adsorbing motzkin paths the adsorption of a motzkin path with lifted endpoints onto an adsorbing line is examined as a model of polymer adsorption the partition function of this model is determined exactly and the free energy is derived by examining the partition function the location of the critical point in the model is given exactly in one case and as the solution of a nonlinear equation in another case the phase diagram of the model is examined and i show that the transition is in general a first order adsorption transition except in cases where one or both endpoints of the path are restricted to be close to the adsorbing line

adsorbing and collapsing directed animals a model of a self interacting directed animal which also interacts with a solid wall is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition the directed animal is confined to a 45 wedge and it interacts with one of the walls of this wedge the existence of a thermodynamic limit in this model shown and the presence of an adsorption transition is demonstrated by using constructive techniques by comparing this model to a process of directed percolation we show that there is also a collapse or transition in this model we examine directed percolation in a wedge to show that there is a collapse phase present for arbitrary large values of the adsorption activity the generating function of adsorbing directed animals in a half space is found next from which we find the tricritical exponents associated with the adsorption transition a full solution for a collapsing directed animal seems intractible so instead we examine the collapse transition of a model of column convex directed animals with a contact activity next

the efficiency and consistency of approximations to the jackknife variance estimators abstract the problem considered is the computation reduction for general delete d jackknife variance estimators the delete d jackknife estimator was proved consistent shao and wu 1986 and in this article its mean squared error is shown to have order o n 2 where n is the sample size these properties are not shared by the traditional delete 1 jackknife in some situations use of the delete d jackknife however requires n d recomputations of a point estimate which increases rapidly as n and d increase using techniques from survey sampling a shortcut can be taken with evaluated only m times m n d the efficiency and consistency of the resulting jackknife sampling hybrid variance estimators jsve s are studied if m is chosen so that n m 0 the increase in mean squared error by using the jsve is relatively negligible for the consistency of jsve m is sufficient hence the jsve with m n can also be used to alleviate the computational burden for the delete 1 jackknife in th

pulled motzkin paths in this paper the models of pulled dyck paths in janse van rensburg 2010 j phys a math theor 43 215001 are generalized to pulled motzkin path models the generating functions of pulled motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a motzkin path pulled at its endpoint see orlandini and whittington 2004 j phys a math gen 37 5305 14 is shown to be r f 0 for forces pushing the endpoint toward the adsorbing line and r f f 1 2cosh f 2sinh f f as f for forces pulling the path away from the x axis in addition the elastic response of a motzkin path pulled at its midpoint is shown to be r f 0 for forces pushing the midpoint toward the adsorbing line and r f f 1 2cosh f 2 sinh f 2 2f as f for forces pulling the path away from the x axis formal combinatorial identities arising from pulled motzkin path models are also presented these identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts

approximation methods for common solutions of generalized equilibrium systems of nonlinear variational inequalities and fixed point problems in this paper we introduce an iterative method for finding a common element of the set of solutions of the generalized equilibrium problems the set of solutions for the systems of nonlinear variational inequalities problems and the set of fixed points of nonexpansive mappings in hilbert spaces furthermore we apply our main result to the set of fixed points of an infinite family of strict pseudo contraction mappings the results obtained in this paper are viewed as a refinement and improvement of the previously known results

convergence and certain control conditions for hybrid iterative algorithms very recently yao et al 2010 4 proposed a hybrid iterative algorithm under the parameter sequences satisfying some quite restrictive conditions they derived a strong convergence theorem in a hilbert space in this paper under the weaker conditions we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings which solves a variational inequality an appropriate example such that all conditions of this result that are satisfied and that other conditions are not satisfied is provided moreover the method of our paper is different from the method in yao et al 2010 4

pulled directed lattice paths the generating functions of models of directed walks pulled by an external force f are determined using the kernel method these paths are models of linear polymers subject to an external force the generating function is related to the generating function of ballot paths and has an unexpected and non physical singularity for the model of dyck paths pulled at its central vertex in each model the force extension curve is determined exactly and has a sigmoid shape partially given by ctanh cf if f is the applied force and where c and c are the model dependent constants this result is consistent with previous results for models of pulled directed paths and also with data obtained from the numerical simulation of self avoiding walk models of linear polymers

a new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization abstract in this paper we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for inverse strongly monotone mappings in a hilbert space under suitable conditions some strong convergence theorems for approximating a common element of the above three sets are obtained as applications at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings the results presented in the paper extend and improve some recent results of yao and yao y y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings appl math comput 186 2 2007 1551 1558 plubtieng and punpaeng s plubtieng r punpaeng a new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings appl math comput 2007 doi 10 1016 j amc 2007 07 075 s takahashi and w takahashi s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2006 506 515 su shang and qin y f su m j shang x l qin an iterative method of solution for equilibrium and optimization problems nonlinear anal 2007 doi 10 1016 j na 2007 08 045 and chang cho and kim s s chang y j cho j k kim approximation methods of solutions for equilibrium problem in hilbert spaces dynam systems appl in print

algorithms for approximating minimization problems in hilbert spaces in this paper we study the following minimization problem minx fix s w m2 12 x 2 h x where b is a bounded linear operator m 0 is some constant h is a potential function for c f fix t is the set of fixed points of nonexpansive mapping s and w is the solution set of an equilibrium problem this paper introduces two new algorithms one implicit and one explicit that can be used to find the solution of the above minimization problem

on an adaptive transformation retransformation estimate of multivariate location an affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied the work is primarily motivated by earlier work on different versions of the multivariate median and their properties we explore an issue related to efficiency and equivariance that was originally raised by bickel and subsequently investigated by brown and hettmansperger our estimate has better asymptotic performance than the vector of co ordinatewise medians when the variables are substantially correlated the finite sample performance of the estimate is investigated by using monte carlo simulations some examples are presented to demonstrate the effect of the adaptive transformation retransformation strategy in the construction of multivariate location estimates for real data

composite models of polygons a composite polygon is composed of a lattice polygon in the square lattice which contains in its interior an internal structure which may also be a lattice polygon or a lattice tree or a lattice animal or a lattice disc or a collection of these the properties of composite polygons are considered in this manuscript in particular i shall consider the growth constants and generating functions of these models as well as the statistical mechanics of interacting models of composite polygons it is shown that there is an adsorption transition of the internal structure on the containing polygon and a transition which corresponds to the inflation of the containing polygon by the internal structure

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

common fixed points of strict pseudocontractions by iterative algorithms in this paper we present iteration schemes to weakly and strongly approximate common fixed points of a finite family of a class of strict pseudocontractions

estimators related to u processes with applications to multivariate medians asymptotic normality if a criterion function g x 1 x m depends on m 1 samples then a natural estimator of arg max p m g x 1 x m is the arg max of a uprocess it is observed that under suitable conditions these estimators are asymptotically normal this is then applied to prove asymptotic normality of liu s simplicial median and of oja s medians in r d

adsorption of uniform lattice animals with specified topology the author studies the effects of topology on the free energy of uniform lattice animals interacting with a surface topology is specified by fixing an abstract graph tau and the lattice animals considered are embeddings of tau in the square and simple cubic lattice he proves that such embeddings in the simple cubic lattice and interacting with a plane have the same free energy as self avoiding walks independent of the choice of tau and independent of whether or not the embeddings are restricted to be uniform for embeddings in the square lattice and interacting with a line he proves that the free energy may differ from that for walks depending on whether tau has a cut edge further restricting the embeddings to be uniform forces the free energy to be different from that for walks for all tau except the tau corresponding to walks and we obtain bounds on the free energy which depend on the number of branches cycles and vertices of degree 3 and 4 in the graph

strong convergence theorems for nonexpansive mappings and inverse strongly monotone mappings abstract in this paper we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a hilbert space then we show that the sequence converges strongly to a common element of two sets using this result we consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly monotone mapping

a general theory for jackknife variance estimation the delete 1 jackknife is known to give inconsistent variance estimators for nonsmooth estimators such as the sample quantiles this well known deficiency can be rectified by using a more general jackknife with d the number of observations deleted depending on a smoothness measure of the point estimator our general theory explains why jackknife works or fails it also shows that i for sufficiently smooth estimators the jackknife variance estimators with bounded d are consistent and asymptotically unbiased and ii for nonsmooth estimators d has to go to infinity at a rate explicitly determined by a smoothness measure to ensure consistency and asymptotic unbiasedness improved results are obtained for several classes of estimators in particular for the sample p quantiles the jackknife variance estimators with d satisfying n 1 2 d rightarrow 0 and n d rightarrow infty are consistent and asymptotically unbiased

viscosity approximation schemes for fixed point problems and equilibrium problems and variational inequality problems abstract in this paper we first introduce a general iterative scheme by halpern approximation method for finding a common element of the set of solutions of an equilibrium problem the set of solutions of the variational inequality for an infinite family of i inverse strongly monotone mappings and the set of common fixed points for a family of infinitely nonexpansive mappings in a hilbert space then we extend the halpern iterative scheme to a general viscosity approximation scheme by a simple and different method as applications we utilize our results to investigate some convergence problems for strictly pseudocontractive mappings and maximal monotone operators the results obtained in this paper extend and improve the recent ones announced by many others

self avoiding walks interacting with a surface discusses two models of polymer adsorption in one model a self avoiding walk on a d dimensional lattice interacts with a d 1 dimensional hyperplane in the other model this walk must also lie in or on one side of this hyperplane both models exhibit non analytic behaviour corresponding to a phase transition but these phase transitions do not occur at the same point the authors give numerical estimates of the locations of these transitions

a cautionary note on robust covariance plug in methods many multivariate statistical methods rely heavily on the sample covariance matrix it is well known though that the sample covariance matrix is highly non robust one popular alternative approach for robustifying the multivariate method is to simply replace the role of the covariance matrix with some robust scatter matrix the aim of this paper is to point out that in some situations certain properties of the covariance matri x are needed for the corresponding robust plug in method to be a valid approach and that not all scatter matrices necessarily possess these important properties in particular the fol lowing three multivariate methods are discussed in this paper independent components analysis observational regression and graphical modeling for each case it is shown that using a symmetrized robust scatter matrix in place of the covariance matrix results in a proper robust multivariate method

an approach to multivariate rank tests in multivariate analysis of variance abstract a class of multivariate rank like quantities is defined and used to develop multivariate tests to mimic popular one dimensional rank tests such as the mann whitney wilcoxon two sample test the jonckheere terpstra test for trend and the kruskal wallis one way analysis of variance test tests in one way analysis of variance are developed based on qualitative orthogonal contrasts allowing decomposition of an overall statistic into asymptotically independent components based on the contrasts the class of tests includes the usual normal theory tests and the componentwise rank tests but the main focus is on the tests based on a particular definition of multivariate rank a study of the pitman efficiency of the latter tests to those based on multivariate medians shows them to be superior at the normal slightly heavy tailed and light tailed distributions whereas the median based tests are superior for heavy tails these results are analogous to the univariate case

on modified iterative method for nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions

convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems abstract the purpose of this work is to introduce a hybrid projection method for finding a common element of the set of a generalized equilibrium problem the set of solutions to a variational inequality and the set of fixed points of a strict pseudo contraction in a real hilbert space

an iterative method of solution for equilibrium and optimization problems abstract in this paper we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping the set of solutions of the variational inequality for an inverse strongly monotone mapping and the set of solutions of an equilibrium problem in a hilbert space we show that the iterative sequence converges strongly to a common element of the three sets the results of this paper extended and improved the results of h iiduka and w takahashi strong convergence theorems for nonexpansive mappings and inverse strongly monotone mappings nonlinear anal 61 2005 341 350 and s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 therefore by using the above result an iterative algorithm for the solution of a optimization problem was obtained

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

estimates of regression coefficients based on the sign covariance matrix the influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the scm regression estimate the estimate is shown to be consistent with a limiting multinormal distribution the influence function as a function of the length of the contamination vector is shown to be linear in elliptic cases for the least squares ls estimate it is quadratic the asymptotic relative efficiencies with respect to the ls estimate are given in the multivariate normal as well as the t distribution cases the scm regression estimate is highly efficient in the multivariate normal case and for heavy tailed distributions it performs better than the ls estimate simulations are used to consider finite sample efficiencies with similar results the theory is illustrated with an example

viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces abstract in this paper we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove a strong convergence theorem which is connected with combettes and hirstoaga s result p l combettes s a hirstoaga equilibrium programming in hilbert spaces j nonlinear convex anal 6 2005 117 136 and wittmann s result r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 using this result we obtain two corollaries which improve and extend their results

viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications abstract in this paper we introduce a general iterative scheme for finding a common element of the set of common solutions of generalized equilibrium problems the set of common fixed points of a family of infinite non expansive mappings strong convergence theorems are established in a real hilbert space under suitable conditions as some applications we consider convex feasibility problems and equilibrium problems the results presented improve and extend the corresponding results of many others

robust multivariate regression we introduce a robust method for multivariate regression based on robust estimation of the joint location and scatter matrix of the explanatory and response variables as a robust estimator of location and scatter we use the minimum covariance determinant mcd estimator of rousseeuw based on simulations we investigate the finite sample performance and robustness of the estimator to increase the efficiency we propose a reweighted estimator selected from several possible reweighting schemes the resulting multivariate regression does not need much computation time and is applied to real datasets we show that the multivariate regression estimator has the appropriate equivariance properties has a bounded influence function and inherits the breakdown value of the mcd estimator these theoretical robustness properties confirm the good finite sample results obtained from the simulations

a viscosity approximation scheme for system of equilibrium problems nonexpansive mappings and monotone mappings abstract in this paper we introduce a new viscosity approximation scheme based on the extragradient method for finding a common element of the set of solutions to a system of equilibrium problems the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions to the variational inequality for a monotone lipschitz continuous mapping several convergence results for the sequences generated by these processes in hilbert spaces were derived

m estimation of multivariate regressions abstract robust alternatives to the seemingly unrelated regression sur estimator of zellner 1962 are proposed for the classical multivariate regression model these weighted m estimators achieve an asymptotic covariance matrix analogous to that of the sur estimator comparisons for the l 1 least absolute deviation case are made with the efficient estimator in the case of elliptically contoured distributions an example reanalyzing the grunfeld investment data using a smooth l 1 like m estimator is discussed in detail in contrast to recent work of hampel ronchetti rousseeuw and stahel 1986 rousseeuw 1987 and oja 1983 the methods studied here are not affine equivariant some remarks on the potential significance of this failing conclude the article

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

a hybrid extragradient method for approximating the common solutions of a variational inequality a system of variational inequalities a mixed equilibrium problem and a fixed point problem abstract in this paper we give a hybrid extragradient iterative method for finding the approximate element of the common set of solutions of a generalized equilibrium problem a system of variational inequality problems a variational inequality problem and a fixed point problem for a strictly pseudocontractive mapping in a real hilbert space further we establish a strong convergence theorem based on this method the results presented in this paper improves and generalizes the results given in yao et al 36 and ceng et al 7 and some known corresponding results in the literature

a directed walk model of a long chain polymer in a slit with attractive walls we present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential we consider three geometric constraints on the ends of the polymer and concentrate on the long chain limit apart from the general interest in the effect of geometrical confinement this can be viewed as a two dimensional model of steric stabilization and sensitized flocculation of colloidal dispersions we demonstrate that the large width limit admits a phase diagram that is markedly different from the one found in a half plane geometry even when the polymer is constrained to be fixed at both ends on one wall we are not able to find a closed form solution for the free energy for finite width at all values of the interaction parameters but we can calculate the asymptotic behaviour for large widths everywhere in the phase plane this allows us to find the force between the walls induced by the polymer and hence the regions of the plane where either steric stabilization or sensitized flocculation would occur

modified block iterative algorithm for quasi ϕ asymptotically nonexpansive mappings and equilibrium problem in banach spaces abstract the purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi asymptotically nonexpansive mappings and the set of an equilibrium problem under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex banach space with the kadec klee property as an application at the end of the paper a numerical example is given the results presented in the paper improve and extend the corresponding results in qin et al convergence theorems of common elements for equilibrium problems and fixed point problem in banach spaces j comput appl math 225 2009 20 30 zhou et al convergence theorems of a modified hybrid algorithm for a family of quasi asymptotically nonexpansive mappings j appl math compt 17 march 2009 doi 10 1007 s12190 009 0263 4 takahashi and zembayshi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 wattanawitoon and kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid syst 3 2009 11 20 and matsushita and takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 and others

self avoiding walks in a slab with attractive walls we consider a self avoiding walk confined between two parallel planes or lines with an energy term associated with each vertex of the walk in the confining planes we allow the energy terms to be different for the top and bottom planes we use exact enumeration and monte carlo methods to investigate the force between the confining planes and how it depends on the width of the slab and on the interaction energy terms the phase diagram is qualitatively similar to that found for a directed walk model

self avoiding walks in wedges the authors consider the number of self avoiding walks confined to a subset zd f of the d dimensional hypercubic lattice zd such that the coordinates x1 x2 xd of each vertex in the walk satisfy x1 or 0 and 0 or xk or fk x1 for k 2 3 d they show that if fk x to infinity as x to infinity the connective constant of walks in zd f is identical to the convective constant of walks in zd they also explore conditions on fk which lead to a smaller connective constant for walks in zd f and in particular consider walks between two parallel d 1 dimensional hyperplanes finally they contrast some of these results with recent work by grimmett on percolation on subsets of the square lattice

an infinite family of adsorption models and restricted lukasiewicz paths we define k l restricted lukasiewicz paths k l 0 and use these paths as models of polymer adsorption we write down a polynomial expression satisfied by the generating function for arbitrary values of k l the resulting polynomial is of degree l 1 and hence cannot be solved explicitly for sufficiently large l we provide two different approaches to obtain the phase diagram in addition to a more conventional analysis we also develop a new mathematical characterisation of the phase diagram in terms of the discriminant of the polynomial and a zero of its highest degree coefficient

a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main theorem extends a recent result of yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings applied mathematics and computation 186 2 2007 1551 1558

estimates of regression coefficients based on lift rank covariance matrix we introduce a new equivariant estimation method of the parameters of the multivariate regression model with q responses and p regressors the estimate matrix is derived from the lift rank covariance matrix lrcm where the lift rank vectors are based on the oja criterion function the k p q variate ranks and k 1 variate lift ranks are constructed using hyperplanes or fits going through k observations the new lrcm regression estimate and the least squares ls estimate are shown to be weighted sums of the elemental estimates based on these hyperplanes the lrcm regression estimate is equivariant and convergent has a limiting multinormal distribution and is highly efficient in the multivariate normal case for heavy tailed distributions it performs better than the standard ls estimate estimation of the variance covariance matrix of the lrcm estimate is briefly discussed the theory is illustrated by simulations and a real data example

on the critical behaviour of a surface interacting linear polymer chain abstract a method based on a real space renormalization group transformation is developed to describe the critical behaviour of a surface interacting linear flexible polymer chain represented by a self avoiding walk it is shown that a lattice model based on a central rule in which the starting point of the walk and the surface are taken to be in the middle of one cell provides a suitable framework to study both the penetrable and impenetrable surfaces in contrast to this a method based on a corner rule in which the starting point of the walk and the surface are fixed to be one corner of a cell cannot describe the behaviour of a chain interacting with an impenetrable surface the value of crossover exponent found by us for a square lattice are in agreement with those expected to be exact for both the cases

strong convergence of shrinking projection methods for quasi φ nonexpansive mappings and equilibrium problems the purpose of this paper is to consider the convergence of a shrinking projection method for a finite family of quasi f nonexpansive mappings and an equilibrium problem strong convergence theorems are established in a uniformly smooth and strictly convex banach space which also enjoys the kadec klee property

exact solution of the discrete 1 1 dimensional rsos model in a slit with field and wall interactions we present the solution of a linear restricted solid on solid rsos model confined to a slit we include a field like energy which equivalently weights the area under the interface and also include independent interaction terms with both walls this model can also be mapped to a lattice polymer model of motzkin paths in a slit interacting with both walls including an osmotic pressure this work generalizes the previous work on the rsos model in the half plane which has a solution that was shown recently to exhibit a novel mathematical structure involving basic hypergeometric functions 3 2 because of the mathematical relationship between the half plane and slit this work hence effectively explores the underlying q orthogonal polynomial structure to that solution it also generalizes two other recent works one on dyck paths weighted with an osmotic pressure in a slit and another concerning motzkin paths without an osmotic pressure term in a slit

self avoiding polygons and walks in slits a polymer in a confined geometry may be modeled by a self avoiding walk or a self avoiding polygon confined between two parallel walls in two dimensions this model involves self avoiding walks or self avoiding polygons in the square lattice between two parallel confining lines interactions of the polymer with the confining walls are introduced by energy terms associated with edges in the walk or polygon which are at or near the confining lines we use transfer matrix methods to investigate the forces between the walk or polygon and the confining lines as well as to investigate the effects of the confining slit s width and of the energy terms on the thermodynamic properties of the walks or polygons in several models the phase diagram found for the self avoiding walk models is qualitatively similar to the phase diagram of a directed walk model confined between two parallel lines as was previously conjectured however the phase diagram of one of our polygon models is found to be significantly different and we present numerical data to support this for that particular model we prove that for any finite values of the energy terms there are an infinite number of slit widths where a polygon will induce a steric repulsion between the confining lines

moment condition tests for heavy tailed time series abstract we develop an asymptotically chi squared statistic for testing moment conditions e m t 0 0 where m t 0 may be weakly dependent scalar components of m t 0 may have an infinite variance and e m t need not exist for any under the alternative score tests are a natural application and in general a variety of tests can be heavy tail robustified by our method including white noise garch affects omitted variables distribution functional form causation volatility spillover and over identification the test statistic is derived from a tail trimmed sample version of the moments evaluated at a consistent plug in t for 0 depending on the test in question and heaviness of tails t may be any consistent estimator including sub t 1 2 convergent and or asymptotically non gaussian ones since t can be assured not to affect the test statistic asymptotically we adapt bootstrap p value occupation time and covariance determinant methods for selecting the trimming fractile in any sample and apply our statistic to tests of white noise omitted variables and volatility spillover we find it obtains sharp empirical size and strong power while conventional tests exhibit size distortions

on variational inclusion and common fixed point problems in hilbert spaces with applications abstract the purpose of this paper is to introduce a general iterative method for finding a common element of the solution set of quasi variational inclusion problems and of the common fixed point set of an infinite family of nonexpansive mappings in the framework hilbert spaces strong convergence of the sequences generated by the purposed iterative scheme is obtained

self avoiding walks and polymer adsorption edge and vertex weighting self avoiding walks interacting with a surface are a useful model of polymer adsorption and one can choose to weight the walk according to the number of vertices or the number of edges in the surface we consider a combined model of self avoiding walks on the d dimensional hypercubic lattice with weights associated with the numbers of vertices and edges in the surface and investigate its phase diagram we also derive inequalities relating the critical points in the edge and vertex weighting schemes

some results on generalized equilibrium problems involving a family of nonexpansive mappings abstract in this paper we introduce an iterative method for finding a common element in the solution set of generalized equilibrium problems in the solution set of variational inequalities and in the common fixed point set of a family of nonexpansive mappings strong convergence theorems are established in the framework of hilbert spaces

exact enumeration results for self avoiding walks on the honeycomb lattice attached to a surface we consider self avoiding walks on the honeycomb lattice interacting with a surface with different energies associated between sites in contact with a linear boundary to the left of the origin and those in contact with the right of the boundary we numerically confirm recent exact results for the polymer adsorption transition and corresponding critical exponents with mixed ordinary and special boundary conditions the phase diagram is elucidated with the aid of some rigorous arguments

motzkin path models of long chain polymers in slits we consider motzkin path models for polymers confined to a slit the path interacts with each of the two confining lines and we define parameters a and b to characterize the strengths of the interactions with the two lines we consider the cases where i each vertex in a confining line contributes to the energy and ii where each edge in a confining line contributes to the energy for the vertex and edge versions of motzkin paths we can find the generating functions and give rigorous explicit expressions for the free energy at some special points in the a b plane and asymptotically i e for large slit widths elsewhere we find regions where the force between the lines is long range and repulsive short range and repulsive and short range and attractive our results indicate that the general form of the phase diagram is model independent and similar to previous results for a dyck path model although the details do depend on the underlying configurational model we also contrast the method used here to find the generating function with the transfer matrix and heap methods

a general iterative method for addressing mixed equilibrium problems and optimization problems abstract in this paper we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem mep the set of fixed points of an infinite family of nonexpansive mappings t n n 1 and the set of solutions of variational inequalities for a inverse strongly monotone mapping in hilbert spaces furthermore we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems our results extend and improve the recent results of yao et al y yao m a noor s zainab y c liou mixed equilibrium problems and optimization problems j math anal appl 354 2009 319 329 y yao m a noor y c liou on iterative methods for equilibrium problems nonlinear anal 70 1 2009 479 509 and many others

affine invariant multivariate multisample sign tests summary invariant sign type tests for the multivariate multisample location models are developed the definition of sign is based on the oja criterion function emphasis is on the twosample location model and the associated equivariant estimate of shift asymptotic theory is developed to provide large sample approximations for the null distribution of the test and to provide a framework for a discussion of efficiency tests are then developed for the one way and two way lay outs