced and we present a new comparison principle meanwhile we extend previous results

nonlinear boundary value problem of first order impulsive functional differential equations this paper discusses nonlinear boundary value problem for first order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques two examples are discussed to illustrate the efficiency of the obtained results

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

global gradient estimates for nonlinear equations of p laplace type from composite materials abstract we study global gradient estimates for the weak solution to divergence form nonlinear elliptic equations with p growth nonlinearities from composite materials we assume that the domain is bounded and is composed of disjoint reifenberg flat domains and the nonlinearities have small bmo seminorms in each subdomain under these assumptions based on our new geometric observation for disjoint reifenberg domains and gradient estimates for nonlinear equations with measurable p growth nonlinearities we establish global w 1 q estimates for p q

gradient estimates for p laplacian equation in composite reifenberg domains abstract we obtain a local gradient estimate for weak solutions of p laplacian type equation in a non smooth domain composed of a finite number of disjoint subdomains with 0 r reifenberg flat boundaries this kind of domain was called 0 r composite reifenberg domain which allows certain subdomain to exist with highly non smooth boundaries worse than reifenberg domain our results improve the known results for such equations

a new numerical approach to solve an elliptic equation a new numerical approach to solve an elliptic partial differential equation that originates from the governing equations of steady state fluid flow and heat transfer is presented the elliptic partial differential equation is transformed by introducing an exponential function to eliminate the convection terms in the equation a fourth order central differencing scheme and a second order central differencing scheme are used to numerically solve the transformed elliptic partial differential equation analytical solutions of this equation are also given comparisons are made between the analytical solutions the numerical results using the present schemes and those using the four classical differencing schemes namely the first order upwind scheme hybrid scheme power law scheme and exponential scheme the comparisons illustrate that the proposed algorithm performs better than the four classical differencing schemes

the method of lower and upper solutions for fourth order singular m point boundary value problems abstract this paper investigates the existence of positive solutions for fourth order singular m point boundary value problems firstly we establish a comparison theorem then we define a partial ordering in c 2 0 1 c 4 0 1 and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 0 1 as well as c 3 0 1 positive solutions our nonlinearity f t x y may be singular at x y t 0 and or t 1

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

a discrepancy measure for improved clustering a discrepancy measure is proposed to improve the clustering of patterns which experience non linear distortions the discrepancy measure is an outcome of a non linear alignment procedure which optimally aligns the elements of patterns in order to minimize the dissimilarity between the patterns the k means clustering algorithm is modified to use the discrepancy measure to compute the similarity between patterns and the cluster centers a series of clustering experiments were conducted on identical data using the modified and standard k means algorithm the results obtained show that clustering performance of the modified algorithm is significantly superior to that of the standard algorithm

lp regularity for fourth order parabolic systems with measurable coefficients we treat fourth order parabolic systems in divergence form with bounded measurable coefficients we establish hessian estimates for such parabolic systems by proving that the lp regularity of the inhomogeneous terms exactly reflects in the regularity of the hessian of the solutions for every p in 1 infty the assumptions are that the coefficients are allowed to be merely measurable in one of spatial variables but averaged in the other spatial variables and time variable

third order moment spectrum and weighted fuzzy classifier for robust 2 d object recognition abstract in this paper a robust position scale and rotation invariant system for the recognition of closed 2 d noise corrupted images using the bispectral features of a contour sequence and the weighted fuzzy classifier are derived the higher order spectrum based on third order moment called a bispectrum is applied to the contour sequences of an image to extract a 15 dimensional feature vector for each of the 2 d images this bispectral feature vector which is invariant to shape translation scale and rotation transformation can be used to represent a 2 d planar image and is fed into a weighted fuzzy classifier for the recognition process the experiments with eight different shapes of aircraft images are presented to illustrate the high performance of the proposed system even when the image is significantly corrupted by noise

unbounded upper and lower solutions method for sturm liouville boundary value problem on infinite intervals abstract unbounded upper and lower solutions theories are established for the sturm liouville boundary value problem of a second order ordinary differential equation on infinite intervals by using such techniques and the schauder fixed point theorem the existence of solutions as well as the positive ones is obtained nagumo conditions play an important role in the nonlinear term involved in the first order derivatives

auto regressive shape classifiers in time varying noise abstract good results have been reported in a number of recent studies where auto regressive shape classifiers have been used to allocate objects to a pre determined number of classes it is shown that this approach may give unsatisfactory results when applied to imaging systems whose noise characteristics vary substantially over time such variation may be due to changes in atmospheric conditions or the relative effect of discretization errors observations are based on the reconstruction of a number of noisy synthetic templates

monotone iterative method for first order functional difference equations with nonlinear boundary value conditions in this paper we show that the method of monotone iterative coupled with the upper and lower solutions is valid to obtain constructive proofs to the existence of solutions for first order functional difference equations with nonlinear boundary value conditions an example is given to illustrate the results obtained

invariant planar shape recognition using dynamic alignment abstract closed planar shapes are modelled by an ordered sequence that represents the euclidean distance between the centroid and all contour pixels of the shape shapes belonging to the same class have similar sequences hence a procedure for classifying shapes is based on the degree of similarity between these sequences in order to determine the similarity between sequences a dynamic alignment process is developed to find the best correspondence between the sequences optimum alignment is obtained by expanding segments of the sequences to minimize a dissimilarity function between the sequences normalization with respect to scaling and rotation is described and an example illustrating the use of dynamic alignment for the classification of noisy shapes is presented

periodic boundary value problems of second order impulsive differential equations abstract this paper discusses periodic boundary value problems of second order impulsive differential equations by using schaeffer s fixed point theorem and monotone iterative technique some existence results are obtained

extremal solutions for third order nonlinear problems with upper and lower solutions in reversed order abstract this paper deals with the existence of extremal solutions for the third order nonlinear boundary value problem u t f t u t t a b u a a u a b u b c in the presence of a pair of lower and upper solutions in reversed order here r r is an increasing homeomorphism f a b r r is a carathedory function and a b c r the proof follows from monotone iterative techniques which are based on suitable anti maximum principles for adequate operators to deduce such results we study some related problems coupled with boundary value conditions of the form p 0 u a q 0 u a a p 1 u b q 1 u b b u a c and u a a u a b u b c

parabolic equations with bmo coefficients in lipschitz domains abstract in this paper we are concerned with certain natural sobolev type estimates for weak solutions of inhomogeneous problems for second order parabolic equations in divergence form the geometric setting is that of time independent cylinders having a space intersection assumed to be locally given by graphs with small lipschitz coefficients the constants of the operator being uniformly parabolic we prove the relevant l p estimates assuming that the coefficients are in parabolic bounded mean oscillation bmo and that their parabolic bmo semi norms are small enough

multiscale fourier descriptors for classifying semivowels in spectrograms abstract fourier descriptors fds have been used successfully to characterize the boundary of objects in images it is demonstrated that fds are appropriate for characterizing objects in speech spectrograms consisting of 40 sounds representing 10 speaker dependent words containing the english semivowels w y l r with 10 fds a 97 5 recognition rate is attained different sounds are misclassified by wide and narrow band methods suggesting that multiscaling and fd changes differences may be appropriate features with a fd difference approach recognition rates equaled or exceeded those obtained with a conventional linear predictive coding lpc classifier as well as those obtained with wide and narrow band fd methods alone

study on monotonicity of boundary value problems of differential equations this article presents two new test methods to decide monotonic increasing or decreasing properties of differential equations for simple problems the eigenfunction test method can be applied to obtain their exact monotonicity or their loosest conditional expression and can contribute to probes into accumulated effect of various terms in equations on their monotonicity secondly the trial function test method sets relatively strict conditions for discrimination of monotonicity but it can verify complex non linear problems in a simple and rapid way therefore these two similar test methods will help to further understand theories on monotonicity thus making it possible to apply monotonic equations more widely to other problems

the detection of dominant points on digital curves by scale space filtering the detection of dominant points is an important preprocessing step for shape recognition an effective method of scale space filtering with a gaussian kernel is introduced to detect dominant points on digital curves the conventional polygonal approximation algorithms are time consuming and need input parameter tuning for gaussian smoothing the noise and quantization error also they are sensitive to scaling and rotation of the object curve the above dit culty can be overcome by finding out the dominant points at each scale by scale space filtering by tracing back the dominant point contours in the scale space image the stable cardinal curvature points can be detected very accurately this new method requires no input parameters and the resultant dominant points do not change under translation rotation and scaling meanwhile a fast convolution algorithm is proposed to detect the dominant points at each scale dominant points scale space gaussian smoothing curvature

hessian estimates for fourth order elliptic systems with singular bmo coefficients in composite reifenberg domains abstract we consider fourth order elliptic systems in divergence form with greatly discontinuous coefficients in a nonsmooth domain our domain is composed of a finite number of disjoint subdomains with r reifenberg flat boundaries and the coefficients which are allowed to have great discontinuity across the boundaries of subdomains have small bmo semi norms on each subdomain our main result is deriving the global w 2 p 1 p regularity with the estimates independent of the distance between the subdomains

fourth order parabolic equations with weak bmo coefficients in reifenberg domains abstract we study optimal w 2 p regularity for fourth order parabolic equations with discontinuous coefficients in general domains we obtain the global w 2 p regularity for each 1 p under the assumption that the coefficients have suitably small bmo semi norm of weak type and the boundary of the domain is reifenberg flat the situation of our main theorem arises when the conductivity on fractals is controlled by a random variable in the time direction

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

a neural network approach to robust shape classification abstract a neural network approach for the classification of closed planar shapes is described the primary foci are the development of an effective representation for planar shapes which may be used in conjunction with neural nets the selection of a suitable neural network structure and determining training methods to increase the degree of robustness in classification a three layer perception using backpropagation is initially trained with contour sequences of noisefree reference shapes and its generalization capability is demonstrated the network is then gradually retrained with increasingly noisy data to improve the robustness of the classifier the advantages and improvement in robustness using this extended training scheme are shown and typical classification results are presented

periodic boundary value problems for the first order impulsive functional differential equations this paper is concerned with the existence of extreme solutions of the periodic boundary value problems for a class of first order functional differential equations we introduce new concept of lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

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

greenʼs function for first order multipoint boundary value problems and applications to the existence of solutions with constant sign abstract we consider a first order linear differential equation subject to boundary value conditions which take into account the values of the function at multiple points in the interval of interest for this problem we calculate the green s function which allows to express in integral form the exact expression of the unique solution to the multipoint boundary value problem under the appropriate conditions from this study some results are derived concerning the existence of solutions with a constant sign that is some comparison results for first order multipoint boundary value problems

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when

existence and comparison results for difference φ laplacian boundary value problems with lower and upper solutions in reverse order abstract this paper is devoted to the study of the existence and comparison results for nonlinear difference laplacian problems with mixed dirichlet neumann and periodic boundary value conditions we deduce existence of extremal solutions of periodic and neumann boundary value problems lying between a pair of lower and upper solutions given in reverse order we prove the optimality of some assumptions in