bounded and zero convergent solutions of second order difference equations abstract in this paper we study boundedness and monotonicity properties of a homogeneous second order linear difference equation under certain conditions it is shown that every solution must eventually be monotonic the question of when such monotonic solutions diverge to infinity or converge to zero and the corresponding impact this behavior has on recessive and dominant solutions is investigated a necessary and sufficient condition for all solutions to be bounded is presented comparison theorems are also discussed

symmetry aware graph matching visual symmetry encodes middle to high level geometric information and plays an important role in many computer vision applications not much effort however has been devoted to utilize symmetry information for graph matching in this paper we propose a new framework for symmetry aware graph matching in the context of image matching in the framework we first define symmetry matrices to characterize the geometric symmetry relation among image features and then develop two methods to discover such symmetry after that we design general strategies to boost graph matching algorithms with symmetry constraints and apply these strategies to several state of the art algorithms for evaluation the proposed symmetry aware graph matching algorithms are first applied to two datasets involving clear symmetry patterns a recently proposed architecture image set and a dental panoramic radiograph collection the results clearly demonstrate the benefits of using symmetry information an experiment is also conducted on a dataset where symmetry is less obvious the results show that our strategies still achieve better of similar performance compared with state of the arts highlightsit is the first time symmetry constraints that are introduced into graph matching the symmetry aware graph matching improves the matching performance a new dataset with annotation for evaluating graph matching is constructed

the karamata integration theorem on time scales and its applications in dynamic and difference equations abstract we derive a time scale version of the well known result from the theory of regular variation namely the karamata integration theorem we show an application of this theorem in asymptotic analysis of linear second order dynamic equations we obtain a classification and asymptotic formulae for all positive solutions which unify extend and improve the existing results in addition we utilize these results in combination with a transformation between equations on different time scales to study the critical double root case in linear difference equations this leads to solving open problems posed in the literature

spherical functions on symmetric cones in this note we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real jordan algebra we use this formula as an inspiration for a similar recursive formula involving the jack polynomials

jack polynomials and some identities for partitions we prove an identity about partitions involving new combinatorial coefficients the proof given is using a generating function as an application we obtain the explicit expression of two shifted symmetric functions related with jack polynomials these quantities are the moments of the a content random variable with respect to some transition probability distributions

half linear differential equations linearization technique and its application abstract oscillatory properties of the half linear second order differential equation r t x c t x 0 x x p 2 x p 1 are investigated where is viewed as a perturbation of an equation of the same form and these properties are compared with the oscillatory behavior of a certain associated linear second order differential equation as a corollary a conjecture posed by the first author in the paper o dosl perturbations of the half linear euler weber differential equations j math anal appl 323 2006 426 440 is proved and some new research problems are formulated

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

invariant functions on lie groups and hamiltonian flows of surface group representations si est le groupe fondamental d une surface orientee fermee s et g est un groupe de lie satisfaisant des conditions tres generales alors l espace hom g g des classes de conjugaison de representation g a une structure symplectique naturelle on etudie la geometrie de cette structure symplectique a l aide d une famille naturelle de fonctions sur hom g g

integral conditions for nonoscillation of second order nonlinear differential equations an extension of the fubini theorem is presented and applied in studying the possible coexistence of nonoscillatory solutions for the differential equation r t x sgnx q t x sgnx some discrepancies among the cases and are illustrated and compared with the linear case in addition when an application to the integral characterization of principal solutions which answers an open problem stated in o dosl a elbert integral characterization of the principal solution of half linear second order differential equations studia sci math hungar 36 2000 455 469 is given

globally consistent correspondence of multiple feature sets using proximal gauss seidel relaxation feature correspondence between two or more images is a fundamental problem towards many computer vision applications the case of correspondence between two images has been intensively studied however few works so far have been concerned with multi image correspondence in this paper we address the problem of establishing a globally consistent correspondence among multiple more than two feature sets given the pairwise feature affinity information our main contribution is to propose a novel optimization framework for solving this problem based on the so called proximal gauss seidel relaxation pgsr the proposed method is distinguished from previous works mainly in three aspects 1 it is more robust to noise and outliers 2 its solution is based on convex relaxation and the principled pgsr method which in general has convergence guarantee 3 the scale of the problem in our method is linear with respect to the number of feature sets making it computationally practical to be used in real world applications experimental results both synthetic and real image datasets have demonstrated the effectiveness and superiority of the proposed method highlightswe study finding globally consistent correspondence from multiple feature sets a novel method is proposed based on proximal gauss seidel relaxation pgsr pgsr is more robust to noise outliers and deformation than competitors the optimization has general convergence guarantee the scale of our formulation is linear w r t the number of feature sets

convex and semi nonnegative matrix factorizations we present several new variations on the theme of nonnegative matrix factorization nmf considering factorizations of the form x fgt we focus on algorithms in which g is restricted to containing nonnegative entries but allowing the data matrix x to have mixed signs thus extending the applicable range of nmf methods we also consider algorithms in which the basis vectors of f are constrained to be convex combinations of the data points this is used for a kernel extension of nmf we provide algorithms for computing these new factorizations and we provide supporting theoretical analysis we also analyze the relationships between our algorithms and clustering algorithms and consider the implications for sparseness of solutions finally we present experimental results that explore the properties of these new methods

on the symplectic geometry of deformations of a hyperbolic surface let r be a riemann surface in this manuscript we consider a geometry on the moduli space x r for r which we regard as the space of equivalence classes of constant curvature metrics on the underlying smooth manifold of r classically the space of flat metrics for a torus is the locally symmetric space 0 2 sl 2 r sl 2 z we shall describe a symplectic geometry for the space of hyperbolic metrics on a surface of negative euler characteristic the teichmiiller space t r a covering of the moduli space is a complex kihler manifold a kuhler metric for t r defined in terms of the petersson product for automorphic forms was introduced by weil 1 the weil petersson metric is invariant under the covering transformations and so projects to the moduli space x r the metric provides a link between the function theory of r and the geometry of x r in the fenchel nielsen manuscript 8 a deformation based on an amalgamation construction for fuchsian groups is introduced the deformation is defined geometrically by cutting the surface along a simple closed geodesic rotating one side of the cut relative to the other and attaching the sides in their new position the hyperbolic metric in the complement of the cut extends to a hyperbolic metric on the new surface choose a free homotopy class a on the surface r then for each marked surface r realize a by the closed geodesic ar the fenchel nielsen deformations for the athen define a 1 parameter group of diffeomorphisms of t r whose infinitesimal generator by definition is the fenchel nielsen vector field ta in 21 the fenchel nielsen deformation was described in terms of quasiconformal mappings and an investigation of the vector fields t was begun the fenchel nielsen vector fields were found to be related to the geodesic length functions 1 introduced by fricke klein to provide coordinates for t r

kneser s theorem in q calculus while difference equations deal with discrete calculus and differential equations with continuous calculus so called q difference equations are considered when studying q calculus in this paper we obtain certain oscillation criteria for second order q difference equations among them a q calculus version of the famous kneser theorem

on a certain asymptotic class of solutions to second order linear q difference equations the paper deals with the linear second order q difference equation y q2t a t y qt b t y t 0 b t 0 considered on q 1 the class of functions satisfying the relation y qt y t t as t for some function is introduced and studied sufficient and necessary conditions are established for the equation to have solutions in this class related results concerning estimates for solutions and non oscillation of all solutions are discussed a comparison with existing results is made and some applications are given

some combinatorial properties of jack symmetric functions if 1 l n then write 2 n or 1 n if p is another partition then write p c j if pi 6 for all i i e if the diagram of 1 contains the diagram of p if ipl ii 1 then write p 2 1 reverse lexicographic order if either j i or the first nonvanishing difference e pi is positive for instance writing 2 1 i for ai i it 5 5 41 32 5 311 221 2111 11111 finally write p i if ipl lal and p1 pl2 pli a1 a2 li for all i macdonald m p 63 call the partial ordering the natural ordering but we will call it the dominance ordering let x x x2 be an infinite set of indeterminates as in mi we

from p adic to real grassmannians via the quantum let f be a local field the action of gln f on the grassmann variety gr m n f induces a continuous representation of the maximal compact subgroup of gln f on the space of l2 functions on gr m n f the irreducible constituents of this representation are parameterized by the same underlying set both for archimedean and non archimedean fields g hill on the nilpotent representations of gln o manuscripta math 82 1994 293 311 a t james a g constantine generalized jacobi polynomials as spherical functions of the grassmann manifold proc london math soc 29 3 1974 174 192 this paper connects the archimedean and non archimedean theories using the quantum grassmannian m s dijkhuizen j v stokman some limit transitions between bc type orthogonal polynomials interpreted on quantum complex grassmannians publ res inst math sci 35 1999 451 500 j v stokman multivariable big and little q jacobi polynomials siam j math anal 28 1997 452 480 in particular idempotents in the hecke algebra associated to this representation are the image of the quantum zonal spherical functions after taking appropriate limits consequently a correspondence is established between some irreducible representations with archimedean and non archimedean origin

half linear equations and characteristic properties of the principal solution abstract the characteristic properties of the principal solution for half linear differential equation a t x b t x 0 where the functions a b are positive and continuous for t 0 and u u p 2u p 1 are investigated in the linear case it is well known that the principal solution is the smallest one in a neighbourhood of infinity we show that this property continues to hold in the half linear case in addition it is proved that the principal solutions can be fully characterized by means of two different integral criteria which reduce to that one well known in the linear case

nonoscillatory half linear differential equations and generalized karamata functions abstract we introduce a natural generalization of the concept of regularly varying functions in the sense of karamata and show that the class of generalized karamata functions is a well suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half linear differential equation of the type a p t y 1 y q t y 1 y 0

perturbations of the half linear euler weber type differential equation abstract we investigate oscillatory properties of the half linear second order differential equation r t x c t x 0 x x p 2 x p 1 viewed as a perturbation of another half linear differential equation of the same form r t x c t x 0 the obtained oscillation and nonoscillation criteria are formulated in terms of the integral c t c t h p t d t where h is a function which is close to the principal solution of in a certain sense a typical model of in applications is the half linear euler weber differential equation with the critical coefficients x p t p p t p log 2 t x 0 p p 1 p p p 1 2 p 1 p p 1 we establish oscillation and nonoscillation criteria for perturbations of this equation some open problems and perspectives of the further research along this line are also formulated

special functions of matrix argument i algebraic induction zonal polynomials and hypergeometric functions hypergeometric functions of matrix argument arise in a diverse range of applications in harmonic analysis multivariate statistics quantum physics molecular chemistry and number theory this paper presents a general theory of such functions for real division algebras these functions which generalize the classical hypergeometric functions are defined by infinite series on the space s s n f of all n x n hermitian matrices over the division algebra f the theory depends intrinsically upon the representation theory of the general linear group g gl n f of invertible n x n matrices over f and the theme of this work is the full exploitation of the inherent group theory the main technique is the use of the method of algebraic induction to realize explicitly the appropriate representations of g to decompose the space of polynomial functions on s and to describe the zonal polynomials from which the hypergeometric functions are constructed detailed descriptions of the convergence properties of the series expansions are given and integral representations are provided future papers in this series will develop the fine structure of these functions 0 introduction we begin a series of articles in which we develop the fine structure of generalized hypergeometric functions of matrix argument by fine structure we allude to the analogues of such classical results as series expansions integral formulas asymptotics differential equations summation formulas addition theorems composition formulas and recurrence relations this first paper in which we simultaneously treat real complex and quaternionic analysis is the result of our desire to present a complete theory of hypergeometric functions of matrix argument over real division algebras not only as a framework for the body of detailed results to follow in later papers but also to clarify the representationtheoretic foundation for such a theory although these hypergeometric functions are of interest on purely analytic grounds they arise in a wide range of applications indeed various classes of received by the editors may 19 1986 1980 malhema1zics s ject claszficain 1985 ren primary 22e30 22e45 33a75 43a85 43a90 62h10 secondary 20g20 32a07 32m15 44a10 62e15 key w and phrases generalized hypergeometric functions zonal polynomials representation theory algebraic induction multivariate statistics general linear group generalized gamma functions pochhammer symbols laplace transforms maximal compact subgroup invariant polynomials positive cones symmetric spaces schur functions special functions of matrix argument the first author is on leave from the university of wyoming the second author was partially supported by the national science foundation under grant mcs 8403381 and by the research council of the university of north carolina b1987 american mathematical society 0002 9947 87 1 00 25 per page

asymptotic properties of kneser solutions to nonlinear second order odes with regularly varying coefficients in this work we investigate properties of a class of solutions to the second order ode p t u t q t f u t 0 on the interval a a 0 where p and q are functions regularly varying at infinity and f satisfies f l 0 f 0 f l 0 with l0 0

power comparison theorems in half linear oscillation theory we compare oscillatory behavior of two half linear differential equations with different powers by the homogeneous functions appearing in these equations our results generalize and extend several previously proved power comparison theorems

spectral analysis of a q difference operator for a number q bigger than 1 we consider a q difference version of a second order singular differential operator which depends on a real parameter we give three exact parameter intervals in which the operator is semibounded from above not semibounded and semibounded from below respectively we also provide two exact parameter sets in which the operator is symmetric and self adjoint respectively our model exhibits a more complex behavior than in the classical continuous case but reduces to it when q approaches 1

lagrangian relaxation graph matching abstract graph matching is a fundamental problem in computer vision area graph matching problem that incorporates pair wise constraints can be formulated as an integer quadratic programming iqp problem with affine mapping constraint since it is known to be np hard approximate relaxation methods are usually required to find approximate solutions in this paper we present a new effective graph matching relaxation method called lagrangian relaxation graph matching lrgm which aims to generate a relaxation model by incorporating the affine mapping constraint into the matching objective optimization there are three main benefits of the proposed lrgm method 1 the nonnegative affine mapping constraint encoding one to one mapping is naturally incorporated in lrgm relaxation via lagrangian regularization 2 by further adding a l 1 norm constraint lrgm can generate a sparse solution empirically and thus returns a desired discrete solution for original iqp matching problem 3 an effective update algorithm is derived to solve the proposed lrgm model theoretically the converged solution can be proven to be karush kuhn tucker kkt optimal experimental results on both synthetic data and real world image datasets show the effectiveness and benefits of the proposed lrgm method

generalized binomial expansion on complex matrix space abstract for an arbitrary spherical function we expand i r x into a spherical series on the open unit ball d for the spectral norm in c r r we also obtain some interesting corollaries in particular we compute the spherical transform of i r x

fast matching of large point sets under occlusions the problem of isometric point pattern matching can be modeled as inference in small tree width graphical models whose embeddings in the plane are said to be globally rigid although such graphical models lead to efficient and exact solutions they cannot generally handle occlusions as even a single missing point may break the rigidity of the graph in question in addition such models can efficiently handle point sets of only moderate size in this paper we propose a new graphical model that is not only adapted to handle occlusions but is much faster than previous approaches for solving the isometric point pattern matching problem we can match point patterns with thousands of points in a few seconds

asymptotic behavior of positive solutions of sublinear differential equations of emden fowler type this paper is concerned with asymptotic analysis of positive solutions of the second order nonlinear differential equation a x t q t f x t 0 where q a 0 is a continuous function which is regularly varying and f 0 0 is a continuous increasing function which is regularly varying of index c 0 1 an application of the theory of regular variation gives the possibility of determining precise information about the asymptotic behavior at infinity of intermediate solutions of eq a

on an extension of the fubini theorem and its applications in odes the paper deals with the extension of the fubini theorem there are given applications for the second order differential nonlinear equations the first application brings comparison results for oscillation of two generalized emden fowler equations the second one shows the similarities and discrepancies for nonoscillatory half linear and linear differential equations

asymptotic formulae for solutions of half linear differential equations we establish asymptotic formulae for regularly varying solutions of the half linear differential equation r t y 1 sgn y p t y 1 sgn y where r p are positive continuous functions on a and 1 the results can be understood in several ways some open problems posed in the literature are solved results for linear differential equations are generalized some of the observations are new even in the linear case a refinement on information about behavior of solutions in standard asymptotic classes is provided a precise description of regularly varying solutions which are known to exist is given regular variation of all positive solutions is proved

a pocs based graph matching algorithm a novel projections onto convex sets pocs graph matching algorithm is presented two way assignment constraints are enforced without using elaborate penalty terms graduated nonconvexity or sophisticated annealing mechanisms to escape from poor local minima results indicate that the presented algorithm is robust and compares favorably to other well known algorithms

differential equations and recursion relations for laguerre functions on symmetric cones we obtain the differential equation and recurrence relations satisfied by the laguerre functions l m on an arbitrary symmetric cone

attributed relational graph matching based on the nested assignment structure in this paper we propose a new arg matching scheme based on the nested assignment structure to assess the similarity between two attributed relational graphs args args are represented by nodes and edges containing unary attributes and binary relations between nodes respectively the nested assignment structure consists of inner and outer steps in the inner step to form a distance matrix combinatorial differences between every pair of nodes in two args are computed by using an assignment algorithm then in the outer step a correspondence between nodes in the two args is established by using an assignment algorithm based on the distance matrix the proposed arg matching scheme consists of three procedures as follows first in the initializing procedure the nested assignment structure is performed to generate an initial correspondence between nodes in two args next the correspondence is refined by iteratively performing the updating procedure which also utilizes the nested assignment structure until the correspondence does not change finally the verifying procedure can be performed in case that some nodes to be matched in the two args are missing from experimental results the proposed arg matching scheme shows superior matching performance and localizes target objects robustly and correctly even in severely noisy and occluded scenes

laplace and segal bargmann transforms on hermitian symmetric spaces and orthogonal polynomials let d g k be a complex bounded symmetric domain of tube type in a complex jordan algebra v and let dr j d d be its real form in a formally real euclidean jordan algebra j v dr h l is a bounded realization of the symmetric cone in j we consider representations of h that are gotten by the generalized segal bargmann transform from a unitary g space of holomorphic functions on d to an l2 space on dr we prove that in the unbounded realization the inverse of the unitary part of the restriction map is actually the laplace transform we find the extension to d of the spherical functions on dr and find their expansion in terms of the l spherical polynomials on d which are jack symmetric polynomials we prove that the coefficients are orthogonal polynomials in an l2 space the measure being the harish chandra plancherel measure multiplied by the symbol of the berezin transform we prove the difference equation and recurrence relation for those polynomials by considering the action of the lie algebra and the cayley transform on the polynomials on d finally we use the laplace transform to study generalized laguerre functions on symmetric cones

asymptotic formulas for non oscillatory solutions of perturbed half linear euler equation abstract we establish asymptotic formulas for non oscillatory solutions of the half linear second order differential equation x t p x c t x 0 where this equation is viewed as a perturbation of the half linear euler equation

the fenchel nielsen deformation the uniformization theorem provides that a riemann surface s of negative euler characteristic has a metric of constant curvature 1 a hyperbolic structure can be understood in terms of its deformations unfortunately the variation of the hyperbolic metric arising from a deformation is not determined by local data if z is a conformal coordinate for s and a ii h ii 00 1 a beltrami differential then dw dz p dj defines a new conformal coordinate and structure si the tensor p may vanish on the open set 0 c s and yet the hyperbolic metrics of s and si do not coincide on this phenomenon presents a s erious difficulty in the deformation theory of hyperbolic structures the fenchel nielsen twist deformation does not share this defect the deformation is defined by cutting the surface along a simple closed geodesic rotating one side of the cut relative to the other and attaching the sides in their new position a geodesic intersecting the cut is deformed to a broken geodesic the hyperbolic structure in the complement of the cut extends naturally to a hyperbolic structure on the new surface the deformation is concentrated at the cut the basic idea for the deformation appears in the work of fricke klein dehn and fenchel nielsen 71 8 in the fenchel nielsen manuscript the deformation was considered extensively coordinates for teichmiller space are defined in terms of the deformation the proper definition is given by a fuchsian group construction calculations are made in terms of unimodular matrices this approach is often cumbersome our basic objective is to give a description of the deformation in terms of quasiconformal mappings the bers embedding of teichmiiller space is central to the analytic theory of deformations using our characterization we calculate the first variation of the bers embedding for the fenchel nielsen deformation the result is a poincare series 6 which already appears in the work of petersson 16

an asymptotic analysis of nonoscillatory solutions of q difference equations via q regular variation abstract we do a thorough asymptotic analysis of nonoscillatory solutions of the q difference equation d q r t d q y t p t y q t 0 considered on the lattice q k k n 0 q 1 we classify the solutions according to various aspects that take into account their asymptotic behavior we show relations among the asymptotic classes for every positive solution we establish asymptotic formulae several discrepancies are revealed when comparing the results with their existing differential equations or difference equations counterparts however it should be noted that many of our observations in the q case have not their continuous or discrete analogies yet important roles in our considerations are played by the theory of q regular variation and various transformations the results are illustrated by examples

generalized binomial expansion on lorentz cones we study some properties of generalized binomial coefficients for symmetric cones and we obtain a generalized binomial expansion formula for lorentz cones

a sparse nonnegative matrix factorization technique for graph matching problems graph matching problem that incorporates pairwise constraints can be cast as an integer quadratic programming iqp since it is np hard approximate methods are required in this paper a new approximate method based on nonnegative matrix factorization with sparse constraints is presented firstly the graph matching is formulated as an optimization problem with nonnegative and sparse constraints followed by an efficient algorithm to solve this constrained problem then we show the strong relationship between the sparsity of the relaxation solution and its effectiveness for graph matching based on our model a key benefit of our method is that the solution is sparse and thus can approximately impose the one to one mapping constraints in the optimization process naturally therefore our method can approximate the original iqp problem more closely than other approximate methods extensive and comparative experimental results on both synthetic and real world data demonstrate the effectiveness of our graph matching method we present a graph matching method based on nmf with sparse constraints our sparse model can incorporate the mapping constraints approximately we show the link between the sparsity of the solution and its effectiveness experimental results show the effectiveness of our graph matching method

q regular variation and q difference equations we introduce the concept of q regularly varying functions and establish basic properties of such functions among other things it is shown that considering regular variation in q calculus is somehow natural and leads to interesting observations and simplifications compared with classical continuous and discrete theories the obtained theory is applied to an investigation of asymptotic behavior of solutions to linear second order q difference equations

branching coefficients of holomorphic representations and segal bargmann transform let d g k be a complex bounded symmetric domain of tube type in a jordan algebra vc and let d h l d v be its real form in a jordan algebra v vc the analytic continuation of the holomorphic discrete series on dopf forms a family of interesting representations of g we consider the restriction on d and the branching rule under h of the scalar holomorphic representations the unitary part of the restriction map gives then a generalization of the segal bargmann transform the group l is a spherical subgroup of k and we find a canonical basis of l invariant polynomials in the components of the schmid decomposition and we express them in terms of the jack symmetric polynomials we prove that the segal bargmann transform of those l invariant polynomials are under the spherical transform on d multi variable wilson type polynomials and we give a simple alternative proof of their orthogonality relation we find the expansion of the spherical functions on d when extended to a holomorphic function in a neighborhood of 0 d in terms of the l spherical holomorphic polynomials on d the coefficients being the wilson polynomials

half linear oscillation criteria perturbation in term involving derivative abstract we consider the nonoscillatory half linear differential equation r t x c t x 0 x x p 2 x p 1 and we study oscillatory properties of its perturbation r t r t x c t c t x 0 we use the riccati technique and relationship between and a certain associated linear equation the results are applied to the perturbed euler type equation

variational technique and principal solution in half linear oscillation criteria we investigate oscillatory properties of half linear differential equations the investigated half linear equation is viewed as a perturbation of another nonoscillatory equation of the same form and perturbation is allowed both in the absolute term and in the derivative term first the sturmian type theorem for solutions of the associated riccati equation is established in the second part of the paper we prove new half linear oscillation criteria using the variational technique

on gradient adaptation with unit norm constraints in this correspondence we describe gradient based adaptive algorithms within parameter spaces that are specified by w 1 where spl middot is any vector norm we provide several algorithm forms and relate them to true gradient procedures via their geometric structures we also give algorithms that mitigate an inherent numerical instability for l sub 2 norm constrained optimization tasks simulations showing the performance of the techniques for independent component analysis are provided

positive solutions of fourth order emden fowler type differential equations in the framework of regular variation abstract the fourth order nonlinear differential equations a x 4 q t x sgn x 0 0 1 with regularly varying coefficient q t are studied in the framework of regular variation it is shown that thorough and complete information can be acquired about the existence of all possible regularly varying solutions of a and their accurate asymptotic behavior at infinity

a nonoscillation theorem for half linear differential equations with periodic coefficients abstract the half linear differential equation p x a t p x b t p x 0 is considered under the assumption that the coefficient a t and an indefinite integral b t of b t are periodic functions with period t 0 it is proved that p 1 p b t a t b t 0 0 t t is sufficient for all nontrivial solutions to be nonoscillatory here p 1 and q y y q 2 y for q p or q p p p 1 the proof is given by means of riccati technique the condition is shown to be sharp sufficient conditions are also presented for all nontrivial solutions are oscillatory in the linear case p 2 some examples and simulations are included to illustrate our results

handbook of differential equations chapter headings definitions and concepts transformations exact analytical methods exact methods for odes exact methods for pdes approximate analytical methods numerical methods concepts numerical methods for odes numerical methods for pdes list of tables list of programs list of figures subject index

summation inequalities and half linear difference equations abstract the aim of this paper is to present new summation inequalities and to show that the half linear difference equation a n x n sgn x n b n x n 1 sgn x n 1 exhibits not only similarities but also some discrepancies with the linear case especially as regards the possible coexistence of the so called extremal solutions some of our results are new also for the linear difference equation

a path following algorithm for the graph matching problem we propose a convex concave programming approach for the labeled weighted graph matching problem the convex concave programming formulation is obtained by rewriting the weighted graph matching problem as a least square problem on the set of permutation matrices and relaxing it to two different optimization problems a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices the concave relaxation has the same global minimum as the initial graph matching problem but the search for its global minimum is also a hard combinatorial problem we therefore construct an approximation of the concave problem solution by following a solution path of a convex concave problem obtained by linear interpolation of the convex and concave formulations starting from the convex relaxation this method allows to easily integrate the information on graph label similarities into the optimization problem and therefore perform labeled weighted graph matching the algorithm is compared with some of the best performing graph matching methods on four data sets simulated graphs qaplib retina vessel images and handwritten chinese characters in all cases the results are competitive with the state of the art

de haan type increasing solutions of half linear differential equations abstract we study asymptotic behavior of eventually positive increasing solutions to the half linear equation r t y 1 sgn y p t y 1 sgn y where r p are positive continuous functions and 1 we give conditions which guarantee that any such a solution is in the class in the de haan sense we also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts the results can be viewed as a half linear extension of existing statements for linear equations but in some aspects they are new also in the linear case

graph matching based on spectral embedding with missing value this paper proposes an efficient algorithm for inexact graph matching based on spectral embedding with missing value we commence by building an association graph model based on initial matching algorithm then by dot product representation of graph with missing value a new embedding method co embedding where the correspondences between unmatched nodes are treated as missing data in an association graph is presented at last a new graph matching algorithm which alternates between the co embedding and point pattern matching is proposed convictive experimental results on both synthetic and real world data demonstrate the effectiveness of the proposed graph matching algorithm

on wishart distribution some extensions this paper proposes a unified approach that enables the wishart distribution to be studied simultaneously in the real complex quaternion and octonion cases under elliptical models in particular the matrix multivariate elliptical distribution the noncentral generalised wishart distribution the joint density of the eigenvalues and the distribution of the maximum eigenvalue are obtained for real normed division algebras

structural graph matching using the em algorithm and singular value decomposition this paper describes an efficient algorithm for inexact graph matching the method is purely structural that is it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes we make two contributions 1 commencing from a probability distribution for matching errors we show how the problem of graph matching can be posed as maximum likelihood estimation using the apparatus of the em algorithm and 2 we cast the recovery of correspondence matches between the graph nodes in a matrix framework this allows one to efficiently recover correspondence matches using the singular value decomposition we experiment with the method on both real world and synthetic data here we demonstrate that the method offers comparable performance to more computationally demanding methods

nonprincipal solutions of half linear second order differential equations abstract we consider the nonoscillatory half linear second order differential equation r t x c t x 0 x x p 2 x p 1 and we suppose that we know its principal solution x we establish an asymptotic formula for nonprincipal solutions of and we use this asymptotic formula to obtain an oscillation criterion for

on super linear emden fowler type differential equations we study the second order emden fowler type differential equation in the super linear case using a holder type inequality we resolve the open problem on the possible coexistence on three possible types of nononscillatory solutions subdominant intermediate and dominant solutions jointly with this sufficient conditions for the existence of globally positive intermediate solutions are established some of our results are new also for the emden fowler equation

increasing solutions of thomas fermi type differential equations the superlinear case abstract an asymptotic analysis of increasing solutions x t of equations of super linear thomas fermi type is performed in the framework of regular variation leading to the accurate behavior of all such x t for t

regular variation on measure chains ukazujeme souvislosti mezi nedavno zavedenou definici regularni variace pomoci delta derivace a definici karamatova typu je dokazana v ta o vno eni a reprezentaci je ukazano e pro rozumnou teorii je pot eba dodatecneho p edpokladu na zrnitost jsou odvozeny r zne vlastnosti regularn se m nicich funkci teorie je aplikovana p i popisu asymptotick ch vlastnosti eseni dynamick ch rovnic druheho adu