on existence of solutions to differential equations or inclusions remaining in a prescribed closed subset of a finite dimensional space abstract this paper is devoted to existence of trajectories to differential equations and inclusions remaining in a given closed or compact set topological properties of the boundary of this set enables us to conclude the existence of such trajectories in many cases

mdghm surf this paper proposes a novel family of local feature descriptors a variant of the speed up robust features surf descriptor which is capable of demonstrably better performance the conventional surf descriptor is an efficient implementation of the sift descriptor although the surf descriptor can represent the nature of the underlying image pattern it is still sensitive to more complicated deformations such as large viewpoint and rotation changes to solve this problem our family of descriptors called mdghm surf is based on the modified discrete gaussian hermite moment mdghm which devises a movable mask to represent the local feature information of non square images whereas conventional surf uses first order derivatives mdghm surf uses mdghm which offers more feature information than first order derivative based local descriptors such as surf and sift consequently by redefining the conventional surf descriptor using mdghm mdghm surf can extract more distinctive features than conventional surf the results of evaluations conducted with six types of deformations indicate that our proposed method outperforms the matching accuracy of other surf related algorithms we propose a novel family of the surf descriptor to solve the sensitivity of the surf we redefine the surf using mdghm mdghm surf the mdghm offers more feature information than the first order derivative based surf the evaluations are conducted with six types of deformations and panoramic image generation the results indicate that our method outperforms other surf related algorithms

on the well posedness of weakly hyperbolic equations with time dependent coefficients in this paper we analyse the gevrey well posedness of the cauchy problem for weakly hyperbolic equations of general form with time dependent coefficients the results involve the order of lower order terms and the number of multiple roots we also derive the corresponding well posedness results in the space of gevrey beurling ultradistributions

on continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument abstract bounded continuous solutions on r of a class of systems of nonlinear functional difference equations with a complicated nonlinear deviation of the argument that depends on unknown functions are studied here

wazewski s method for systems of dynamic equations on time scales abstract in the paper the wazewski s method which is well known for ordinary differential equations is developed for a system of dynamic equations on an arbitrary time scale sufficient conditions guaranteeing the existence of at least one solution with a graph staying in a previously defined open set are derived this result generalizing some previous results concerning the asymptotic behavior of solutions of discrete equations is suitable for investigating of asymptotic behavior of solutions of dynamical systems a relevant example is considered

bounded solutions of nonlinear discrete equations abstract the goal of this paper is to give sufficient conditions for the existence of bounded solutions of a system of discrete equations u k 1 f k u k k a a 1 a 2 with a n n 0 1 and f n a r n r n a principle giving sufficient conditions for the existence of at least one initial problem generating solution with its graph staying in a previously prescribed domain for every k a a 1 a 2 is formulated illustrative examples are considered as well

wazewski theorem on time scales with a set of egress points that is not the whole boundary abstract in the paper the celebrated wazewski retract method is developed for planar dynamic equations on an arbitrary time scale without a restrictive assumption that the whole boundary of a set of constraints where we look for solutions is a set of egress points as a consequence some recently published results are essentially generalized one transparent example illustrating the main theorem is presented the results are new and more general even for ordinary difference equations

weakly hyperbolic equations with non analytic coefficients and lower order terms in this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time dependent coefficients and lower order terms we prove the gevrey well posedness of the cauchy problem under c k regularity of coefficients of the principal part and natural levi conditions on lower order terms which may be only continuous in the case of analytic coefficients in the principal part we establish the c infty well posedness the proofs are based on using the quasi symmetriser for the corresponding companion system and inductions on the order of equation and on the frequency regions the main novelty compared to the existing literature is the possibility to include lower order terms to the equation which have been untreatable until now in these problems as well as considering any space dimensions we also give results on the ultradistributional and distributional well posedness of the problem and we look at new effects for equations with discontinuous lower order terms

well posedness of hyperbolic systems with multiplicities and smooth coefficients we study hyperbolic systems with multiplicities and smooth coefficients in the case of non analytic smooth coefficients we prove well posedness in any gevrey class and when the coefficients are analytic we prove c infty well posedness the proof is based on a transformation to block sylvester form introduced by d ancona and spagnolo boll umi 8 1b 169 185 1998 which increases the system size but does not change the eigenvalues this reduction introduces lower order terms for which appropriate levi type conditions are found these translate then into conditions on the original coefficient matrix this paper can be considered as a generalisation of garetto and ruzhansky math ann 357 2 401 440 2013 where weakly hyperbolic higher order equations with lower order terms were considered

asymptotic behaviour of solutions of systems of discrete equations via liapunov type technique abstract the second liapunov method serves as a powerful tool for the investigation of the stability of the trivial solution of ordinary differential equations systems and discrete equations systems in the presented paper a liapunov type qualitative approach is used for the investigation of asymptotic behaviour of the solutions of systems of discrete equations conditions for the existence of continuum of solutions the graphs of which remain within a given prescribed set are formulated for the general systems of discrete equations u k f k u k an additional advantage of the presented approach consists of the fact that no assumption concerning the existence of the trivial solution or the existence of an equilibrium point of systems considered is assumed moreover the asymptotic behaviour of solutions of some classes of linear difference systems is given by means of concrete asymptotic formulae several illustrative examples are considered too

wazewski type theorem for non autonomous systems of equations with a disconnected set of egress points in this paper we study an asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form y t f t y t where f t r n r n and t is a time scale for a given set t r n we formulate conditions for function f which guarantee that at least one solution y of the above system stays in unlike previous papers the set is considered in more general form i e the time section t is an arbitrary closed bounded set homeomorphic to the disk for every t t and the boundary t does not contain only egress points thanks to this we can investigate a substantially wider range of equations with various types of bounded solutions a relevant example is considered the results are new also for non autonomous systems of difference equations and the systems of impulsive differential equations

asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points abstract in this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form y t f t y t where f t r n r n and t is a time scale for a given set t r n we formulate the conditions for function f which guarantee that at least one solution y of the above system stays in the dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well a linear system with singularity at infinity is considered as an example

retract principle for neutral functional differential equations abstract the investigation of asymptotic behaviour of solutions of ordinary differential equations is often based on the application of the retract principle initially developed for ordinary differential equations this technique was extended to other classes of equations not answered remains a problem concerning the possibility of extending this principle to neutral differential equations the goal of the present paper is to partially fill this gap and develop a corresponding technique for the application of this principle the applicability of the main result is illustrated on a nonlinear equation and sufficient conditions for existence of a positive solution are derived

unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations abstract the existence and uniqueness of bounded continuous solutions on the real line of a general class of nonlinear functional equations with quite complicated deviations dependent of unknown functions are established in this paper

third order homogeneous weakly hyperbolic equations with nonanalytic coefficients abstract we consider the cauchy problem for homogeneous linear third order weakly hyperbolic equations with time depending coefficients we study the relation between the regularity of the coefficients and the gevrey class in which the cauchy problem is well posed

wave equation for operators with discrete spectrum and irregular propagation speed given a hilbert space mathcal h we investigate the well posedness of the cauchy problem for the wave equation for operators with a discrete non negative spectrum acting on mathcal h we consider the cases when the time dependent propagation speed is regular holder and distributional we also consider cases when it is strictly positive strictly hyperbolic case and when it is non negative weakly hyperbolic case when the propagation speed is a distribution we introduce the notion of very weak solutions to the cauchy problem we show that the cauchy problem for the wave equation with the distributional coefficient has a unique very weak solution in an appropriate sense which coincides with classical or distributional solutions when the latter exist examples include the harmonic and anharmonic oscillators the landau hamiltonian on mathbb r n uniformly elliptic operators of different orders on domains hormander s sums of squares on compact lie groups and compact manifolds operators on manifolds with boundary and many others

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

discrete retract principle for systems of discrete equations abstract a power tool for investigation of various problems of ordinary differential equations as well as delayed differential equations is a retraction method the development of this method is discussed here in the case of system discrete equations corresponding definition of a point of a type of strict egress for a given set with respect to the system of discrete equations u k f k u k is given in an example it is shown that this definition cannot exactly copy the analogous one known from the theory of ordinary differential equations conditions for existence of at least one solution with graph remaining in a given set are formulated the proof is based on idea of a retract principle in construction of a retract mapping the property of continuous dependence on their initial data is used illustrative applications are considered too

image analysis by fractional order orthogonal moments orthogonal moments play an important role in image analysis and other similar applications however existing orthogonal moments are restricted to integer order and little investigation of non integer order orthogonal moments has been conducted to date in this paper a general framework of real order orthogonal moments also known as fractional order orthogonal moments is proposed in this general framework fractional order orthogonal moments can be defined in cartesian and polar coordinate systems shifted legendre polynomials are implemented in this paper to investigate the properties of fractional order orthogonal moments a series of experiments are performed which demonstrate that fractional order orthogonal moments are not only capable of region of interest roi feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition

wave equation for sums of squares on compact lie groups in this paper we investigate the well posedness of the cauchy problem for the wave equation for sums of squares of vector fields on compact lie groups we obtain the loss of regularity for solutions to the cauchy problem in local sobolev spaces depending on the order to which the hormander condition is satisfied but no loss in globally defined spaces we also establish gevrey well posedness for equations with irregular coefficients and or multiple characteristics as in the sobolev spaces if formulated in local coordinates we observe well posedness with the loss of local gevrey order depending on the order to which the hormander condition is satisfied

a note on weakly hyperbolic equations with analytic principal part in this note we show how to include low order terms in the c well posedness results for weakly hyperbolic equations with analytic time dependent coefficients this is achieved by doing a different reduction to a system from the previously used one we find the levi conditions such that the c well posedness continues to hold

anti lyapunov method for systems of discrete equations abstract in the present paper problems concerning the qualitative behaviour of solutions of discrete equations are considered a general principle which gives a guarantee that the graph of at least one solution stays in a prescribed domain is formulated as a consequence the auxiliary tool namely a method of regular polyfacial sets is developed and an application of the general principle is given this application is based with exceptions on the fact that points of the boundary of a domain considered are strict egress points such a situation is often in the theory of ordinary differential equations termed the anti lyapunov case illustrative applications and examples are given and open problems are formulated

hyperbolic systems with non diagonalisable principal part and variable multiplicities i well posedness in this paper we analyse the well posedness of the cauchy problem for a rather general class of hyperbolic systems with space time dependent coefficients and with multiple characteristics of variable multiplicity first we establish a well posedness result in anisotropic sobolev spaces for systems with upper triangular principal part under interesting natural conditions on the orders of lower order terms below the diagonal namely the terms below the diagonal at a distance k to it must be of order k this setting also allows for the jordan block structure in the system second we give conditions for the schur type triangularisation of general systems with variable coefficients for reducing them to the form with an upper triangular principal part for which the first result can be applied we give explicit details for the appearing conditions and constructions for 2 times 2 and 3 times 3 systems complemented by several examples

automatic panoramic image stitching using invariant features this paper concerns the problem of fully automated panoramic image stitching though the 1d problem single axis of rotation is well studied 2d or multi row stitching is more difficult previous approaches have used human input or restrictions on the image sequence in order to establish matching images in this work we formulate stitching as a multi image matching problem and use invariant local features to find matches between all of the images because of this our method is insensitive to the ordering orientation scale and illumination of the input images it is also insensitive to noise images that are not part of a panorama and can recognise multiple panoramas in an unordered image dataset in addition to providing more detail this paper extends our previous work in the area brown and lowe 2003 by introducing gain compensation and automatic straightening steps

hyperbolic equations with non analytic coefficients we prove that the cauchy problem for a hyperbolic homogeneous equation with mathcal c infty coefficients depending on time is well posed in every gevrey class although in general it is not well posed in mathcal c infty provided the characteristic roots satisfy the condition lambda i t 2 lambda j t 2 leq m lambda i t lambda j t 2 quad i neq j

asymptotic formulae for the solutions of a linear delay difference equation consider the linear delay difference equation xn 1 xn anxnk where an s are real numbers and k is a positive integer in this paper we establish asymptotic formulae for the solutions of the above equation assuming n 0 an p for some p 1 the asymptotic formulae are given by an appropriate recursive sequence for p 1 2 3 4 we present explicit formulae we also construct an example which shows that some comparison results in a recent paper of yan and qian are incorrect

representation of solutions of discrete delayed system x k 1 ax k bx k m f k with commutative matrices abstract in the investigation performed we give on half infinity discrete intervals formulas for solution of initial problem of linear discrete systems x k 1 a x k b x k m f k with constant square matrices a b such that a b b a det a 0 and with a vector function f k corresponding representations are obtained with the aid of so called discrete matrix delayed exponential which permits to represent solutions in a matrix form similarly as for ordinary differential systems with constant matrices or as well as for differential systems with constant matrices and constant delay

bayesian model estimation and selection for epipolar geometry and generic manifold fitting computer vision often involves estimating models from visual input sometimes it is possible to fit several different models or hypotheses to a set of data and a decision must be made as to which is most appropriate this paper explores ways of automating the model selection process with specific emphasis on the least squares problem of fitting manifolds in particular algebraic varieties e g lines algebraic curves planes etc to data points illustrated with respect to epipolar geometry the approach is bayesian and the contribution three fold first a new bayesian description of the problem is laid out that supersedes the author s previous maximum likelihood formulations this formulation will reveal some hidden elements of the problem second an algorithm mapsac is provided to obtain the robust map estimate of an arbitrary manifold third a bayesian model selection paradigm is proposed the bayesian formulation of the manifold fitting problem uncovers an elegant solution to this problem for which a new method gric for approximating the posterior probability of each putative model is derived this approximations bears some similarity to the penalized likelihoods used by aic bic and mdl however it is far more accurate in situations involving large numbers of latent variables whose number increases with the data this will be empirically and theoretically demonstrated

homogeneous weakly hyperbolic equations with time dependent analytic coefficients abstract this paper concerns the cauchy problem for homogeneous weakly hyperbolic equations with time depending analytic coefficients we give a sufficient condition for the c well posedness which is also necessary if the space dimension is equal to one the main point of the paper consists in expressing our condition only in terms of the coefficients of the operator without needing to know the behavior of the characteristic roots this is made possible by using the so called standard symmetrizer of a companion hyperbolic matrix

hyperbolic second order equations with non regular time dependent coefficients in this paper we study weakly hyperbolic second order equations with time dependent irregular coefficients this means assuming that the coefficients are less regular than holder the characteristic roots are also allowed to have multiplicities for such equations we describe the notion of a very weak solution adapted to the type of solutions that exist for regular coefficients the construction is based on considering friedrichs type mollifiers of coefficients and corresponding classical solutions and their quantitative behaviour in the regularising parameter we show that even for distributional coefficients the cauchy problem does have a very weak solution and that this notion leads to classical or to ultradistributional solutions under conditions when such solutions also exist in concrete applications the dependence on the regularising parameter can be traced explicitly

true multi image alignment and its application to mosaicing and lens distortion correction multiple images of a scene are related through 2d 3d view transformations and linear and nonlinear camera transformations we present an algorithm for true multi image alignment that does not rely on the measurements of a reference image being distortion free the algorithm is developed to specifically align and mosaic images using parametric transformations in the presence of lens distortion when lens distortion is present none of the images can be assumed to be ideal in our formulation all the images are modeled as intensity measurements represented in their respective coordinate systems each of which is related to an ideal coordinate system through an interior camera transformation and an exterior view transformation the goal of the accompanying algorithm is to compute an image in the ideal coordinate system while solving for the transformations that relate the ideal system with each of the data images key advantages of the technique presented in this paper are i no reliance on one distortion free image ii ability to register images and compute coordinate transformations even when the multiple images are of an extended scene with no overlap between the first and last frame of the sequence and iii ability to handle linear and nonlinear transformations within the same framework results of applying the algorithm are presented for the correction of lens distortion and creation of video mosaics