continuum percolation in two dimensions monte carlo tests of scaling and universality for non interacting discs detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2l2 ordinary lattke percolation would correspond to the discs being situated on the vertices of a j2l x j2l lattice computer simulations are carried out for a sequence of increasing system sizes ranging from l 20 to l 1000 for each value of l a large number of realisations are generated for 25 values of the disc concentration x we calculate a variety of estimates for the threshold parameter x as well as the critical exponents p y t and v our exponent estimates are in close agreement with accepted values for ordinary lattice percolation therefore this continuum system appears to be in the same universality class as lattice percolation

a new completely general class of variational inclusions with noncompact valued mappings abstract in this paper we introduce and study a new completely general class of variational inclusions with noncompact valued mappings and construct some new iterative algorithms we prove the existence of solutions for the completely general class of variational inclusions and the convergence of iterative sequences generated by the algorithms

a new system of generalized nonlinear quasi variational like inclusions with a monotone operators in banach spaces in this paper we study some properties of a monotone operator in banach space give the notion of proximal mapping associated with the a monotone operator and show its lipschitz continuity we also consider a new system of generalized nonlinear quasi variational like inclusions with a monotone operators in banach spaces and constructed a new iterative algorithm for solving the system of generalized nonlinear quasi variational like inclusions in banach spaces under suitable assumptions we prove the convergence of the iterative sequences generated by the algorithm

perturbed proximal point algorithms for general quasi variational like inclusions in this paper we introduce two new concepts of subdifferential and proximal mappings of proper functionals on hilbert spaces the existence and lipschitz continuity of proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of general quasi variational like inclusions and develop some new perturbed proximal point algorithms of mann and ishikawa type for finding the approximate solutions of the general quasi variational like inclusions the convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed our algorithms and results improve and generalize many known results in the literature

long time dynamics close to a percolation threshold abstract the response function for random walks on a bond disordered lattice is calculated in the effective medium approximation ema the basis for this approximation is reviewed and several exact limits preserved by this model are noted for low density bond disorder the velocity autocorrelation function is calculated from the ema and compared with exact expansions to order c2 more generally the long time dynamics is shown to have a universal form over a wide range of densities however at densities close to the percolation threshold this form is modified in particular the amplitudes of the long time tails are found to be divergent at the threshold indicating a crossover to a qualitatively different dynamics this crossover phenomenon is investigated analytically and numerically for the ema

variational inclusions with a general h monotone operator in banach spaces in this paper we introduce a new class of operator general h monotone operators in banach space we define a proximal mapping associated with the general h monotone operator and show its lipschitz continuity we also consider a new class of variational inclusions involving these general h monotone operators and constructed a new iterative algorithm for solving the variational inclusion in banach spaces under some suitable conditions we prove the convergence of the iterative sequence generated by the algorithm

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

generalized strongly nonlinear quasivariational inequalities abstract in this paper we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a generalized strongly nonlinear variational inequality and a generalized strongly nonlinear complementarity problem an algorithm for finding the approximate solution of generalized strongly nonlinear quasivariational inequalities and generalized strongly nonlinear quasicomplementarity problems is also given as special cases these results include the corresponding results of fang and peterson noor siddiqi and ansari and ding

algorithm for solving a new class of generalized nonlinear implicit quasi variational inclusions in banach spaces abstract in this paper we introduce and study a new class of generalized nonlinear implicit quasi variational inclusions with general h monotone operator in banach spaces by using the proximal mapping and nadler s theorem we suggest and analyze a class of iterative algorithm for solving the generalized nonlinear implicit quasi variational inclusion first an existence theorem of solutions for the generalized nonlinear implicit quasi variational inclusion is proved under suitable assumptions then the convergence of the iterative sequences generated by the new algorithm is proved

on a conjecture of alley and alder for fluids and lorentz models we discuss a conjecture of alley and alder predicting a relation between the four point and the two point velocity autocorrelation functions for fluids and lorentz models at sufficiently long times if the conjecture is correct a modified burnett coefficient can be defined which has a finite value contrary to the ordinary burnett coefficient which is divergent the conjecture is tested for four classes of models with different methods for three dimensional fluids mode coupling theory yields a negative result the conjecture is confirmed for thed dimensional deterministic lorentz gas d 2 and for a class ofd dimensional stochastic lorentz models d 1 by low density kinetic theory as well as by rigorous results available for one dimension for yet another class of one dimensional stochastic lorentz models which are exactly solvable in one dimension the result is negative again all four classes of models show long time tails in the velocity autocorrelation function and have a finite diffusion coefficient

transport properties of the one dimensional stochastic lorentz model i velocity autocorrelation function point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables stationary renewal process for a fixed configuration of scatterers a particle performs the following random walk the particle starts at the pointx with velocity 1 in between scatterers the particle moves freely at a scatterer the particle is either transmitted or reflected both with probability 1 2 for given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations if this variable is averaged over the distribution of scatterers it decays not faster thant 3 2

a new class of completely generalized quasi variational inclusions in banach spaces in this paper a new notion of j proximal mapping for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space is introduced the existence and lipschitz continuity of j proximal mapping of a lower semicontinuous subdifferentiable proper functional are proved by applying the concept we introduce and study a new class of completely generalized quasi variational inclusions in reflexive banach spaces a novel and innovative iterative algorithm for finding the approximate solutions is suggested and analyzed the convergence criteria of the iterative sequences generated by the new iterative algorithm is also given these algorithm and existence result generalize many known results under hilbert space setting in recent literature to reflexive banach spaces

long time tails in a lorentz gas to investigate the approach to the asymptotic long time behaviour in a d dimensional lorentz gas we have calculated the t 2 d2 correction to the long time tail t 1 d2 in the velocity autocorrelation function using low density kinetic theory the results are compared with existing computer simulations

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

variational convergence of a new proximal algorithm for nonlinear general a monotone operator equation systems in banach spaces abstract the purpose of this paper is to introduce the notion of general a monotone operators in banach spaces and the new proximal mapping associated with the general a monotone operators by using alber s inequalities and the new proximal mapping technique the variational convergence of a new proximal algorithm for nonlinear general a monotone operator equation systems with relaxed cocoercive operators in banach spaces is introduced and studied our results improve and generalize the corresponding results of recent works

renormalization group approach to random walks on disordered lattices one dimensional random walks with static disorder are analyzed using a real space renormalization group procedure the presence of disorder leads to a non markovian description of the macroscopic behavior of the random walk we consider random walks with nearest neighbor hopping described by a master equation with both on site and site to site disorder in the transition matrix site to site disorder leads to a generalized diffusion coefficient with at 3 2 long time tail whereas on site disorder leads to a generalized burnett coefficient with at 1 2 long time tail

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

strongly nonlinear quasivariational inequalities abstract in this paper we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area we also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone

a perturbed algorithm for variational inclusions a perturbed method for solving a new class of variational inclusions is presented and a convergence result which includes as a special case some known results in this field is given

boundary value maps szego maps and intertwining operators we consider one series of unitarizable representations the cohomological induced modules aq a with dominant regular infinitesimal character the minimal k type ir v of aq a determines a homogeneous vector bundle v g k the derived functor modules can be realized on the solution space of a first order differential operator da on v barchini knapp and zierau gave an explicit integral map s from the derived functor module realized in the langlands classification into the space of smooth sections of the vector bundle v g k in this paper we study the asymptotic behavior of elements in the image of s we obtain a factorization of the standard intertwining opeartors into the composition of the szego map s and a passage to boundary values 0 introduction let g be a linear connected semisimple lie group and let k be a maximal compact subgroup of g we assume that rank g rank k in this situation the cohomologically induced representation aq a with dominant regular infinitesimal character can be realized on solution spaces of invariant differential equations in g k see wo b 2 the minimal k type r v of aq a determines an homogeneous vector bundle vtr g k corresponding to certain choices of positive roots there is defined a certain homogeneous first order differential operator d on vtu in bkz and b 1 the authors gave an explicit nonzero integral map s from the derived functor module realized in the langlands classification to the space of smooth sections of the vector bundle vt g k the image of s is annihilated by the differential operator d when the representation under consideration is in the discrete series of g the differential operator vd coincides with schmid s differential operator s in this case the s transform was introduced by knapp and wallach in kw the realization of irreducible unitary representations in the g k picture generalizes bargmann s formulation of holomorphic discrete series of su 1 1 bar in terms of semisimple lie groups functions on the circle suggest non unitary principal series and holomorphic functions on the disk suggest discrete series representations the s transform in kw reduces in limiting cases limits of discrete series for su 1 1 to the szeg6 kernel for the disk see k 1 thus we call s a szeg6 map received by the editors february 17 1995 and in revised form october 9 1995 1991 mathematics subject classification primary 22c05 22e45 22e46 1997 american mathematical society 1877 this content downloaded from 207 46 13 124 on wed 22 jun 2016 05 42 59 utc all use subject to http about jstor org terms

positive energy representations holomorphic discrete series and finite dimensional irreps let g be a semi simple non compact lie group with unitary lowest highest weight representations we consider explicitly the relation among three types of representations of g positive energy unitary lowest weight representations holomorphic discrete series representations and non unitary finite dimensional irreps we consider mainly the conformal groups soo n 2 treating in full detail the cases n 1 3 4

knapp wallach szegő integrals ii the higher parabolic rank case let g be a connected reductive linear lie group with compact center and real rank 1 for each integer k 1 k 1 and each discrete series representation x of g an explicit embedding of g into a generalized principal series representation induced from a parabolic subgroup of rank k is given the existence of such embeddings was proved by w schmid in this paper an explicit integral formula with szegb kernel is given which provides these mappings

knapp wallach szego integrals and generalized principal series representations the parabolic rank one case abstract to each discrete series representation of a connected semisimple lie group g with finite center a g equivariant embedding into a generalized principal series representation is given this representation is induced from specified parameters on a maximal parabolic subgroup of g and the mapping is defined by an integral formula analogous to the szego integral introduced by knapp and wallach for a minimal parabolic subgroup in a limiting case embeddings of limits of discrete series representations are obtained and used to exhibit a reducibility theorem

long time tails in stationary random media ii applications in a previous paper we developed a mode coupling theory to describe the long time properties of diffusion in stationary statistically homogeneous random media here the general theory is applied to deterministic and stochastic lorentz models and several hopping models the mode coupling theory predicts that the amplitudes of the long time tails for these systems are determined by spatial fluctuations in a coarse grained diffusion coefficient and a coarse grained free volume for one dimensional models these amplitudes can be evaluated and the mode coupling theory is shown to agree with exact solutions obtained for these models for higher dimensional lorentz models the formal theory yields expressions which are difficult to evaluate for these models we develop an approximation scheme based upon projecting fluctuations in the diffusion coefficient and free volume onto fluctuations in the density of scatterers

generalized quasi variational like inclusions with nonconvex functionals in this paper two new concepts of h subdifferential and h proximal mappings of a proper functional is introduced in hilbert spaces the existence and lipschitz continuity of h proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of generalized quasi variational like inclusions with a nonconvex functional a new iterative algorithms for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given these algorithm and existence result generalize many known results in the literature

perturbed ishikawa type iterative algorithm for generalized quasivariational inclusions in this paper a perturbed ishikawa type iterative algorithm of solving a new class of generalized nonlinear implicit quasivariational inclusions are suggested and analysed first an existence theorem of solutions for generalized nonlinear implicit quasivariational inclusion is proved under suitable assumptions then the convergence of the perturbed ishikawa type iterative sequences generated by the new algorithm is proved as special cases some known results are also discussed

strong convergence theorems for relatively nonexpansive mappings in banach spaces with applications in this paper some properties of the generalized f projection operator are proved in banach spaces using these results the strong convergence theorems for relatively nonexpansive mappings are studied in banach spaces as applications the strong convergence of general h monotone mappings in banach spaces is also given the results presented in this paper generalize and improve the main results of matsushita and takahashi 2005 9

h φ η monotone operators in banach spaces with an application to variational inclusions in this paper we introduce and study a new class of h f email protected operators in banach spaces we define a proximal mapping associated with the h f email protected operator and show its lipschitz continuity as an application we consider the solvability for a class of variational inclusions involving the h f email protected operators in banach spaces by using the technique of proximal mapping an iterative algorithm for solving such class of variational inclusions is constructed in banach spaces under some suitable conditions we prove the convergence of iterative sequence generated by the algorithm

random walk in dynamically disordered chains poisson white noise disorder exact solutions are given for a variety of models of random walks in a chain with time dependent disorder dynamic disorder is modeled by white poisson noise models with site independent global and site dependent local disorder are considered results are described in terms of an affective random walk in a nondisordered medium in the cases of global disorder the effective random walk contains multistep transitions so that the continuous limit is not a diffusion process in the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion difficulties associated with the continuous limit representation of random walk in a disordered chain are discussed in particular we consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute

convergence analysis of new over relaxed proximal point algorithm frameworks with errors and applications to general a monotone nonlinear inclusion forms abstract the purpose of this paper is to introduce and study a new class of over relaxed proximal point algorithm frameworks with errors based on general a monotonicity further by using alber s inequalities the definition of normalized duality mapping on the dual spaces of banach spaces and the new proximal mapping technique associated with the general a monotone operators we discuss the approximation solvability of general a monotone nonlinear inclusion forms in banach spaces and prove the convergence analysis of iterative sequences generated by the algorithm frameworks via applying the lipschitz continuity of m 1 that is the inverse of multi valued operator m and the lipschitz continuity of proximal mapping associated with the general a monotone operators respectively finally some applications are given to show that the results presented in this paper improve generalize and unify the corresponding results of recent works

reexamination of the long range potts model a multicanonical approach we investigate the critical behavior of the one dimensional q state potts model with long range lr interaction 1 r d sigma using a multicanonical algorithm the recursion scheme initially proposed by berg is improved so as to make it suitable for a large class of lr models with unequally spaced energy levels the choice of an efficient predictor and a reliable convergence criterion is discussed we obtain transition temperatures in the first order regime which are in far better agreement with mean field predictions than in previous monte carlo studies by relying on the location of spinodal points and resorting to scaling arguments we determine the threshold value sigma c q separating the first and second order regimes to two digit precision within the range 3 leq q leq 9 we offer convincing numerical evidence supporting sigma c q 1 0 for all q by virtue of an unusual finite size effect namely finite size scaling predicts a continuous transition in the thermodynamic limit despite the first order nature of the transition at finite size a qualitative account in terms of correlation lengths is provided finally we find the crossover between the lr and short range regimes to occur inside a narrow window 1 0 sigma 1 2 thus lending strong support to sak s scenario

generalized mixed equilibrium problems with generalized α η monotone bifunction in topological vector spaces the purpose of this paper is to introduce a new class of the generalized mixed equilibrium problems with a new definition of the relaxed monotonicity for bi functions in topological vector spaces by employing the kkm technique and under some appropriate assumptions on the considering nonlinear mappings we obtain the existence of a solution for the generalized mixed equilibrium problems with the new concept of the relaxed monotonicity and coercivity condition in order to relax the compactness of the domains of the nonlinear mappings in the setting of topological vector spaces moreover the compactness and convexness of the solution set are investigated the results in the paper extend and generalize the corresponding results especially sintunavarat 2013 20 in this area by providing mild assumptions in order to guarantee the existence of a solution for the generalized mixed equilibrium problem

a new class of variational inclusions with b monotone operators in banach spaces in this paper we introduce and study a new class of variational inclusions in banach spaces for solving such class of variational inclusions we introduce a new notion of b monotone operator and prove the lipschitz continuity of the proximal mapping associated with the b monotone operator by using the proximal mapping an iterative algorithm for solving such class of variational inclusions is constructed in banach spaces under some suitable conditions we prove the convergence of iterative sequence generated by the algorithm

parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings a new class of parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings is introduced by applying resolvent operator technique of h maximal monotone mapping and the property of fixed point set of set valued contractive mappings the behavior and sensitivity analysis of the solution set of the parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings are studied the continuity and lipschitz continuity of the solution set with respect to the parameter are proved under suitable assumptions our approach and results are new and improve unify and extend previous many known results in this field

exact solutions for spectra and green s functions in random one dimensional systems for chains of harmonic oscillators with random masses a set of equations is derived which determine the spatial fourier components of the average one particle green s function these equations are valid for complex values of the frequency a relation between the spectral density and functions introduced by schmidt is discussed exact solutions for this green s function and the less complicated characteristics function the analytic continuation into the complex frequency plane of the accumulated spectral density and the inverse localization length of the eigenfunctions are derived for exponential distributions of the masses for some cases the characteristic function is calculated numerically for gamma distributions the equations are cast in the form of ordinary higher order differential equations these have been solved numerically for determining the characteristic function for arbitrary mass distributions a cumulant expansion and a peculiar symmetry of the green s function are discussed the method is also applied to chains where the spring constants and or the masses have random values also for these systems exact solutions are discussed for exponential distributions e g of both masses and spring constants the characteristic function is expressed in bessel functions the relation with certain random relaxation models is shown finally x y hamiltonians with random exchange constants and or magnetic fields or equivalently tight binding electron models with diagonal and or off diagonal disorder are considered here the green s function does not depend on the wave number if the distribution of exchange constants is symmetric around the origin new solutions for the characteristic function and green s function are derived for a number of cases including exponentially distributed magnetic fields and power law distributed exchange constants

iterative algorithms for a new system of nonlinear variational inclusions with a η accretive mappings in banach spaces in this paper we introduce and study a new system of nonlinear variational inclusions with a h accretive mappings in banach spaces by using the resolvent operator associated with a h accretive mappings we construct some new iterative algorithms for approximating the solution of this system of variational inclusions we also prove the existence of solutions and the convergence of the sequences generated by the algorithm in banach spaces the results presented in this paper extend and improve some known results in the literature

long time tails in lattice lorentz gases we consider a lorentz gas on a square lattice with a fraction c of scattering sites the collision laws are deterministic fixed mirror model or stochastic with transmission reflection and deflection probabilities and respectively if all mirrors are parallel the mirror model is exactly solvable for the general case a self consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function 0 t and the tensor correlation q 0 q t withq x y both functions showt 2 tails as opposed to the continuous lorentz gas where the tails are respectivelyt 2 andt 3 inclusion of the self consistent ring collisions increases the low density coefficient of the tail in 0 t by 30 100 as compared to the simple ring collisions depending on the model parameters

systematic density expansion of transport properties of random lattices abstract using kinetic theory methods we develop systematic expansions in powers of the concentration of impurities scatterers super non conducting bonds sites and apply them to calculate explicity to linear and quadratic order in the concentration moments of displacement velodity autocorrelation functions etc of random walks on square and simple cubic lattices with site or bond disorder lattice lorentz gas ant and termite models site and bond percolation special attention is given to the velocity autocorrelation function cage effect long time tail and its comparison with results of computer simulations

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

general a monotone operators and perturbed iterations for nonlinear set valued relaxed cocoercive operator inclusion problems in this paper we introduce the notion of general a monotone operators in banach spaces study some properties of general a monotone operator and the new proximal mapping associated with the general a monotone operators by using alber s inequalities nalder s results and the new proximal mapping technique we also construct two new class of perturbed iterative algorithms with mixed errors for solving a new class of nonlinear set valued relaxed cocoercive operator inclusions and study applications of general a monotone operators to the approximation solvability of the nonlinear set valued relaxed cocoercive operator inclusion problems in banach spaces furthermore the general a monotone operators are illustrated by some examples the results presented in this paper improve and generalize the corresponding results on strongly monotone quasi variational inclusions and nonlinear implicit quasi variational inclusions

crossover dynamics in bond disordered lattices the asymptotic dynamics of the percolation model for a bond disordered lattice is studied the velocity autocorrelation function vacf is investigated for arbitrary concentration of disorder in two and three dimensions using an effective medium approximation ema corrections to the long time tails away from the percolation threshold and to the percolation tails at the threshold are calculated a characteristic time scale for the long time tails is identified and found to diverge at the threshold sufficiently close to the threshold the two types of asymptotic dynamics can be identified clearly for times greater than and less than this characteristic time respectively an approximate scaling of the ema equation is obtained near the threshold for investigation of the crossover region more generally the ema equation is solved numerically for arbitrary concentration in two dimensions to exhibit the complete time dependence of the vacf in all domains near and far from the threshold

general algorithm of solutions for nonlinear variational inequalities in banach space abstract in this paper we shall study a class of general nonlinear variational inequalities in reflexive banach spaces by applying a minimax inequality obtained by the author some existence uniqueness theorems of solutions for the general nonlinear variational inequalities are proved next by applying the auxiliary problem technique we suggest an innovative iterative algorithm to compute the approximate solutions of the general nonlinear variational inequality finally the convergence criteria is also discussed

h monotone operator and resolvent operator technique for variational inclusions in this paper we introduce a new class of monotone operators h monotone operators the resolvent operator associated with an h monotone operator is defined and its lipschitz continuity is presented we also introduce and study a new class of variational inclusions involving h monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures