limit cycle oscillation of missile control fin with structural non linearity non linear aeroelastic characteristics of a deployable missile control fin with structural non linearity are investigated a deployable missile control fin is modelled as a two dimensional typical section model doublet point method is used for the calculation of supersonic unsteady aerodynamic forces and aerodynamic forces are approximated by using the minimum state approximation for non linear flutter analysis structural non linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method the linear and non linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio from the non linear flutter analysis various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary the non linear flutter characteristics and the non linear aeroelastic responses are investigated

first order linear fuzzy differential equations under generalized differentiability first order linear fuzzy differential equations are investigated we interpret a fuzzy differential equation by using the strongly generalized differentiability concept because under this interpretation we may obtain solutions which have a decreasing length of their support which means a decreasing uncertainty in several applications the behaviour of these solutions better reflects the behaviour of some real world systems derivatives of the h difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations using different versions of the variation of constants formula some examples show the rich behaviour of the solutions obtained

fuzzy differential equations and the extension principle we study the cauchy problem for differential equations considering its parameters and or initial conditions given by fuzzy sets these fuzzy differential equations are approached in two different ways a by using a family of differential inclusions and b the zadeh extension principle for the solution of the model we conclude that the solutions of the cauchy problem obtained by both are the same we also provide some illustrative examples

on a class of fuzzy functional differential equations in this paper we establish the local and global existence and uniqueness results for fuzzy functional differential equations for the local existence and uniqueness we use the method of successive approximations and for global existence and uniqueness we use the contraction principle also we apply these results to fuzzy differential equations with distributed delays and fuzzy population models

note on numerical solutions of fuzzy differential equations by predictor corrector method in the present note it is shown that the examples presented in a recent paper by allahviranloo et al are incorrect namely the exact solutions proposed by the authors are not solutions of the given fuzzy differential equations fdes the correct exact solutions are also presented here together with some results for characterizing solutions of fdes under hukuhara differentiability by an equivalent system of odes in this way a new direction for the numerical solutions of fdes is proposed

pose estimation with segmentation consistency in this paper we propose a novel method that treats pose estimation as a problem with the constraints of human segmentation consistency from single images different from the previous paper we integrate pose estimation and object segmentation into a joint optimization with the support of segmentation consistency we can obtain more reliable pose results through analyzing the energy function of pose estimation and human segmentation we convert the pose estimation into a binary optimization problem that has the same formation as segmentation the top down pose shape cues bottom up visual cues and the consistency constraints that penalize the mismatching of pose and human foreground are incorporated into our final objective function qualitative and quantitative experimental results demonstrate the merits of our method in pose estimation on ramanan benchmark and buffy data sets

bifurcation analysis of airfoils in incompressible flow abstract bifurcations of airfoils with non linear pitching stiffness in incompressible flow are investigated the harmonic balance method which is more practical is adopted for the analysis and numerical integration results are used as standards of checking analytical solutions calculated by asymptotic expansion method and averaging method with the aid of computer algebra have confirmed the feasibility of the harmonic balance method

analysis of limit cycle flutter of an airfoil in incompressible flow both experimental and theoretical analyses are perfomed to investigate several types of self excited oscillations of a two dimensional wing model with non linear pitching stiffiness free play non linearity receives especial attention in the low speed wind tunnel test of the wing model with free play in pitch an interesting case of double limit cycle flutter is found subsequent harmonic balance analyses ascertain not only these two sustained oscillations but also two other unstable limit cycles a digital simulation method is also used for flutter analysis the theoretical results agree well with the experimental data

existence of solutions to fuzzy differential equations with generalized hukuhara derivative via contractive like mapping principles abstract we study the existence and uniqueness of solution for fuzzy initial value problems in the setting of a generalized hukuhara derivative and by using some recent results of fixed point of weakly contractive mappings on partially ordered sets

generalized fuzzy differentiability with lu parametric representation in the present paper we use a new generalization of the hukuhara difference and derivative for fuzzy valued functions and we study several properties of the new concepts in the setting of the lu parametric representation of fuzzy numbers assessed both from theoretical and computational points of view

numerical solution of hybrid fuzzy differential equation ivps by a characterization theorem in this paper we study hybrid fuzzy differential equation initial value problems ivps we consider the problem of finding their numerical solutions by using a recent characterization theorem of bede for fuzzy differential equations we prove a corollary to bede s characterization theorem and give a characterization theorem for hybrid fuzzy differential equation ivps then we prove that any suitable numerical method for odes can be applied piecewise to numerically solve hybrid fuzzy differential equation ivps numerical examples are provided which connect the new results with previous findings

on the fuzzy initial value problem abstract the initial value problem x t f t x t x 0 x 0 with fuzzy initial value and with deterministic or fuzzy function f is considered two different approaches viz the extension principle and the use of extremal solutions of deterministic initial value problems are applied generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated

existence of global solutions to nonlinear fuzzy volterra integro differential equations abstract in this paper we introduce new solutions for fuzzy differential equations as mixed solutions and prove the existence and uniqueness of global solutions for fuzzy initial value problems involving integro differential operators of volterra type one example is also given by applying mixed solution concept to fuzzy linear differential equations for obtaining their global solutions

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

runge kutta methods for fuzzy differential equations abstract fuzzy differential equations fdes generalize the concept of crisp initial value problems in this article we deal with the numerical solution of fdes the notion of convergence of a numerical method is defined and a category of problems which is more general than the one already found in the numerical analysis literature is solved efficient s stage runge kutta methods are used for the numerical solution of these problems and the convergence of the methods is proved several examples comparing these methods with the previously developed euler method are displayed

two step runge kutta methods implicit two step runge kutta methods are studied it will be shown that these methods require fewer stages to achieve the same order as one step runge kutta methods which means the two step methods are potentially more efficient than one step methods order conditions are derived and examples of two step one stage methods of order 2 and two step two stage methods of order 4 are presented stability properties of these methods with respect to y ay are studied and a stable two step methods of order 2 are characterized two step two stage methods of order 4 which are a stable are found by an extensive computer search semi implicit two stage methods of order 4 were also constructed this is in contrast to the situation encountered in the runge kutta theory where the unique two stage method of order 4 is not semi implicit

unsharp masking using quadratic filter for the enhancement of fingerprints in noisy background the paper summarizes the design and implementation of a quadratic edge detection filter based on volterra series the filter is employed in an unsharp masking scheme for enhancing fingerprints in a dark and noisy background the proposed filter can account for much of the polynomial nonlinearities inherent in the input image and can replace the conventional edge detectors like laplacian log etc the application of the new filter is in forensic investigation where enhancement and identification of latent fingerprints are key issues the enhancement of images by the proposed method is superior to that with unsharp masking scheme employing conventional filters in terms of the visual quality the noise performance and the computational complexity making it an ideal candidate for latent fingerprint enhancement

on random fuzzy differential equations we consider a cauchy problem in a random fuzzy setting under the condition of lipschitzean right hand side the existence and uniqueness of the solution is proven also the continuous dependence on the right hand side and initial condition is shown some kind of boundedness of the solution is established

an investigation of stability of a control surface with structural nonlinearities in supersonic flow using zubov s method it is well known that the presence of nonlinearities may significantly affect the aeroelastic response of an aerospace vehicle structure in this paper the aeroelastic behaviour at high mach numbers of an all moving control surface with a nonlinearity in the root support is investigated very often under certain flight conditions a stable equilibrium point corresponding to zero displacement of the structure together with an unstable limit cycle arising from a sub critical hopf bifurcation results from the presence of the nonlinearity the dynamic aeroelastic response to external excitation is also of interest and when sinusoidal forcing is applied the stable equilibrium point may then be replaced by a periodic attractor and the limit cycle by an unstable multi periodic solution with or without this forcing there is an attractor which will possess a domain of attraction in this paper the problem of estimating these domains of attraction is tackled using zubov s method in the absence of forcing the method is applied directly to the aeroelastic equations while for the forced system the method of averaging is applied to approximate the aeroelastic equations by an autonomous system the behaviour of the system with forcing is also investigated for flight speeds below a threshold which may occur where the unstable limit cycle of the unforced system disappears in this regime the nonlinear system may nevertheless still possess multiple attractors and their domains of attraction are investigated again using an averaged form of the aeroelastic equations in this study the nonlinearity in the root support was assumed to be due to a cubic hardening restoring moment the zubov approach which always yields conservative estimates was shown to be capable of rapidly giving a good indication of stability domain boundaries under many conditions although this investigation focuses on an aeroelastic system the general form of equations considered arises in many other settings so that the approach would be relevant to a whole range of engineering applications

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

a generalization of hukuhara difference and division for interval and fuzzy arithmetic we propose a generalization of the hukuhara difference first the case of compact convex sets is examined then the results are applied to generalize the hukuhara difference of fuzzy numbers using their compact and convex level cuts finally a similar approach is suggested to attempt a generalization of division for real intervals and fuzzy numbers applications to solving interval and fuzzy linear equations and fuzzy differential equations are shown

a note on zadeh s extensions let f rn rn and f f rn f r n be zadeh s extension of f to the space of fuzzy compact sets f rn the aim of this paper is to show that if f is continuous then f f rn d f rn d is also continuous d being the supremum over hausdorff distances between their corresponding level sets

revisiting fuzzy differential equations abstract we revisit the original formulation of fuzzy differential equations fdes and provide examples to show that the theory of fdes is richer than the corresponding theory of ordinary differential equations odes and therefore need not be rejected the alternative formulation in terms of differential inclusions does not always have advantage over odes as claimed we also discuss a stability result via lyapunov functions in this setup

numerical solutions of fuzzy differential equations abstract numerical algorithms for solving fuzzy ordinary differential equations fode are considered a scheme based on the classical euler method is discussed in detail and this is followed by a complete error analysis the algorithm is illustrated by solving several linear and nonlinear fuzzy cauchy problems

fuzzy stochastic differential systems abstract basing on the work of feng fuzzy sets and systems 102 1999 271 280 on mean square calculus for fuzzy stochastic processes we discuss in this paper the general theory of fuzzy stochastic differential systems including the existence and uniqueness of a solution the continuity of the solution with respect to the initial value and the stability of systems when there are perturbations of the coefficients and the initial conditions the explicit representation of solutions for the first order linear fuzzy stochastic systems are established

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

analytical and numerical solutions of fuzzy differential equations in this paper we study analytical and numerical solutions of fuzzy differential equations based on the extension principle for linear fuzzy differential equations we state some results on the behaviour of the solutions and study their relationship with the generalised hukuhara derivative in order to approximate the solutions of linear and non linear fuzzy differential equations we propose a new fuzzification of the classical euler method and then incorporate an unconstrained optimisation technique this combination offers a powerful tool to tackle uncertainty in any numerical method an efficient computational algorithm is also provided to guarantee the convexity of fuzzy solutions on the time domain several illustrative examples are given

numerical solutions of fuzzy differential equations by an efficient runge kutta method with generalized differentiability in this paper an extended fourth order runge kutta method is studied to approximate the solutions of first order fuzzy differential equations using a generalized characterization theorem in this method new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f instead of using the evaluations of f only the proposed extended runge kutta method and its error analysis which guarantees pointwise convergence are given in detail furthermore the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments

arbitrary body segmentation in static images in this paper a novel method for segmenting arbitrary human body in static images is proposed with the body probability map obtained by the pictorial structure model we develop a superpixel based em like algorithm to refine the map which can then serve as the seeds of graph cuts optimization to better obtain the final segmentation we propose a novel 1 based graph cuts algorithm which uses the sparse coding to construct the initialized graph and calculates the terminal links t links and neighborhood links n links simultaneously from the constructed graph by employing this 1 based graph cuts we can effectively and efficiently segment the human body from static images the experiments on the publicly available challenging datasets demonstrate that our method outperforms many state of the art methods on human body segmentation

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

numerical solutions of fuzzy differential equations by extended runge kutta like formulae of order 4 in this paper we apply a numerical algorithm for solving the fuzzy first order initial value problem based on extended runge kutta like formulae of order 4 we use seikkala s derivative the elementary properties of this new solution are given we use the extended runge kutta like formulae in order to enhance the order of accuracy of the solutions using evaluations of both f and f instead of the evaluations of f only

an iterative procedure for nonlinear flutter analysis an iterative procedure in the frequency domain is presented for flutter analysis of large dynamic systems with multiple structural nonlinearities the major components of the procedure are the describing function approach for system linearization a structural dynamics modification method for shifting system mode shapes and frequencies and a complex eigenvalue algorithm for solution of the flutter equation the purpose of the procedure is to achieve alignment of the oscillatory amplitude in each nonlinear spring with the describing function prediction of stiffness before computing the final stability characteristics the result is a system tuned to the flutter frequency at the time of instability to support the development and validation of the procedure several describing functions are formulated and a quantitative measure of the errors in each is presented validation of the iterative method is accomplished through examples involving dynamic systems of increasing complexity coupled with various representations of the unsteady aerodynamic forces both numerical simulations and experimental data are used to compare with the iterative predictions in the cases studied the agreement is good to excellent with the method accurately predicting the amplitude of a limit cycle flutter as well as the initial disturbance required to produce flutter

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

a general class of two step runge kutta methods for ordinary differential equations a general class of two step runge kutta methods that depend on stage values at two consecutive steps is studied these methods are special cases of general linear methods introduced by butcher and are quite efficient with respect to the number of function evaluations required for a given order general order conditions are derived using the approach proposed recently by albrecht and examples of methods are given up to the order 5 these methods can be divided into four classes that are appropriate for the numerical solution of nonstiff or stiff differential equations in sequential or parallel computing environments

interval cauchy problem with a second type hukuhara derivative in this paper we consider interval differential equations such the equations can be appropriate in modeling of dynamical systems under presence of uncertainty of parameters we study an interval initial value problem with a second type hukuhara derivative by an example of real world application we indicate the advantages of the usage of such a kind of interval valued derivative a continuous dependence of the solution on initial value and right hand side of the equation is shown the existence of approximate local solutions is proven and then it is used in the derivation of existence of at least one local solution to interval cauchy problem with second type hukuhara derivative the compactness of solutions set is also stated finally the explicit formulae for local solutions to linear interval differential equations are provided

an investigation of stability in the large behaviour of a control surface with structural non linearities in supersonic flow it is well known that the presence of non linearities may significantly affect the aeroelastic response of an aerospace vehicle structure in this paper the aeroelastic behaviour at high mach numbers of an all moving control surface with a non linearity in the root support is investigated very often a stable equilibrium point corresponding to zero displacement of the structure together with an unstable limit cycle arising from a sub critical hopf bifurcation results from the presence of the non linearity the stable equilibrium point will then possess a domain of attraction in this paper this situation is investigated by first applying the averaging method to obtain a new set of aeroelastic equations in which the limit cycle is replaced by an unstable equilibrium point a fourth order power series approximation to the stable manifold in the neighbourhood of this equilibrium point is then determined from the stable manifold predictions of the domain of attraction of the stable equilibrium point may then be made the method is applied to two examples in which the non linearity in the root support was due to either a cubic hardening restoring moment or the presence of freeplay the approximation to the stable manifold was sufficient to enable significant information about the domain of attraction of the stable equilibrium point of the control surface to be obtained agreement with predictions from numerical integration of the aeroelastic equations in the time domain was shown to be generally good in the cases considered though outside the region of validity of the stable manifold expansion discrepancies will occur the averaging method was shown to be sufficiently accurate for this analysis even when the non linearities could not be considered as weak

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

fuzzy differential equations we will concentrate on the second order linear constant coefficient ordinary differential equation for x in interval i i can be 0 t for t 0 or i can be 0 the initial conditions are y 0 0 y 0 1 we assume g is continuous on i

comparation between some approaches to solve fuzzy differential equations in this paper we study the class of fuzzy differential equations where the dynamics is given by a continuous fuzzy mapping which is obtained via zadeh s extension principle we get a fuzzy solution for this class of fuzzy differential equations and several illustrative examples are presented we also give some properties and we show the relationships with others interpretation finally we propose a numerical procedure for obtaining the fuzzy solution

almost periodic fuzzy number valued functions in this paper we develop a theory of almost periodic fuzzy functions i e of the almost periodic functions of real variable and with values fuzzy real numbers although the class of fuzzy real numbers does not form a linear normed space the majority of main properties of almost periodic functions with values in banach spaces are extended to this case applications to fuzzy differential equations and to fuzzy dynamical systems are given

objcut efficient segmentation using top down and bottom up cues we present a probabilistic method for segmenting instances of a particular object category within an image our approach overcomes the deficiencies of previous segmentation techniques based on traditional grid conditional random fields crf namely that 1 they require the user to provide seed pixels for the foreground and the background and 2 they provide a poor prior for specific shapes due to the small neighborhood size of grid crf specifically we automatically obtain the pose of the object in a given image instead of relying on manual interaction furthermore we employ a probabilistic model which includes shape potentials for the object to incorporate top down information that is global across the image in addition to the grid clique potentials which provide the bottom up information used in previous approaches the shape potentials are provided by the pose of the object obtained using an object category model we represent articulated object categories using a novel layered pictorial structures model nonarticulated object categories are modeled using a set of exemplars these object category models have the advantage that they can handle large intraclass shape appearance and spatial variation we develop an efficient method objcut to obtain segmentations using our probabilistic framework novel aspects of this method include 1 efficient algorithms for sampling the object category models of our choice and 2 the observation that a sampling based approximation of the expected log likelihood of the model can be increased by a single graph cut results are presented on several articulated e g animals and nonarticulated e g fruits object categories we provide a favorable comparison of our method with the state of the art in object category specific image segmentation specifically the methods of leibe and schiele and schoenemann and cremers

generalized derivative and π derivative for set valued functions in this paper we study the generalized derivative and the p derivative for interval valued functions we show the connections between these derivatives some illustrative examples and applications to interval differential equations and fuzzy functions are presented

nonlinear response of aeroservoelastic systems using discrete state space approach a generalized direct simulation method using a discrete time domain state space approach for transient response of both open and closed loop nonlinear aeroelastic systems is developed based on a nonlinear parameter scheme that divides the nonlinear system into sublinear systems the method first assembles a set of discrete time domain state space equations and then computes the transient response by switching the time integration procedure between this set of state space equations in so doing various nonlinearities in structures aerodynamics and or control systems can be included the method is validated by correlating the transient response of a three degree of freedom airfoil section in freeplay with the experimental and numerical results obtained by conner et al the stability of a strut braced wing with buckling effects at two trim conditions is also studied which shows that the aeroelastic stability of the present strut braced wing is trim condition dependent such results clearly could not be obtained if using a linear aeroelastic analysis