on the numerical treatment of nonconvex energy problems multilevel decomposition methods for hemivariational inequalities abstract the variational formulation of mechanical problems involving nonmonotone possibly multivalued material or boundary laws leads to hemivariational inequalities since the underlying energy super potentials generally lack both convexity and smoothness these problems cannot be treated by the classical nonlinear analysis methods here we propose a method for the solution of a wide family of hemivariational inequalities it is based on a multilevel decomposition of the admissible solution space combined interactively with an appropriate structure decomposition which gives rise to a finite number of variational inequalities involving convex but nonsmooth energy functionals the latter can be solved easily using existing convex minimization algorithms concluding numerical examples illustrate the applicability of the approach

thresholding of digital images using two dimensional entropies abstract thresholding is an important form of image segmentation and is a first step in the processing of images for many applications the selection of suitable thresholds is ideally an automatic process requiring the use of some criterion on which to base the selection one such criterion is the maximization of the information theoretic entropy of the resulting background and object probability distributions most processes using this concept have made use of the one dimensional 1d grey level histogram of the image in an effort to use more of the information available in the image the present approach evaluates two dimensional 2d entropies based on the 2d grey level local average grey level histogram or scatterplot the 2d threshold vector that maximizes both background and object class entropies is selected

coercive and semicoercive hemivariational inequalities variational inequalities have a concrete mechanical meaning they are expressions of the principle of virtual work or power in its inequality form in the case of lack of monotonicity of the underlying stress strain or reaction displacement conditions or equivalently if the corresponding energy functionals are nonconvex the variational expressions are no longer variational inequalities another type of inequality expression arises as variational formulation of the problem these expressions have been introduced in mechanics by the author and are called hemivariational inequalities the aim of this paper is the formulation of an abstract mathematical theory for coercive and semicoercive hemivariational inequalities

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

on the superlinear convergence of a trust region algorithm for nonsmooth optimization it is proved that the second order correction trust region algorithm of fletcher 5 ensures superlinear convergence if some mild conditions are satisfied

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

a fast two dimensional entropic thresholding algorithm abstract two dimensional 2d entropic thresholding is one of the important thresholding techniques for image segmentation the selection of the global threshold vector is usually through a maximin optimization procedure a fast two phase 2d entropic thresholding algorithm is proposed in order to reduce the computation time first 9l 2 3 candidate threshold vectors are estimated from a quantized image of the original the global threshold vector is then obtained by checking candidates only the optimal computation complexity is o l 2 3 by quantizing the gray level into l 2 3 levels experimental results show that the processing time of each image is reduced from more than 2 h to about 2 min the required memory space is also greatly reduced

cyclic hodge integrals and loop schur functions abstract we conjecture an evaluation of three partition cyclic hodge integrals in terms of loop schur functions our formula implies the orbifold gromov witten donaldson thomas correspondence for toric calabi yau threefolds with transverse a n singularities we prove the formula in the case where one of the partitions is empty and thus establish the orbifold gromov witten donaldson thomas correspondence for local toric surfaces with transverse a n singularities

gromov witten donaldson thomas correspondence for toric 3 folds we prove the equivariant gromov witten theory of a nonsingular toric 3 fold x with primary insertions is equivalent to the equivariant donaldson thomas theory of x as a corollary the topological vertex calculations by agangic klemm marino and vafa of the gromov witten theory of local calabi yau toric 3 folds are proven to be correct in the full 3 leg setting

fast adaptive pnn based thresholding algorithms abstract thresholding is a fundamental operation in image processing based on the pairwise nearest neighbor technique and the variance criterion this theme presents two fast adaptive thresholding algorithms the proposed first algorithm takes o m k m time where k denotes the number of thresholds specified by the user m denotes the size of the compact image histogram and the parameter has the constraint 1 m on a set of different real images experimental results reveal that the proposed first algorithm is faster than the previous three algorithms considerably while having a good feature preserving capability the previous three mentioned algorithms need o m k time given a specific peak signal to noise ratio psnr we further present the second thresholding algorithm to determine the number of thresholds as few as possible in order to obtain a thresholded image satisfying the given psnr the proposed second algorithm takes o m k m n time where n and denote the image size and the fewest number of thresholds required respectively some experiments are carried out to demonstrate the thresholded images that are encouraging since the time complexities required in our proposed two thresholding algorithms are polynomial they could meet the real time demand in image preprocessing

delamination of composites as a substationarity problem numerical approximation and algorithms abstract a method for the effective numerical treatment of the delamination problem in laminated composites is proposed the interaction between the laminae due to the binding material is described by means of a nonmonotone possibly multivalued law such laws express a variety of limit phenomena related to the discontinuous loss of resistance at the interface by using the methods of nonsmooth mechanics the problem is written as a hemivariational inequality and is transformed into a substationarity problem for nonconvex nonsmooth energy functions using the appropriate finite element discretization the latter problem is formulated in finite dimensions a domain decomposition type numerical approximation is proposed and a new algorithm is developed for the numerical treatment of the delamination problem numerical examples verify the theoretically predicted stability accuracy and speed of the method and illustrate its properties and applicability

gray level image thresholding based on fisher linear projection of two dimensional histogram abstract thresholding is an important form of image segmentation and is a first step in the processing of images for many applications the selection of suitable thresholds is ideally an automatic process requiring the use of some criterion on which the selection is based most such criteria are only based on the one dimensional id gray level histogram of image in an effort to use more information available in the image the present approaches use the criteria based on the two dimensional 2d histogram of the image however these methods which simply extend the 1d histogram based algorithms to the 2d histogram give rise to the exhaustive search for the threshold values in this paper an optimal projection of the 2d histogram is derived by applying fisher linear discriminant the optimal projection turns out to be the local average histogram analysis and experimental results show that thresholding an image based on the local average histogram one can obtain segmentation better than that of those simply using criteria based on 2d histogram while the spent computation time is as much as that costed by the ones using criteria based on 1d histogram

on the approximation of nonmonotone multivalued problems by monotone subproblems abstract structures involving zig zag type reaction displacement or stress strain laws i e nonmonotone possibly multivalued laws cannot be effectively treated by the classical numerical methods for nonlinear laws in order to calculate the arising free boundaries accurately we propose a new approximation method of the nonmonotone problem by monotone ones the proposed method finds its justification in the approximation of a hemivariational inequality by a sequence of variational inequalities also the case of combining this procedure with fixed point algorithms to treat more complicated problems is considered the numerical methods proposed are illustrated mainly by numerical examples which are described in detail

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

convergence properties of algorithms for nonlinear optimization this paper reviews some of the most successful methods for unconstrained constrained and nondifferentiable optimization calculations particular attention is given to the contribution that theoretical analysis has made to the development of algorithms it seems that practical considerations provide the main new ideas and that subsequent theoretical studies give improvements to algorithms coherence to the subject and better understanding

a thresholding method based on two dimensional renyi s entropy in this paper we present a new thresholding technique based on two dimensional renyi s entropy the two dimensional renyi s entropy was obtained from the two dimensional histogram which was determined by using the gray value of the pixels and the local average gray value of the pixels this new method extends a method due to sahoo et al pattern recognition 30 1997 71 and includes a previously proposed global thresholding method due to abutaleb pattern recognition 47 1989 22 further our method extends a global thresholding method due to chang et al ieee trans image process 4 1995 370 to the two dimensional setting the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

a combinatorial proof of the giambelli identity for schur functions the giambelli identity provides a formula for expressing an arbitrary schur function of shape as a determinant of schur functions of hook shapes l 1k we give the first complete combinatorial proof of the giambelli identity we show how to derive various hook formulas from the giambelli identity and show how to extend our methods to derive extensions of the giambelli identity and the hook formula for the number of standard tableaux to certain skew shapes

the orbifold topological vertex abstract we develop a topological vertex formalism for computing the donaldson thomas invariants of calabi yau orbifolds the basic combinatorial object is the orbifold vertex v g a generating function for the number of 3d partitions asymptotic to 2d partitions and colored by representations of a finite abelian group g acting on c 3 in the case where g z n acting on c 3 with transverse a n 1 quotient singularities we give an explicit formula for v g in terms of schur functions we discuss applications of our formalism to the donaldson thomas crepant resolution conjecture and to the orbifold donaldson thomas gromov witten correspondence we also explicitly compute the donaldson thomas partition function for some simple orbifold geometries the local football p a b 1 and the local b z 2 gerbe