nonlinear relaxed cocoercive variational inclusions involving a η accretive mappings in banach spaces in this paper we introduce a new concept of a h accretive mappings which generalizes the existing monotone or accretive operators we study some properties of a h accretive mappings and define resolvent operators associated with a h accretive mappings by using the new resolvent operator technique we also construct a new perturbed iterative algorithm with mixed errors for a class of nonlinear relaxed cocoercive variational inclusions involving a h accretive mappings and study applications of a h accretive mappings to the approximation solvability of this class of nonlinear relaxed cocoercive variational inclusions in q uniformly smooth banach spaces our results improve and generalize the corresponding results of recent works

global schrodinger maps in dimensions d 2 small data in the critical sobolev spaces we consider the schrodinger map initial value problem t on r d r 0 0 where r d r s 2 r 3 is a smooth function in all dimensions d 2 we prove that the schrodinger map initial value problem admits a unique global smooth solution 2 c r h 1 q q2 s 2 provided that the data 02 h 1 q is smooth and satises the smallness condition

blowup dynamics for smooth data equivariant solutions to the critical schrodinger map problem we consider the energy critical schrodinger map problem with the 2 sphere target for equivariant initial data of homotopy index k 1 we show the existence of a codimension one set of smooth well localized initial data arbitrarily close to the ground state harmonic map in the energy critical norm which generates finite time blowup solutions we give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy

the canny edge detector revisited canny ieee trans pattern anal image proc 8 6 679 698 1986 suggested that an optimal edge detector should maximize both signal to noise ratio and localization and he derived mathematical expressions for these criteria based on these criteria he claimed that the optimal step edge detector was similar to a derivative of a gaussian however canny s work suffers from two problems first his derivation of localization criterion is incorrect here we provide a more accurate localization criterion and derive the optimal detector from it second and more seriously the canny criteria yield an infinitely wide optimal edge detector the width of the optimal detector can however be limited by considering the effect of the neighbouring edges in the image if we do so we find that the optimal step edge detector according to the canny criteria is the derivative of an isef filter proposed by shen and castan graph models image proc 54 112 133 1992 in addition if we also consider detecting blurred or non sharp gaussian edges of different widths we find that the optimal blurred edge detector is the above optimal step edge detector convolved with a gaussian this implies that edge detection must be performed at multiple scales to cover all the blur widths in the image we derive a simple scale selection procedure for edge detection and demonstrate it in one and two dimensions

mixed equilibrium problems sensitivity analysis and algorithmic aspect abstract the aim of this paper is twofold first it is to extend the sensitivity analysis framework developed recently for variational inequalities to mixed equilibrium problems the second is to propose iterative methods for solving this kind of problems in the process we establish an equivalence between an extended version of wiener hopf equations and the given problems relying on a generalization of the yosida approximation notion our results generalize results obtained for optimization variational inequalities complementarity problems and problems of nash equilibria

large data well posedness in the energy space of the chern simons schrodinger system abstract we consider the initial value problem for the chern simons schrodinger system which is a gauge covariant schrodinger system in r t r x 2 with a long range electromagnetic field we show that in the coulomb gauge it is locally well posed in h s for s 1 and the solution map satisfies a local in time weak lipschitz bound by energy conservation we also obtain a global regularity result the key is to retain the non perturbative part of the derivative nonlinearity in the principal operator and exploit the dispersive properties of the resulting paradifferential type principal operator using adapted u p and v p spaces

optimal edge detectors for ramp edges it is argued that the best way to model an edge is by assuming all ideal mathematical function passed through a low pass filter and and immersed in noise using techniques similar to those developed by j canny 1983 1986 and l a spacek 1986 optimal filters are derived for ramp edges of various slopes the optimal nonrecursive filter for ideal step edges is then derived as a limiting case of the filters for ramp edges because there are no step edges in images edge detection is improved when the ramp filter is used instead of the filters developed for step edges for practical purposes some convolution masks are given which can be used directly for edge detection without the need to go into the details of the subject

sensitivity analysis for generalized nonlinear parametric a η m maximal monotone operator inclusion systems with relaxed cocoercive type operators abstract by using lim s inequalities nadler s results the new parametric resolvent operator technique associated with a m maximal monotone operators in this paper the existence theorem for a new class of generalized nonlinear parametric a m maximal monotone operator inclusion systems with relaxed cocoercive type operators in hilbert spaces is analyzed and established our results generalize sensitivity analysis results of other recent works on strongly monotone quasi variational inclusions nonlinear implicit quasi variational inclusions and nonlinear mixed quasi variational inclusion systems in hilbert spaces

existence and convergence theorems for a class of multi valued variational inclusions in banach spaces abstract an existence theorem for a new class of multi valued variational inclusion problems is established in smooth banach spaces further it is shown that a sequence of a mann type iteration algorithm is strongly convergent to the solutions in this class of variational inclusion problems

statistical edge detection learning and evaluating edge cues we formulate edge detection as statistical inference this statistical edge detection is data driven unlike standard methods for edge detection which are model based for any set of edge detection filters implementing local edge cues we use presegmented images to learn the probability distributions of filter responses conditioned on whether they are evaluated on or off an edge edge detection is formulated as a discrimination task specified by a likelihood ratio test on the filter responses this approach emphasizes the necessity of modeling the image background the off edges we represent the conditional probability distributions nonparametrically and illustrate them on two different data sets of 100 sowerby and 50 south florida images multiple edges cues including chrominance and multiple scale are combined by using their joint distributions hence this cue combination is optimal in the statistical sense we evaluate the effectiveness of different visual cues using the chernoff information and receiver operator characteristic roc curves this shows that our approach gives quantitatively better results than the canny edge detector when the image background contains significant clutter in addition it enables us to determine the effectiveness of different edge cues and gives quantitative measures for the advantages of multilevel processing for the use of chrominance and for the relative effectiveness of different detectors furthermore we show that we can learn these conditional distributions on one data set and adapt them to the other with only slight degradation of performance without knowing the ground truth on the second data set this shows that our results are not purely domain specific we apply the same approach to the spatial grouping of edge cues and obtain analogies to nonmaximal suppression and hysteresis

on schrodinger maps we study the question of well posedness of the cauchy problem for schrodinger maps from 2 to the sphere 2 or to 2 the hyperbolic space the idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear schrodinger system of equations and then study this modified schrodinger map system msm we then prove local well posedness of the cauchy problem for the msm with minimal regularity assumptions on the data and outline a method to derive well posedness of the schrodinger map itself from it in proving well posedness of the msm the heart of the matter is resolved by considering truly quatrilinear forms of weighted l2 functions 2002 wiley periodicals inc

parametric generalized set valued variational inclusions and resolvent equations abstract in this paper we develop the sensitivity analysis for generalized set valued variational inclusions and generalized resolvent equations we establish the equivalence between the parametric generalized set valued variational inclusions and parametric generalized resolvent equations by using the resolvent operator technique without assuming the differentiability of the given data

sensitivity analysis framework for variational inequalities in this paper a sensitivity analysis framework is developed for variational inequalities the perturbed solution to a parametric variational inequality problem is shown to be continuous and directionally differentiable under appropriate second order and regularity assumptions moreover this solution is once continuously differentiable if strict complementarity also holds

nonlinear parametric multi valued variational inclusion systems involving a η accretive mappings in banach spaces abstract in this paper by using the new parametric resolvent operator technique associated with a accretive mappings we analyze and establish an existence theorem for new nonlinear parametric multi valued variational inclusion systems involving a accretive mappings in banach spaces our results generalize sensitivity analysis results of other recent works on strongly monotone quasi variational inclusions nonlinear implicit quasi variational inclusions and nonlinear mixed quasi variational inclusion systems

a new generalised α scale spaces quadrature filters abstract the scale spaces is a recent theory that open new possibilities of phase based image processing it is a parameterised class 0 1 of linear scale space representations which allows a continuous connection beyond the well known gaussian scale space 1 in this paper we make use of this unified representation to derive new families of band pass quadrature filters built from derivatives and difference of the scale space generating kernels this construction leads to generalised kernel filters including the commonly known families derived from the gaussian and the poisson kernels the properties of each family are first studied and then experiments on one and two dimensional signals are shown to exemplify how the suggested filters can be used for edge detection this work is complemented by an experimental evaluation which demonstrates that the new proposed filters are a good alternative to the commonly used log gabor filter

equivariant schrodinger maps in two spatial dimensions we consider equivariant solutions for the schrodinger map problem from 2 1 to s2 with energy less than 4 and show that they are global in time and scatter

an unconstrained lagrangian formulation and conservation laws for the schrodinger map system we consider energy critical schrodinger maps from r2 into s2 and h2 viewing such maps with respect to orthonormal frames on the pullback bundle provides a gauge field formulation of the evolution we show that this gauge field system is the set of euler lagrange equations corresponding to an action that includes a chern simons term we also introduce the stress energy tensor and derive conservation laws in conclusion we offer comparisons between schrodinger maps and the closely related chern simons schrodinger system

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

on fixed point stability for set valued contractive mappings with applications to generalized differential equations where d x c inf d x c a set valued mapping t x c x is a ci 1 and for x y e x if x is complete then every set valued contraction has a fixed point i e a point x with x e tx the set of fixed points of t will be denoted by f t stability of fixed points of set valued contractions was investigated in 12 and lo in lo a stability theorem was proved under some rather restrictive conditions including i the domain of the maps being a closed convex bounded subset of a hilbert space ii the image of each point under each map being a closed convex subset theorem 1 below removes these conditions