tilting modules and tilting torsion theories abstract we generalize basic results about classical tilting modules and partial tilting modules to the infinite dimensional case over an arbitrary ring r the methods employed combine classical techniques of representation theory of finite dimensional algebras with new techniques of the theory of modules using a generalization of the bongartz lemma we characterize tilting torsion theories in mod r i e torsion theories induced by infinitely generated tilting modules we investigate lattices gen p p of torsion classes induced by partial tilting modules p applying our results to tilting torsion classes we prove a version of the brenner butler theorem and a generalization of the assem smalo theorem to the case when r is artinian

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

analogues of non gibbsianness in joint measures of disordered mean field models it is known that the joint measures on the product of spin space and disorder space are very often non gibbsian measures for lattice systems with quenched disorder at low temperature are there reflections of this non gibbsianness in the corresponding mean field models we study the continuity properties of the conditional probabilities in finite volume of the following mean field models a joint measures of random field ising b joint measures of dilute ising c decimation of ferromagnetic ising the conditional probabilities are functions of the empirical mean of the conditionings so we look at the large volume behavior of these functions to discover non trivial limiting objects for a we find 1 discontinuous dependence for almost any realization and 2 dependence of the conditional probabilities on the phase in contrast to that we see continuous behavior for b and c for almost any realization this is in complete analogy to the behavior of the corresponding lattice models in high dimensions it shows that non gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean field models

on the gibbsian nature of the random field kac model under block averaging we consider the kac ising model in an arbitrary configuration of local magnetic fields left eta kern 1pt i right i quad quad in quad kern 1pt quad mathbb z d in any dimension d at any inverse temperature we investigate the gibbs properties of the renormalized infinite volume measures obtained by block averaging any of the gibbs measures corresponding to fixed with block length small enough compared to the range of the kac interaction we show that these measures are gibbs measures for the same renormalized interaction potential this potential depends locally on the field configuration and decays exponentially uniformly in for which we give explicit bounds the construction of the potential is based on a high temperature type cluster expansion

shrinking projection methods for firmly nonexpansive mappings abstract the purpose of this paper is to study the shrinking projection method for firmly nonexpansive mappings the method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping

improved perturbation expansion for disordered systems beating griffiths singularities we introduce a new expansion to prove exponential clustering of connected correlations in a large class of disordered systems our expansion converges for values of the temperature and magnetic field where standard cluster expansions diverge due to the presence of griffiths type singularities it is organized inductively over an infinite sequence of increasing distance scales in each induction step one redefines what is means by the unperturbed system a procedure somewhat reminiscent of k a m theory our techniques may be useful in dealing with the so called large field problem in real space renormalization group schemes

strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces the purpose of the paper is to introduce modified halpern and ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in banach spaces we also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction

typical configurations for one dimensional random field kac model in this paper we study the typical profiles of a random field kac model we give upper and lower bounds of the space scale where the profiles are constant the results hold almost surely with respect to the realizations of the random field the analysis is based on a block spin construction deviation techniques for the local empirical order parameters and concentration inequalities for the realizations of the random magnetic field for the upper bound we exhibit a scale related to the law of the iterated logarithm where the random field makes an almost sure fluctuation that obliges the system to break its rigidity for the lower bound we prove that on a smaller scale the fluctuations are not strong enough to allow this transition

convergence of the modified mann s iteration method for asymptotically strict pseudo contractions abstract let c be a closed convex subset of a real hilbert space h and assume that t is an asymptotically strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the modified mann s algorithm generates a sequence x n via the formula x n 1 n x n 1 n t n x n n 0 it is proved that if the control sequence n is chosen so that n 1 for some 0 1 then x n converges weakly to a fixed point of t we also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence

renormalization group in the uniqueness region weak gibbsianity and convergence we analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature we prove weak gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system the correlation length or the critical length for metastability or both thus to perturbatively treat the problem we have to use a scale adapted expansion moreover such a model below the critical temperature resembles a disordered system in the presence of griffiths singularity then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached

relative entropy and variational properties of generalized gibbsian measures we study the relative entropy density for generalized gibbs measures we first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of almost gibbsian measures almost sure continuity of conditional probabilities for quasilocal measures we obtain a full variational principle for the joint measures of the random field ising model we show that the weak gibbs property holds with an almost surely rapidly decaying translation invariant potential for these measures we show that the variational principle fails as soon as the measures lose the almost gibbs property these examples suggest that the class of weakly gibbsian measures is too broad from the perspective of a reasonable thermodynamic formalism

corrections to the critical temperature in 2d ising systems with kac potentials we consider ad 2 ising system with a kac potential whose mean field critical temperature is 1 calling 0 the kac parameter we prove that there existsc 0 so that the true inverse critical temperature cr 1 by2 log 1 for anyb c and correspondingly small we also show that if 0 andb c suitably then the correlation functions normalized and rescaled converge to those of a non gaussian euclidean field theory

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

realization of the hybrid method for mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space h in order to overcome this weakness nakajo and takahashi proposed the hybrid method for mann s iteration process x 0 c chosen arbitrarily y n n x n 1 n tx n c n z c y n z x n z q n z c x 0 x n z x n 0 x n 1 p c n q n x 0 n 0 1 2 where c is a nonempty closed convex subset of h t c c is a nonexpansive mapping and p k is the metric projection from h onto a closed convex subset k of h however it is difficult to realize this iteration process in actual computing programs because the specific expression of p c n q n x 0 cannot be got in general in the case where c h we obtain the specific expression of p c n q n x 0 and thus the hybrid method for mann s iteration process can be realized easily numerical results show advantages of our result

strong convergence of modified ishikawa iteration for two asymptotically nonexpansive mappings and semigroups abstract in this paper we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a hilbert space moreover we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings our results extend and improve the recent ones announced by kim and xu t w kim h w xu strong convergence of modified mann iteration for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 and many others

strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified mann method

strong convergence of the modified mann iterative method for strict pseudo contractions in this paper we introduce a modified mann iterative process for approximating a common fixed point of a finite family of strict pseudo contractions in hilbert spaces we establish the strong convergence theorem of the general iteration scheme under some mild conditions our results extend and improve the recent ones announced by many others

low temperature dynamics of the curie weiss model periodic orbits multiple histories and loss of gibbsianness we consider the curie weiss model at initial temperature 0 1 in vanishing external field evolving under a glauber spin flip dynamics with temperature 0 1 we study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity bad points we provide a complete analysis of the transition between gibbsian and non gibbsian behavior as a function of time extending earlier work for the case of independent spin flip dynamics

strong convergence theorems for solving equilibrium problems and fixed point problems of ξ strict pseudo contraction mappings by two hybrid projection methods in this paper we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a x strict pseudo contraction mapping in hilbert spaces we obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes the results presented in the paper extend and improve some recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 346 tada and takahashi a tada w takahashi weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem j optim theory appl 133 2007 359 370 and ceng et al l c ceng s al homidan q h ansari j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 and many others

strong convergence of projection scheme for zeros of maximal monotone operators abstract a projection scheme with errors for zeros of maximal monotone operators is introduced and some strong convergence theorems are obtained in a real uniformly smooth and uniformly convex banach space e it is also shown how to compute common zeros of finitely many maximal monotone operators in e

propagation of gibbsianness for infinite dimensional gradient brownian diffusions we study the strong gibbsian character on mathbb r mathbb z d of the law at time t of an infinite imensional gradient brownian diffusion when the initial distribution is gibbsian

weakly gibbsian representations for joint measures of quenched lattice spin models can the joint measures of quenched disordered lattice spin models with finite range on the product of spin space and disorder space be represented as suitably generalized gibbs measures of an annealed system we prove that there is always a potential depending on both spin and disorder variables that converges absolutely on a set of full measure w r t the joint measure weak gibbsianness this positive result is surprising when contrasted with the results of a previous paper k6 where we investigated the measure of the set of discontinuity points of the conditional expectations investigation of a s gibbsianness in particular we gave natural negative examples where this set is even of measure one including the random field ising model further we discuss conditions giving the convergence of vacuum potentials and conditions for the decay of the joint potential in terms of the decay of the disorder average over certain quenched correlations we apply them to various examples from this one typically expects the existence of a potential that decays superpolynomially outside a set of measure zero our proof uses a martingale argument that allows to cut an infinite volume analogue of the quenched free energy into local pieces along with generalizations of kozlov s constructions

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

partial tilting and cotilting bimodules abstract let r and s be arbitrary associative rings the purpose of this paper is to study the equivalences induced by hom r v v s and their derived functors and the dualities induced by hom r w hom s w and their derived functors with v s r partial tilting bimodule and w s r partial cotilting bimodule without any finiteness condition

phase transition in the 3d random field ising model we show that the three dimensional ising model coupled to a small random magnetic field is ordered at low temperatures this means that the lower critical dimension dl for the theory isdl 2 settling a long controversy on the subject our proof is based on an exact renormalization group rg analysis of the system this analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of imry and ma the rg acts in the space of ising models and in the space of random field distributions driving the former to zero temperature and the latter to zero variance

robustness of the non gibbsian property some examples we discuss some examples of measures on lattice systems which lack the property of being a gibbs measure in a rather strong sense

projections of gibbs measures may be non gibbsian consider the phase of the two dimensional nearest neighbor ferromagnetic ising model at a temperature belowt c let be the restriction of this measure to a coordinate axis we prove that there is no one dimensional translation invariant summable interaction for which is a gibbs measure this is proven by showing that if such an interaction existed would have large deviation properties different from those it actually has percolation methods are used in the proof

graded cluster expansion for lattice systems in this paper we develop a general theory which provides a unified treatment of two apparently different problems the weak gibbs property of measures arising from the application of renormalization group maps and the mixing properties of disordered lattice systems in the griffiths phase we suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely large regions are widely separated we then show how it is possible to construct a convergent multi scale cluster expansion

explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps weak and strong convergence theorems for the approximation of common fixed points of a finite family of asymptotically strictly pseudocontractive mappings are proved in hilbert spaces using an explicit averaging cyclic algorithm

loss without recovery of gibbsianness during diffusion of continuous spins we consider a specific continuous spin gibbs distribution t 0 for a double well potential that allows for ferromagnetic ordering we study the time evolution of this initial measure under independent diffusions

strong convergence of a new iterative scheme for a finite family of strict pseudo contractions the purpose of this paper is to introduce a new iterative scheme for finding a common fixed point of a finite family of strict pseudo contractions the results obtained in this paper extend and improve the corresponding results of marino colao qin and kang g marino v colao x qin s m kang strong convergence of the modified mann iterative method for strict pseudo contractions comput math appl 57 2009 455 465

pseudo free energies and large deviations for non gibbsian fkg measures a large deviation theorem for the invariant measures of translation invariant attractive interacting particle systems on 0 1 zd is proven in this way a pseudo free energy and pressure is defined for ergodic systems the large deviations property holds with the usual scaling the case of non ergodic systems is also discussed a similar result holds for occupation times the perturbation by an external field is treated

tilting modules of finite projective dimension tilting modules are well known and are useful in the representation theory of artinian algebras 2 4 6 11 the purpose of this paper is to define tilting modules of finite projective dimension and prove some fundamental results a unital left a module a t over a ring a is said to be a tilting module of projective dimension 0 is an integer if it satisfies the following three conditions 1 a t has a projective resolution

continuous spin mean field models limiting kernels and gibbs properties of local transforms we extend the notion of gibbsianness for mean field systems to the setup of general possibly continuous local state spaces we investigate the gibbs properties of systems arising from an initial mean field gibbs measure by application of given local transition kernels this generalizes previous case studies made for spins taking finitely many values to the first step in the direction to a general theory containing the following parts 1 a formula for the limiting conditional probability distributions of the transformed system it holds both in the gibbs and in the non gibbs regime and invokes a minimization problem for a constrained rate function 2 a criterion for gibbsianness of the transformed system for initial lipschitz hamiltonians involving concentration properties of the transition kernels and 3 a continuity estimate for the single site conditional distributions of the transformed system while 2 and 3 have provable lattice counterparts the characterization of 1 is stronger in m

two connections between random systems and non gibbsian measures in this contribution we discuss the role disordered or random systems have played in the study of non gibbsian measures this role has two main aspects the distinction between which has not always been fully clear 1 from disordered systems disordered systems can be used as a tool analogies with as well as results and methods from the study of random systems can be employed to investigate non gibbsian properties of a variety of measures of physical and mathematical interest 2 of disordered systems non gibbsianness is a property of various joint measures describing quenched disordered systems we discuss and review this distinction and a number of results related to these issues moreover we discuss the mean field version of the non gibbsian property and present some ideas how a kac limit approach might connect the finite range and the mean field non gibbsian properties

degree of convergence of modified averaged iterations for fixed points problems and operator equations abstract let h be a real hilbert space we propose a modification for averaged mappings to approximate the unique fixed point of a mapping t h h such that t is boundedly lipschitzian and t is monotone we not only prove strong convergence theorems but also determine the degree of convergence using this result an iteration process is given for finding the unique solution of the equation a x f where a h h is strongly monotone and boundedly lipschitzian

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

critical behavior of the two dimensional spin diluted ising model via the equilibrium ensemble approach the equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two dimensional ising model in the presence of quenched random site dilution the numerical transfer matrix technique in semi infinite strips of finite width together with phenomenological renormalization and conformal invariance is particularly suited to putting the equilibrium ensemble approach to work a method by which to extract with great precision the critical temperature of the model is proposed and applied a more systematic finite size scaling analysis than in previous numerical studies has been performed a parallel investigation along the lines of the two main scenarios currently under discussion namely the logarithmic corrections scenario with critical exponents fixed in the ising universality class versus the weak universality scenario critical exponents varying with the degree of disorder is carried out in interpreting our data maximum care is constantly taken to be open to both possibilities a critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite size data s1063 651x 99 16110 5

interfaces and typical gibbs configurations for one dimensional kac potentials we consider a one dimensional ising spin system with a ferromagnetic kac potential j r j having compact support we study the system in the limit 0 below the lebowitz penrose critical temperature where there are two distinct thermodynamic phases with different magnetizations we prove that the empirical spin average in blocks of size 1 for any positive converges as 0 to one of the two thermodynamic magnetizations uniformly in the intervals of size p for any given positivep 1 we then show that the intervals where the magnetization is approximately constant have lengths of the order of exp c 1 c 0 and that when normalized they converge to independent variables with exponential distribution we show this by proving large deviation estimates and applying the ventsel and friedlin methods to gibbs random fields finally if the temperature is low enough we characterize the interface namely the typical magnetization pattern in the region connecting the two phases

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

strong convergence theorem of an iterative method for variational inequalities and fixed point problems in hilbert spaces in this paper we introduce a new iteration method based on the hybrid method in mathematical programming and the descent like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in hilbert spaces our method modifies and improves some methods in literature

asymptotically strict pseudocontractive mappings in the intermediate sense abstract it is proved that the modified mann iteration process x n 1 1 n x n n t n x n n n where n is a sequence in 0 1 with n 1 for some 0 1 converges weakly to a fixed point of an asymptotically strict pseudocontractive mapping t in the intermediate sense which is not necessarily lipschitzian we also develop cq method for this modified mann iteration process which generates a strongly convergent sequence

the low temperature phase of kac ising models we analyze the low temperature phase of ferromagnetic kax ising models in dimensionsd 2 we show that if the range of interactions is 1 then two disjoint translation invariant gibbs states exist if the inverse temperature satisfies 1 n where d 1 2d 2 d 1 for any e 0 the proof involves the blocking procedure usual for kac models and also a contour representation for the resulting long range almost continuous spin system which is suitable for the use of a variant of the peierls argument

strong convergence for a countable family of strict pseudocontractions in q uniformly smooth banach spaces we introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q uniformly smooth and uniformly convex banach spaces we then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions our results mainly improve and extend the results announced by yao et al y yao y c liou g marino strong convergence of two iterative algorithms for nonexpansive mappings in hilbert spaces fixed point theory appl 2009 2009 7 pages doi 10 1155 2009 279058 art id 279058

generalizing morita duality a homological approach let r and s be arbitrary associative rings given a bimodule rws we denote by and the functors hom w and ext1 w where r or s the functors r and s are right adjoint with the evaluation maps as unities a module m is reflexive if m is an isomorphism in this paper we give for a weakly cotilting bimodule rws the notion of reflexivity we construct large abelian subcategories mr and ms where the functors r and s are left adjoint and a cotilting theorem holds

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

strong convergence of a proximal type algorithm in a banach space in this paper we study strong convergence of the proximal point algorithm it is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator but it fails to converge strongly then in math program 87 2000 pp 189 202 solodov and svaiter introduced the new proximal type algorithm to generate a strongly convergent sequence and established a convergence property for it in hilbert spaces our purpose is to extend solodov and svaiter s result to more general banach spaces using this we consider the problem of finding a minimizer of a convex function

iterative methods for strict pseudo contractions in hilbert spaces abstract let t i i 1 n be n strict pseudo contractions defined on a closed convex subset c of a real hilbert space h consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem we will prove the weak convergence of these algorithms moreover by applying additional projections we further prove that these algorithms can be modified to have strong convergence

majority rule at low temperatures on the square and triangular lattices we consider the majority rule renormalization group transformation applied to nearest neighbor ising models for the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low then the transformation is not defined we use the methods of van enter fewrnandez and sokal who proved the renormalized measure is not gibbsian for 7 by 7 blocks if the temperature is too low for the triangular lattice we prove that a zero temperature majorityrule transformation may be defined the resulting renormalized hamiltonian is local with 14 different types of interactions

spin flip dynamics of the curie weiss model loss of gibbsianness with possibly broken symmetry we study the conditional probabilities of the curie weiss ising model in vanishing external field under a symmetric independent stochastic spin flip dynamics and discuss their set of points of discontinuity bad points we exhibit a complete analysis of the transition between gibbsian and non gibbsian behavior as a function of time extending the results for the corresponding lattice model where only partial answers can be obtained for initial temperature beta 1 geq 1 we prove that the time evolved measure is always gibbsian for frac 2 3 leq beta 1 1 the time evolved measure loses its gibbsian character at a sharp transition time for beta 1 frac 2 3 we observe the new phenomenon of symmetry breaking in the set of points of discontinuity bad points corresponding to non zero spin average appear at a sharp transition time and give rise to biased non gibbsianness of the time evolved measure these bad points become neutral at a later transition time while the measure stays non gibbs in our proof we give a detailed description of the phase diagram of a curie weiss random field ising model with possibly non symmetric random field distribution based on bifurcation analysis

hybrid ishikawa iterative methods for a nonexpansive semigroup in hilbert space in this paper on the base of the ishikawa iteration method and the hybrid method in mathematical programming we give two new strong convergence methods for finding a point in the common fixed point set of a nonexpansive semigroup in hilbert space

strong convergence theorem for pseudo contractive mappings in hilbert spaces abstract the purpose of this paper is to construct an ishikawa type of hybrid algorithm for pseudo contractive mappings in hilbert spaces our results extend the recent ones announced by yao et al y h yao y c liou g marino a hybrid algorithm for pseudo contractive mappings nonlinear anal 71 2009 4997 5002 and many others

projection algorithms for solving nonmonotone equilibrium problems in hilbert space we propose two projection algorithms for solving an equilibrium problem where the bifunction is not required to be satisfied any monotone property under assumptions on the continuity convexity of the bifunction and the nonemptyness of the solution set of the minty equilibrium problem we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the primal equilibrium problem respectively

on the ising model with random boundary condition the infinite volume limit behavior of the 2d ising model under possibly strong random boundary conditions is studied the model exhibits chaotic size dependence at low temperatures and we prove that the and phases are the only almost sure limit gibbs measures assuming that the limit is taken along a sparse enough sequence of squares in particular we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces in order to exclude mixtures as possible limit points a detailed multi scale contour analysis is performed

on some algorithms in banach spaces finding fixed points of nonlinear mappings abstract by using a modification of the hybrid method in mathematical programming we give some new algorithm to find out a fixed point of mappings which are in some sense non expansive our results hold in reflexive strictly convex smooth banach spaces with the kadec klee property