on some third order nonlinear boundary value problems existence location and multiplicity results abstract we prove an ambrosetti prodi type result for the third order fully nonlinear equation u t f t u t u t u t s p t with f 0 1 r 3 r and p 0 1 r continuous functions s r under several two point separated boundary conditions from a nagumo type growth condition an a priori estimate on u is obtained an existence and location result will be proved by degree theory for s r such that there exist lower and upper solutions the location part can be used to prove the existence of positive solutions if a non negative lower solution is considered the existence nonexistence and multiplicity of solutions will be discussed as s varies

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

solvability of some third order boundary value problems with asymmetric unbounded nonlinearities abstract in this paper we present existence and location results for the third order separated boundary value problems u t f t u t u t u t with the boundary conditions u a a u a b u b c or u a a c 1 u a c 2 u a b c 3 u b c 4 u b c with c 1 c 2 c 3 c 4 r and a b c r we assume f a b r 3 r is a continuous function satisfying one sided nagumo type condition which allows an asymmetric unbounded behaviour the arguments used concern leray schauder degree and lower and upper solution techniques

third order differential equations with integral boundary conditions abstract in this paper we study nonlinear third order differential equations with integral boundary conditions we provide sufficient conditions on the nonlinearity and the functions appearing in the boundary conditions that guarantee the existence of at least one solution to our problem our technique is based on a priori bounds and fixed point theorems

on the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions abstract we prove the existence of extremal solutions for the third order discontinuous functional nonlinear problem u t f t u u t u t for a e t a b u a a a r l 1 u u u a u b u a 0 l 2 u u a u b u b 0 by using a fixed point theorem after having established some existence results for some auxiliary second order nonlinear problems we observe that together with the discontinuities allowed on the spacial variable u with adequate modifications of technical type analogous results can be obtained when the equation has a second member not necessarily continuous in u

qualitative features and the generalized hough transform abstract in this paper we show how the use of qualitative features can enhance the performance of recognition and localization techniques in particular the generalized hough transform qualitative features i e scene features with qualitative attributes assigned to them are shown to be effective in pruning the search space of possible scene interpretations and also reducing the number of spurious interpretations explored by the recognition and localization technique the redundancy of the computed transform and the probability of spurious peaks of significant magnitude due to random accumulation of evidence are two criteria by which the performance of the generalized hough transform is judged the straightforward generalized hough transform shows a high probability of spurious peaks of significant magnitude even for small values of redundancy and small magnitude of the search space of scene interpretations the use of qualitative features enables us to come up with a weighted generalized hough transform where each match of a scene feature with a model feature is assigned a weight based on the qualitative attributes assigned to the scene feature these weights could be looked upon as membership function values for the fuzzy sets defined by these qualitative attributes analytic expressions for the probability of accumulation of random events within a bucket are derived for the weighted generalized hough transform and compared with the corresponding expression for the straightforward generalized hough transform the weighted generalized hough transform is shown to perform better than the straightforward generalized hough transform an experiment for the recognition of polyhedral objects from range images is described using dihedral junctions as features for matching and pose computation the experimental results bring out the advantages of the weighted generalized hough transform over the straightforward generalized hough transform

lie hamilton systems on the plane properties classification and applications we study lie hamilton systems on the plane i e systems of first order differential equations describing the integral curves of a t dependent vector field taking values in a finite dimensional real lie algebra of planar hamiltonian vector fields with respect to a poisson structure we start with the local classification of finite dimensional real lie algebras of vector fields on the plane obtained in a gonzalez lopez n kamran and p j olver proc london math soc 64 339 1992 and we interpret their results as a local classification of lie systems moreover by determining which of these real lie algebras consist of hamiltonian vector fields with respect to a poisson structure we provide the complete local classification of lie hamilton systems on the plane we present and study through our results new lie hamilton systems of interest which are used to investigate relevant non autonomous differential equations e g we get explicit local diffeomorphisms between such systems in particular the milne pinney second order kummer schwarz complex riccati and buchdahl equations as well as some lotka volterra and nonlinear biomathematical models are analysed from this lie hamilton approach

lie hamilton systems on the plane applications and superposition rules a lie hamilton lh system is a nonautonomous system of first order ordinary differential equations describing the integral curves of a t dependent vector field taking values in a finite dimensional real lie algebra of hamiltonian vector fields with respect to a poisson structure we provide new algebraic geometric techniques to easily determine the properties of such lie algebras on the plane e g their associated poisson bivectors we study new and known lh systems on with physical biological and mathematical applications new results cover cayley klein riccati equations the here defined planar diffusion riccati systems complex bernoulli differential equations and projective schrodinger equations constants of motion for planar lh systems are explicitly obtained which in turn allow us to derive superposition rules through a coalgebra approach

integrable deformations of oscillator chains from quantum algebras a family of completely integrable nonlinear deformations of systems of n harmonic oscillators are constructed from the non standard quantum deformation of the sl 2 algebra explicit expressions for all the associated integrals of motion are given and the long range nature of the interactions introduced by the deformation is shown to be linked to the underlying co algebra structure separability and superintegrability properties of such systems are analysed and their connection with classical angular momentum chains is used to construct a non standard integrable deformation of the xxx hyperbolic gaudin system

a numerical and asymptotic study of some third order ordinary differential equations relevant to draining and coating flows some draining or coating fluid flow problems in which surface tension forces are important can be described by third order ordinary differential equations accurate computations are provided here

from constants of motion to superposition rules for lie hamilton systems a lie system is a non autonomous system of first order differential equations possessing a superposition rule i e a map expressing its general solution in terms of a generic finite family of particular solutions and some constants lie hamilton systems form a subclass of lie systems whose dynamics is governed by a curve in a finite dimensional real lie algebra of functions on a poisson manifold it is shown that lie hamilton systems are naturally endowed with a poisson coalgebra structure this allows us to devise methods for deriving in an algebraic way their constants of motion and superposition rules we illustrate our methods by studying kummer schwarz equations riccati equations ermakov systems and smorodinsky winternitz systems with time dependent frequency

explicit solutions of the generalized kdv equations with higher order nonlinearity by constructing auxiliary functions and equations we find some new explicit solutions of the generalized kdv equations with higher order nonlinearity in particular we get the peaked solitary wave solutions of the generalized kdv equations

center of schrodinger algebra and annihilators of verma modules for schrodinger algebra abstract let c be the center of the schrodinger algebra s 1 we prove that the center of the universal enveloping algebra u s 1 is u c we also characterize the annihilators of the irreducible verma modules of s 1

higher order boundary value problems with φ laplacian and functional boundary conditions we study the existence of solutions of the boundary value problem f u n 1 t f t u t u t u n 1 t 0 email protected 0 1 g i u u u n 1 u i 0 0 i 0 n 2 g n 1 u u u n 1 u n 2 1 0 where n 2 f and g i i 0 n 1 are continuous and f is a caratheodory function we obtain an existence criterion based on the existence of a pair of coupled lower and upper solutions we also apply our existence theorem to derive some explicit conditions for the existence of a solution of a special case of the above problem in our problem both the differential equation and the boundary conditions may have dependence on all lower order derivatives of the unknown function and many boundary value problems with various boundary conditions studied extensively in the literature are special cases of our problem consequently our results improve and cover a number of known results in the literature examples are given to illustrate the applicability of our theorems

a systematic construction of completely integrable hamiltonians from coalgebras a universal algorithm to construct n particle classical and quantum completely integrable hamiltonian systems from representations of coalgebras with casimir elements is presented in particular this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of hamiltonian systems with coalgebra symmetry in order to illustrate this general method the algebra and the oscillator algebra are used to derive new classical integrable systems including a generalization of gaudin calogero systems and oscillator chains quantum deformations are then used to obtain some explicit integrable deformations of the previous long range interacting systems and a non coboundary deformation of the 1 1 poincare algebra is shown to provide a new ruijsenaars schneider like hamiltonian

the combinatorics of local constraints in model based recognition and localization from sparse data the problem of recognizing what objects are where in the workspace of a robot can be cast as one of searching for a consistent matching between sensory data elements and equivalent model elements in principle this search space is enormous and to control the potential combinatorial explosion constraints between the data and model elements are needed a set of constraints for sparse sensory data that are applicable to a wide variety of sensors are derived and their characteristics are examined known bounds on the complexity of constraint satisfaction problems are used together with explicit estimates of the effectiveness of the constraints derived for the case of sparse noisy three dimensional sensory data to obtain general theoretical bounds on the number of interpretations expected to be consistent with the data it is shown that these bounds are consistent with empirical results reported previously the results are used to demonstrate the graceful degradation of the recognition technique with the presence of noise in the data and to predict the number of data points needed in general to uniquely determine the object being sensed

twin monotone positive solutions to a singular nonlinear third order differential equation abstract this paper discusses the existence of at least one or two nondecreasing positive solutions for the following singular nonlinear third order differential equation x t t f t x t 0 a t b x a x a x b 0 where 0 is a parameter c a b r f c a b 0 r t may be singular at t a b and f t s may be singular at s 0 green s function and the fixed point theorem of cone expansion and compression type are utilized to illustrate the results four nontrivial examples are included

n dimensional integrability from two photon coalgebra symmetry a wide class of hamiltonian systems with n degrees of freedom and endowed with at least n 2 functionally independent integrals of motion in involution is constructed by making use of the two photon lie poisson coalgebra h6 the set of n 2 constants of the motion is shown to be a universal one for all these hamiltonians irrespective of the dependence of the latter on several arbitrary functions and n free parameters within this large class of quasi integrable n dimensional hamiltonians new families of completely integrable systems are identified by finding explicitly a new independent integral through the analysis of the sub coalgebra structure of h6 in particular new completely integrable n dimensional hamiltonians describing natural systems geodesic flows and static electromagnetic hamiltonians are presented

motion field and optical flow qualitative properties it is shown that the motion field the 2 d vector field which is the perspective projection on the image plane of the 3 d velocity field of a moving scene and the optical flow defined as the estimate of the motion field which can be derived from the first order variation of the image brightness pattern are in general different unless special conditions are satisfied therefore dense optical flow is often ill suited for computing structure from motion and for reconstructing the 3 d velocity field by algorithms which require a locally accurate estimate of the motion field a different use of the optical flow is suggested it is shown that the smoothed optical flow and the motion field can be interpreted as vector fields tangent to flows of planar dynamical systems stable qualitative properties of the motion field which give useful informations about the 3 d velocity field and the 3 d structure of the scene usually can be obtained from the optical flow the idea is supported by results from the theory of structural stability of dynamical systems

1 1 schrodinger lie bialgebras and their poisson lie groups all lie bialgebra structures for the 1 1 dimensional centrally extended schrodinger algebra are explicitly derived and proved to be of coboundary type therefore since all of them come from a classical r matrix the complete family of schrodinger poisson lie groups can be deduced by means of the sklyanin bracket all possible embeddings of the harmonic oscillator extended galilei and gl 2 lie bialgebras within the schrodinger classification are studied as an application new quantum hopf algebra deformations of the schrodinger algebra including their corresponding quantum universal r matrices are constructed

quantum symmetries of q difference equations a general method is presented to determine the symmetry operators of linear q difference equations it is applied to q difference analogs of the helmoltz heat and wave equations in diverse dimensions the symmetries are found to generate q deformations of classical lie algebras the method of separation of variables is used to obtain solutions which are seen to involve many basic special functions this allows the derivation of various identities and formulas for these q functions

physically based active shape models initialization and optimization in this paper we describe a new approach for 2 d object segmentation using an automatic method applied on images with problems as partial information overlapping objects many objects in a single scene severe noise conditions and locating objects with a very high degree of deformation we use a physically based shape model to obtain a deformable template which is defined on a canonical orthogonal coordinate system the proposed methodology works starting from the output of an edge detector which is processed to automatically obtain an approximation of the shape the final estimation of the shapes is obtained fitting a deformable template model which is defined on a learned surface of deformation results from biological images are presented

classification of real three dimensional poisson lie groups all real three dimensional poisson lie pl groups are explicitly constructed and fully classified under group automorphisms by making use of their one to one correspondence with the complete classification of real three dimensional lie bialgebras given in gomez 2000 j math phys 41 4939 many of these 3d pl groups are non coboundary structures whose poisson brackets are given here for the first time casimir functions for all three dimensional pl groups are given and some features of several pl structures are commented

lie bi algebra structures for centrally extended two dimensional galilei algebra and their lie poisson counterparts all bi algebra structures for centrally extended galilei algebra are classified the corresponding lie poisson structures on centrally extended galilei group are found

a novel fixed point iteration method for the solution of third order boundary value problems in this work a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications the method is based on embedding green s functions into well known fixed point iterations including picard s and krasnoselskii mann s schemes convergence of the numerical method is proved by manipulating the contraction principle the effectiveness of the proposed approach is established by implementing it on several numerical examples including linear and nonlinear third order boundary value problems the results show highly accurate approximations when compared to exact and existing numerical solutions

sensitivity analysis for matching and pose computation using dihedral junctions abstract recognition via localization is a popular approach in 3 d object recognition this approach relies on the propagation of constraints that arise from the matches of local geometric features and could therefore be treated as a constraint satisfaction problem hough clustering which verifies the consistency of local geometric constraints by determining the pose of the object in parameter space is a popular technique owing to its conceptual simplicity and potential ease of parallelization our previous work has shown the usefulness of dihedral junctions for the recognition and localization of polyhedral objects and dihedral feature junctions for the recognition and localization of curved objects made up of piecewise combinations of conical cylindrical and spherical surfaces experimental results from our previous work showed that the computed pose parameters are sensitive to the difference in the included angle between the scene and model dihedral junctions or the scene and model dihedral feature junctions a formal analysis of the sensitivity of the computed pose to the difference in the included angle between the scene and model dihedral junctions or the scene and model dihedral feature junctions is presented in this paper the results of the formal sensitivity analysis were found to be in conformity with the experimental results from our previous work and so the work presented in this paper could be treated as a sequel to our previous work based on the results of the sensitivity analysis the rotation parameters were found to be more sensitive than the translation parameters which in comparison were far more robust it is also shown how the introduction of redundancy in parameter space results in greater robustness in the computed pose although the analysis in this paper is based on the matching of dihedral junctions or dihedral feature junctions the approach taken in the sensitivity analysis is general and can be applied to the matching based on other feature types

existence result for a third order ode with nonlinear boundary conditions in presence of a sign type nagumo control abstract in this work we provide an existence and location result for the third order nonlinear differential equation u t f t u t u t u t where f a b r 3 r is a continuous function and two types of boundary conditions u a a u b u b 0 u a b or u a a u a u a 0 u b c with r 2 r continuous functions monotonous in the second variable and a b c r we assume that f satisfies a sign type nagumo condition which allows an asymmetric unbounded behaviour on the nonlinearity the arguments used concern leray schauder degree theory and lower and upper solutions technique

simple harish chandra modules over super schrodinger algebra in 1 1 dimensional spacetime the n 1 super schrodinger algebra s 1 1 in 1 1 dimensional spacetime contains a subalgebra isomorphic to osp 1 2 module let v be a simple weight module for the n 1 super schrodinger algebra s 1 1 but not a simple osp 1 2 module let supp v if v is neither a highest weight module nor a lowest weight module for s 1 1 we prove that supp v z and all non trivial weight spaces of v have the same dimension we prove that if v is a harish chandra module then it is a highest weight module or lowest weight module or a twisted localization of a highest weight module

a q schrodinger algebra its lowest weight representations and generalized q deformed heat schrodinger equations we construct a q deformation of the centrally extended schrodinger algebra and an algebraic representation theory through lowest weight representations we use verma modules over calculate their singular vectors and factorize the verma modules by submodules built on the singular vectors we also give a realization of with q difference operators and obtain a polynomial realization of the lowest weight representations and an infinite family of q difference equations which may be called generalized q deformed heat schrodinger equations we also apply our methods to the on shell q schrodinger algebra proposed by floreanini and vinet

an iterative hough procedure for three dimensional object recognition abstract this paper describes an iterative hough procedure for recognizing images of three dimensional objects straight line segments in the image are matched by finding the parameters of a viewing transformation of a three dimensional model consisting of line segments assuming the scale of the object is known there are three orientation and two translation parameters to be estimated initially a sparse regular subset of parameters and transformations is evaluated for goodness of fit then the procedure is repeated by successively subdividing the parameter space near current best estimates or peaks

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

simple weight modules for schrodinger algebra abstract let v be a simple weight module for the schrodinger algebra s 1 but not a simple sl 2 module let supp v if v is neither a highest weight module nor a lowest weight module for s 1 we prove that supp v z and all non trivial weight spaces of v have the same dimensions finally we construct an example of a simple s 1 module with infinite dimensional weight spaces

the combinatorics of object recognition in cluttered environments using constrained search abstract the problem of recognizing rigid objects from noisy sensory data has been successfully attacked in previous work by using a constrained search approach empirical investigations have shown the method to be very effective when recognizing and localizing isolated objects but less effective when dealing with occluded objects where much of the sensory data arises from objects other than the one of interest when clustering techniques such as the hough transform are used to isolate likely subspaces of the search space empirical performance in cluttered scenes improves considerably in this note we establish formal bounds on the combinatorics of this approach under some simple assumptions we show that the expected complexity of recognizing isolated objects is quadratic in the number of model and sensory fragments but that the expected complexity of recognizing objects in cluttered environments is exponential in the size of the correct interpretation we also provide formal bounds on the efficacy of using the hough transform to preselect likely subspaces showing that the problem remains exponential but that in practical terms the size of the problem is significantly decreased

a third order boundary value problem with one sided nagumo condition abstract in this paper we present an existence and location result for the third order separated boundary value problem u t f t u t u t u t u a a u a 0 u b 0 where f a b r 3 r is a continuous function and a r one sided nagumo condition lower and upper solutions a priori estimates and leray schauder degree play an important role in the arguments

free q schrodinger equation from homogeneous spaces of the 2 dim euclidean quantum group after a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups the quantum hyperboloidqh and the quantum planeqp are determined as homogeneous spaces offq e 2 the canonical action ofeq 2 is used to define a naturalq analog of the free schrodinger equation that is studied in the momentum and angular momentum bases in the first case the eigenfunctions are factorized in terms of products of twoq exponentials in the second case we determine the eigenstates of the unitary representation which in theqp case are given in terms of hahn exton functions introducing the universalt matrix foreq 2 we prove that the hahn exton as well as jacksonq bessel functions are also obtained as matrix elements oft thus giving the correct extension to quantum groups of well known methods in harmonic analysis

representations and clebsch gordan coefficients for the jordanian quantum algebra representation theory for the jordanian quantum algebra is developed closed form expressions are given for the action of the generators of on the basis vectors of finite dimensional irreducible representations it is shown how representation theory of has a close connection to the combinatorial identities involving summation formulae a general formula is obtained for the clebsch gordan coefficients of these clebsch gordan coefficients are shown to coincide with those of su 2 for but for they are in general a non zero monomial in

lie bialgebra quantizations of the oscillator algebra and their universal r matrices all coboundary lie bialgebras and their corresponding poisson lie structures are constructed for the oscillator algebra generated by quantum oscillator algebras are derived from these bialgebras by using the lyakhovsky and mudrov formalism and for some cases quantizations at both algebra and group levels are obtained including their universal r matrices

finite dimensional indecomposable modules for schrodinger algebra in this paper we give a classification of finite dimensional indecomposable modules of the schrodinger algebra

boson representations non standard quantum algebras and contractions a gelfan d dyson mapping is used to generate a one boson realization for the non standard quantum deformation of which directly provides its infinite and finite dimensional irreducible representations tensor product decompositions are worked out for some examples relations between contraction methods and boson realizations are also explored in several contexts so a class of two boson representations for the non standard deformation of is introduced and contracted to the non standard quantum 1 1 poincar representations likewise a quantum extended hopf algebra is constructed and non standard quantum oscillator algebra representations are obtained from it by means of another contraction procedure

quasi whittaker modules for the schrodinger algebra abstract in this paper we construct a class of new modules for the schrodinger algebra s called quasi whittaker modules different from 30 the quasi whittaker module is not induced by the borel subalgebra of the schrodinger algebra related with the triangular decomposition but by its heisenberg subalgebra h we prove that a simple s module v is a quasi whittaker module if and only if v is a locally finite h module furthermore we classify simple quasi whittaker modules by central character of u s and their quasi whittaker functions finally we characterize arbitrary quasi whittaker modules

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

classification of simple weight modules with finite dimensional weight spaces over the schrodinger algebra we classify simple weight modules with finite dimensional weight spaces over the centrally extended complex schrodinger algebra in 1 1 dimensional space time our arguments use the descriptio

a jordanian quantum two photon schrodinger algebra a non standard quantum deformation of the two photon algebra is constructed and its quantum universal r matrix is given representations of this new quantum algebra are studied on the fock space and translated into fock bargmann realizations that provide a direct formalism for the definition of deformed states of light finally the isomorphism between and the 1 1 schrodinger algebra is used to introduce a new non standard hopf algebra deformation of this latter symmetry algebra

irreducible decomposition for tensor product representations of jordanian quantum algebras tensor products of irreducible representations of the jordanian quantum algebras and are considered for both the highest weight finite dimensional representations of and the lowest weight infinite dimensional ones of it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding lie algebras

lower and upper solutions for a fully nonlinear beam equation abstract in this paper the two point fourth order boundary value problem is considered u i v f t u u u u 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r 4 r is a continuous function satisfying a nagumo type condition we prove the existence of a solution lying between lower and upper solutions using an a priori estimation lower and upper solutions method and degree theory the same arguments can be used with adequate modifications for any type of two point boundary value problem including all derivatives until order three with the second and the third derivatives given in different end points an application to the extended fisher kolmogorov problem will be obtained

duality for the jordanian matrix quantum group we find the hopf algebra dual to the jordanian matrix quantum group as an algebra it depends only on the sum of the two parameters and is split into two subalgebras with three generators and with one generator the subalgebra is a central hopf subalgebra of the subalgebra is not a hopf subalgebra and its co algebra structure depends on both parameters we discuss also two one parameter special cases g h and g h the subalgebra is a hopf algebra and coincides with the algebra introduced by ohn as the dual of the subalgebra is isomorphic to u sl 2 as an algebra but has a nontrivial co algebra structure and again is not a hopf subalgebra of

pose determination of a three dimensional object using triangle pairs a procedure is presented to estimate the unconstrained three dimensional location and orientation of an object with a known shape when it is visible in a single image using a generalized hough transform all six parameters of the object position are estimated from the distribution of values determined by matching triples of points on the object to possibly corresponding triples in the image most likely candidates for location are found and then the remaining rotational parameters are evaluated two solutions are generally admitted to the distribution by every match of triangles the number of possible matches is reduced by checking a simple geometric relation among triples even with partial occlusion experiments indicate that the procedure is very reliably accurate although optimization can further improve estimates of the parameters

on the sensitivity of the hough transform for object recognition object recognition from sensory data involves in part determining the pose of a model with respect to a scene a common method for finding an object s pose is the generalized hough transform which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters large clusters of similar transformations in that space are taken as evidence of a correct match a theoretical analysis of the behavior of such methods is presented the authors derive bounds on the set of transformations consistent with each pairing of data and model features in the presence of noise and occlusion in the image bounds are provided on the likelihood of false peaks in the parameter space as a function of noise occlusion and tessellation effects it is argued that haphazardly applying such methods to complex recognition tasks is risky as the probability of false positives can be very high

universal r matrix for non standard quantum a universal r matrix for the non standard jordanian quantum deformation of is presented a family of solutions of the quantum yang baxter equation is obtained from some finite dimensional representations of this lie bialgebra quantization of