tricriticality and the blume capel model a monte carlo study within the microcanonical ensemble the microcanonical partition function ensuremath omega ensuremath alpha n e of a three dimensional ferromagnetic simple cubic blume capel model is calculated for several coupling ratios ensuremath alpha close to and on the first order side of the tricritical point to this end a single monte carlo simulation of a suitably extended partition function for systems of l ifmmode times else texttimes fi l ifmmode times else texttimes fi l spins with l ensuremath in 8 10 12 14 18 was performed a finite system analog of the latent heat is introduced in order to define a tricritical point in finite systems as well an empirical scaling of its coordinates to the thermodynamic limit yields ensuremath alpha t 2 84479 ifmmode pm else textpm fi 0 00030 for the tricritical coupling ratio and k b t t j 1 4182 ifmmode pm else textpm fi 0 0055 for the tricritical transition temperature the results are compared with values obtained on fcc lattices

generalized iterative process and associated regularization for j pseudomonotone mixed variational inequalities a generalized iterative process for solving mixed variational inequalities with j pseudomonotone operators in uniformly smooth banach spaces is proposed and its weak convergence is established an application to the stationary filtration problem is given for such variational inequalities a generalized iterative regularization method is constructed and its weak convergence under the assumption that the iterative parameter may vary from step to step is analyzed our results extend and generalize the corresponding theorems of a m saddeek s a ahmed convergence analysis of iterative methods for some variational inequalities with j pseudomonotone operators in uniformly smooth banach spaces appl sci comput accepted for publication a m saddeek s a ahmed on the convergence of some iteration processes for j pseudomonotone mixed variational inequalities in uniformly smooth banach spaces math comput modell 46 3 4 2007 557 572

microcanonical finite size scaling in the microcanonical ensemble suitably defined observables show nonanalyticities and power law behavior even for finite systems for these observables a microcanonical finite size scaling theory is established and combined with the experimentally observed power law behavior scaling laws are obtained which relate exponents of the finite system and critical exponents of the infinite system to the system size dependence of the affiliated microcanonical observables

on the steepest descent approximation method for the zeros of generalized accretive operators abstract in this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator defined on a uniformly smooth banach space our study is based on an important result of reich s reich an iterative procedure for constructing zeros of accretive sets in banach spaces nonlinear anal 2 1978 85 92 and given results extend and improve some of the earlier results which include the steepest descent approximation method

logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

on the application of the critical minimum energy subspace method to disordered systems abstract we discuss the recent application to strongly disordered systems of the critical minimum energy subspace crmes method used to limit the energy subspace of the wang landau sampling we compare with our results on the 3d random field ising model obtained by a multi range wang landau simulation over the whole energy range we point out some problems that may arise when applying the crmes scheme to models having a complex free energy landscape

a rigorous theory of finite size scaling at first order phase transitions a large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered the dependence of the finite volume magnetizationm per h l in cubes of sizel d under periodic boundary conditions on the external fieldh is analyzed for the case where two phases coexist at the infinite volume transition pointh t we prove that independent of the details of the model the finite volume magnetization per lattice site behaves likem per h t m tanh ml d h ht withm per h denoting the infinite volume magnetization and m 1 2 m per h t 0 m per h t 0 introducing the finite size transition pointh m l as the point where the finite volume susceptibility attains the maximum we show that in the case of asymmetric field driven transitions its shift ish t h m l o l 2d in contrast to claims in the literature starting from the obvious observation that the number of stable phases has a local maximum at the transition point we propose a new way of determining the pointh t from finite size data with a shift that is exponentially small inl finally the finite size effects are discussed also in the case where more than two phases coexist

finite size scaling for potts models recently borgs and koteck developed a rigorous theory of finite size effects near first order phase transitions here we apply this theory to the ferromagneticq state potts model which forq large andd 2 undergoes a first order phase transition as the inverse temperature is varied we prove a formula for the internal energy in a periodic cube of side lengthl which describes the rounding of the infinite volume jump e in terms of a hyperbolic tangent and show that the position of the maximum of the specific heat is shifted by m l inq e l d o l 2d with respect to the infinite volume transition point t we also propose an alternative definition of the finite volume transition temperature t l which might be useful for numerical calculations because it differs only by exponentially small corrections from t

density of states of classical spin systems with continuous degrees of freedom in the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions in this approach the quantities of interest are exclusively expressed as derivatives of the entropy s ln omega where omega is the density of states obviously the density of states has to be known with very high accuracy for this kind of analysis important progress has been achieved recently in the computation of the density of states of classical systems as new types of algorithms have been developed here we extend one of these methods originally formulated for systems with discrete degrees of freedom to systems with continuous degrees of freedom as an application we compute the density of states of the three dimensional xy model and demonstrate that critical quantities can directly be determined from the density of states of finite systems in cases where the degrees of freedom take continuous values

iterative process with errors of nonlinear equations involvingm accretive operators abstract let x be a uniformly smooth and uniformly convex banach space and t d t x x be an m accretive operator with the domain d t and the range r t for any given f x we prove that the mann and ishikawa type iterative sequences with errors converge strongly to the unique solution of the equation x tx f where t may not be lipschitz some related results deal with the convergence of mann and ishikawa type iterative sequences with errors for approximating a solution of a continuous dissipative operator equation

picard iterations for solution of nonlinear equations in certain banach spaces abstract let e be a real uniformly smooth banach space and let a d a e e be locally lipschitzian and strongly quasi accretive it is proved that a picard recursion process converges strongly to the unique solution of the equation ax f f r a with the convergence being at least as fast as a geometric progression related results deal with the convergence of picard iterations to the fixed point of locally lipschitzian strong hemicontractions t and to the solutions of nonlinear equations of the forms x ax f and x ax f where a is an accretive type map

iterative solution of nonlinear equations of accretive and pseudocontractive types abstract let e be a real uniformly smooth banach space let a d a e 2 e be an accretive operator that satisfies the range condition and a 1 0 let n and n be two real sequences satisfying appropriate conditions and for z e arbitrary let the sequence x n be generated from arbitrary x 0 e by x n 1 x n n u n n x n z u n ax n n 0 assume that u n is bounded it is proved that x n converges strongly to some x a 1 0 furthermore if k is a nonempty closed convex subset of e and t k k is a bounded continuous pseudocontractive map with f t tx x it is proved that for arbitrary z k the sequence x n generated from x 0 k by x n 1 x n n i t x n n x n z n 0 where n and n are real sequences satisfying appropriate conditions converges strongly to a fixed point of t

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

existence of solutions and convergence of iterative algorithms for a system of generalized nonlinear mixed quasi variational inclusions in this paper we introduce and study a new system of generalized nonlinear mixed quasi variational inclusions in q uniformly smooth banach spaces we prove the existence and uniqueness of solutions for this system of generalized nonlinear mixed quasi variational inclusions we also prove the convergence of several new two step iterative algorithms with or without errors for this system of generalized nonlinear mixed quasi variational inclusions the results in this paper extend and improve some known results in the literature

iterative solution of nonlinear equations involving set valued uniformly accretive operators abstract let e be a real normed linear space and let a e 2 e be a uniformly continuous and uniformly quasi accretive multivalued map with nonempty closed values such that the range of i a is bounded and the inclusion f ax has a solution x e it is proved that ishikawa and mann type iteration processes converge strongly to x further if t e 2 e is a uniformly continuous and uniformly hemicontractive set valued map with bounded range and a fixed point x e it is proved that both the mann and ishikawa type iteration processes converge strongly to x the strong convergence of these iteration processes with errors is also proved

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

continuous phase transitions with a convex dip in the microcanonical entropy the appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition however a convex dip also shows up in some systems with a continuous transition as for example in the baxter wu model and in the four state potts model in two dimensions we demonstrate that the appearance of a convex dip in those cases can be traced back to a finite size effect the properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite size scaling theory for continuous phase transitions results obtained from numerical simulations corroborate the predictions of the scaling theory

on the asymptotic behavior of nonlinear semigroups and the range of accretive operators ii abstract it is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in banach spaces when such an evolution equation is governed by an accretive operator then its solutions give rise to a nonlinear contraction semigroup in this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators we also derive new results on their behavior at the origin it turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin author

approximation of solutions of generalized equations of hammerstein type let h be a real hilbert space for each i 1 2 m let f i k i h h be bounded and monotone mappings assume that the generalized hammerstein equation u i 1 mk if iu 0 has a solution in h we construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized hammerstein equation

finite size scaling analysis of the critical behavior of the baxter wu model abstract we use the recently developed critical minimum energy subspace crmes approximation scheme to study the critical behavior of the baxter wu model this scheme uses only a properly determined part of the energy spectrum and allows us to obtain high accuracy for relatively large systems with considerably reduced computational effort the density of states is constructed by a multi range wang landau sampling and from this we obtain the critical properties of specific heat and of the reduced binder cummulant the good agreement of our results with existing exact solutions demonstrates the accuracy of our approximation technique

convergence and almost stability of ishikawa iterative scheme with errors for m accretive operators let x be a uniformly smooth real banach space and t x x be a generalized lipschitzian and m accretive operator it is proved that under suitable conditions the ishikawa iterative schemes with errors both converges strongly to the unique solution of the nonlinear operator equation x tx f and is almost stable a few related results deal with the operator equations for the dissipative type operator the results presented in this paper extend substantially the corresponding results in 1 2

the solution by iteration of nonlinear equations in uniformly smooth banach spaces abstract letebe a uniformly smooth banach space and lett d t e ebe a strong pseudocontraction with an open domaind t ineand a fixed pointx d t we establish the strong convergence of the mann and ishikawa iterative processes with errors to the fixed point oft related results deal with the iterative solution of operator equations of the formsf txandf x tx 0 whentis a set valued strongly accretative operator our theorems include the cases in which the operatortis defined only locally explicit error estimates are also given

error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth banach spaces abstract let x be a uniformly smooth banach space and t x x a strongly accretive operator in this paper we give the error bounds for the approximation solutions of the nonlinear equation tx f generated by both the mann and the ishikawa iteration process on the other hand let k be a nonempty convex subset of x and t k k a strictly pseudocontractive mapping the related results deal with the error bounds for the iterative approximation of the fixed point of t generated by these two processes

an analysis of a multi level projected steepest descent iteration for nonlinear inverse problems in banach spaces subject to stability constraints we consider nonlinear inverse problems described by operator equations in banach spaces assuming conditional stability of the inverse problem that is assuming that stability holds on a compact convex subset of the domain of the operator we introduce a novel nonlinear projected steepest descent iteration and analyze its convergence to an approximate solution given limited accuracy data we proceed with developing a multi level algorithm based on a nested family of compact convex subsets on which stability holds and the stability constants are ordered growth of the stability constants is coupled to the increase in accuracy of approximation between neighboring levels to ensure that the algorithm can continue from level to level until the iterate satisfies a desired discrepancy criterion after a finite number of steps

prox regular sets and epigraphs in uniformly convex banach spaces various regularities and other properties we continue the study of prox regular sets that we began in a previous work in the setting of uniformly convex banach spaces endowed with a norm both uniformly smooth and uniformly convex e g l p w m p spaces we prove normal and tangential regularity properties for these sets and in particular the equality between mordukhovich and proximal normal cones we also compare in this setting the proximal normal cone with different holderian normal cones depending on the power types s q of moduli of smoothness and convexity of the norm in the case of sets that are epigraphs of functions we show that j primal lower regular functions have prox regular epigraphs and we compare these functions with poliquin s primal lower nice functions depending on the power types s q of the moduli the preservation of prox regularity of the intersection of finitely many sets and of the inverse image is obtained under a calmness assumption a conical derivative formula for the metric projection mapping of prox regular sets is also established among other results of the paper it is proved that the attouch wets convergence preserves the uniform r prox regularity property and that the metric projection mapping is in some sense continuous with respect to this convergence for such sets

on first order phase transitions in microcanonical and canonical non extensive systems abstract two examples of microcanonical potts models two dimensional nearest neighbor and mean field are considered via exact enumeration of states and analytical asymptotic methods in the interval of energies corresponding to a first order phase transition both of these models exhibit a convex dip in the entropy vs energy plot and a region with negative specific heat within the dip it is observed that in the nearest neighbor model the dip flattens and disappears as the lattice size grows while in the mean field model the dip persists even in the limit of an infinite system if formal transitions from microcanonical to canonical ensembles and back are performed for an infinite but non extensive system the convex dip in the microcanonical entropy plot disappears

strong convergence theorem for approximation of solutions of equations of hammerstein type abstract let h be a real hilbert space let k f h h be bounded continuous and monotone mappings suppose that u h is a solution to the hammerstein equation u k f u 0 we construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the hammerstein equation furthermore we give some examples to show that our result is interdisciplinary in nature covers a large variety of areas and should be of much interest to a wide audience

finite size behaviour of the microcanonical specific heat for models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non monotonic behaviour of the microcanonical specific heat as a function of the system size this is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system a phenomenological theory is developed which permits us to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents

on a new system of generalized mixed quasi variational like inclusions involving a η m accretive operators with applications in this paper we introduce a new and interesting system of generalized mixed quasi variational like inclusions with a h m accretive operators and relaxed cocoercive mappings which contains variational inequalities variational inclusions systems of variational inequalities systems of variational like inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the a h m accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unifies extends and improves some known results in the literature

strong convergence theorem for integral equations of hammerstein type in hilbert spaces let h be a real hilbert space let f h h be a bounded coercive and maximal monotone mapping let k h h be a bounded and maximal monotone mapping let k and f satisfy the range condition suppose that u h is a solution to hammerstein equation u kfu 0 we construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the hammerstein equation our iterative scheme in this paper seems far simpler than the iterative scheme used by chidume and ofoedu 2011 13 and their strong assumption is dispensed with we give some examples of our result so that it will find serious applications and be of much interest to our readers

the learning rate of lp coefficient regularized shannon sampling algorithm in the present paper we provide an investigation on the learning rate of the shannon sampling algorithms with l p coefficient regularization we give the upper bounds for the sample error and the regularization error with the convex inequality in l p spaces and show the approximation error by a k functional whose convergence rate can be sum up to the translation network approximation basing on these estimates we show an explicit learning rate in possibility

the viscosity approximation method for asymptotically nonexpansive mappings in banach spaces abstract a recent trend in the iterative methods for constructing fixed points of nonlinear mappings is to use the viscosity approximation technique the advantage of this technique is that one can find a particular solution to the associated problems and in most cases this particular solution solves some variational inequality in this paper we try to extend this technique to find a particular common fixed point of a finite family of asymptotically nonexpansive mappings in a banach space which is reflexive and has a weakly continuous duality map both implicit and explicit viscosity approximation schemes are proposed and their strong convergence to a solution to a variational inequality is proved

viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings abstract let x be a reflexive and smooth real banach space which has a weakly sequentially continuous duality mapping in this paper we consider the following viscosity approximation scheme x n 1 n 1 f x n 1 n 1 t n 1 x n where f is a generalized contraction mapping for infinitely many nonexpansive self mappings t 1 t 2 t 3 in x we establish a strong convergence result which generalizes some results in the literature

on the iteratively regularized gauss newton method in banach spaces with applications to parameter identification problems in this paper we propose an extension of the iteratively regularized gauss newton method to the banach space setting by defining the iterates via convex optimization problems we consider some a posteriori stopping rules to terminate the iteration and present the detailed convergence analysis the remarkable point is that in each convex optimization problem we allow non smooth penalty terms including l 1 and total variation like penalty functionals this enables us to reconstruct special features of solutions such as sparsity and discontinuities in practical applications some numerical experiments on parameter identification in partial differential equations are reported to test the performance of our method

proximal normal cone analysis on smooth banach spaces and applications unlike the frechet penot clarke and other order one notions of normal cones the notion of proximal normal cone describes variational behavior of order two and most of results on proximal normal cone are established in the hilbert space framework a possible reason is that in a general banach space such as in the classical banach spaces l p and l p with 1 leq p 2 the proximal normal cone of a smooth subset a at every point of a may consist of the zero element only nevertheless on the other hand we show in this paper that for a fairly big class of smooth banach spaces including the classical banach spaces l p and l p with 2 leq p infty the consideration of proximal normal cones provides a lot of useful information especially for leading to satisfactory treatment for constrained optimization problems some of our results are new even in the hilbert space case

ensemble inequivalence in systems with long range interactions ensemble inequivalence has been observed in several systems in particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long range interactions we display a connection between such behaviour and a mean field like structure of the partition function since short range models cannot display this kind of behaviour this strongly suggests that such systems are necessarily non mean field in the sense indicated here we illustrate our results showing an application to the blume emery griffiths model we further show that a broad class of systems with non integrable interactions are indeed of mean field type in the sense specified so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble

margin error bounds for support vector machines on reproducing kernel banach spaces support vector machines which maximize the margin from patterns to the separation hyperplane subject to correct classification have received remarkable success in machine learning margin error bounds based on hilbert spaces have been introduced in the literature to justify the strategy of maximizing the margin in svm recently there has been much interest in developing banach space methods for machine learning large margin classification in banach spaces is a focus of such attempts in this letter we establish a margin error bound for the svm on reproducing kernel banach spaces thus supplying statistical justification for large margin classification in banach spaces

characteristic inequalities of uniformly convex and uniformly smooth banach spaces abstract let x be a real banach space with dual x and moduli of convexity and smoothness x e and x respectively for 1 p denotes the duality mapping from x into 2 x with gauge function t p 1 and j p denotes an arbitrary selection for j p let a r 0 0 t is strictly increasing and there exists c 0 such that t c x t 2 and f r 0 0 t is convex nondecreasing and there exists k 0 such that k x it is proved that x is uniformly convex if and only if there is a a such that x y p x p p j p x y x y x y x and x is uniformly smooth if and only if there is a f such that x y p x p p j p x y x y x y x where for given function f f x y is defined by f x y p 0 1 x ty x p t f t y x ty x dt these inequalities which have various applications can be regarded as general banach space versions of the well known polarization identity occurring in hilbert spaces

monte carlo study of the pure and dilute baxter wu model we studied the pure and dilute baxter wu bw models using the wang landau wl sampling method to calculate the density of states dos we first used the exact result for the dos of the ising model to test our code then we calculated the dos of the dilute ising model to obtain a phase diagram in good agreement with previous studies we calculated the energy distribution together with its first second and fourth moments to give the specific heat and the energy fourth order cumulant better known as the binder parameter for the pure bw model for small samples the energy distribution displayed a doubly peaked shape and finite size scaling analysis showed the expected reciprocal scaling of the positions of the peaks with l the energy distribution yielded the expected bw 2 3 critical exponent for the specific heat the binder parameter minimum appeared to scale with lattice size l with an exponent b equal to the specific heat exponent its location temperature showed a large correction to scaling term 1 0 248 0 025 for the dilute bw model we found a clear crossover to a single peak in the energy distribution even for small sizes and the expected 0 was recovered

resolvent operator technique for generalized implicit variational like inclusion in banach space a new class of g accretive mappings is introduced and studied in banach space by using the properties of g accretive mappings the concept of resolvent operators associated with the classical m accretive operators is extended and an iterative algorithm for a new class of generalized implicit variational like inclusion involving g accretive mappings and its convergence results are established in banach space

a necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations abstract a necessary and sufficient condition is established which ensures the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space

demiclosedness principle and convergence theorems for k strictly asymptotically pseudocontractive maps let e be a real q uniformly smooth banach space which is also uniformly convex for example lp or lp spaces 1 p and k a nonempty closed convex not necessarily bounded subset of e let t k k be a k strictly asymptotically pseudocontractive map with a nonempty fixed point set it is proved that i t is demiclosed at 0 furthermore weak and strong convergence of an averaging iteration method to a fixed point of t are proved

strong convergence theorems for maximal monotone mappings in banach spaces let e be a uniformly convex and 2 uniformly smooth real banach space with dual e let a e e be a lipschitz continuous monotone mapping with a 1 0 for given u x1 e let xn be generated by the algorithm xn 1 nu 1 n xn najxn n 1 where j is the normalized duality mapping from e into e and n and n are real sequences in 0 1 satisfying certain conditions then it is proved that under some mild conditions xn converges strongly to x e where jx a 1 0 finally we apply our convergence theorems to the convex minimization problems

the iterative solution of the equation f x tx for a monotone operator t in lp spaces suppose t is a multivalued monotone operator not necessarily continuous with open domain d t in lp 2 p f r i t and the equation f x tx has a solution q d t then there exists a neighbourhood b d t of q and a real number r1 0 such that for any r r1 for any initial guess x1 b and any singlevalued section t0 of t the sequence xn n 1 generated from x1 by xn 1 1 cn xn cn f t0xn remains in d t and converges strongly to q with xn q 0 n 1 2 furthermore for x lp e e

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

microcanonical finite size scaling in second order phase transitions with diverging specific heat a microcanonical finite size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so called quotients method to the microcanonical ensemble the ansatz is tested numerically in two models where the canonical specific heat diverges at criticality thus implying fisher renormalization of the critical exponents the three dimensional ferromagnetic ising model and the two dimensional four state potts model where large logarithmic corrections are known to occur in the canonical ensemble a recently proposed microcanonical cluster method allows simulating systems as large as l 1024 potts or l 128 ising the quotients method provides accurate determinations of the anomalous dimension ensuremath eta and of the fisher renormalized thermal ensuremath nu exponent while in the ising model the numerical agreement with our theoretical expectations is very good in the potts case we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data

first order transition features of the triangular ising model with nearest and next nearest neighbor antiferromagnetic interactions abstract we implement a new and accurate numerical entropic scheme to investigate the first order transition features of the triangular ising model with nearest neighbor j nn and next nearest neighbor j nnn antiferromagnetic interactions in ratio r j nn j nnn 1 important aspects of the existing theories of first order transitions are briefly reviewed tested on this model and compared with previous work on the potts model using lattices with linear sizes l 30 40 100 120 140 160 200 240 360 and 480 we estimate the thermal characteristics of the present weak first order transition our results improve the original estimates of rastelli et al and verify all the generally accepted predictions of the finite size scaling theory of first order transitions including transition point shifts thermal and magnetic anomalies however two of our findings are not compatible with current phenomenological expectations the behavior of transition points derived from the number of phases parameter is not in accordance with the theoretically conjectured exponentially small shift behavior and the well known double gaussian approximation does not correctly describe higher correction terms of the energy cumulants it is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections

resolving the order of phase transitions in monte carlo simulations the authors made a monte carlo simulation of the two dimensional potts model with q 3 4 and 5 to examine the question whether numerical methods can distinguish the order of a phase transition for the subtle cases that this model exemplifies they found that the finite size scaling test for susceptibilities has sufficient power for this purpose whereas the simple method of detecting metastability signals often fails

convergence rates for inverse problems with impulsive noise we study inverse problems f f g with perturbed right hand side g rm obs corrupted by so called impulsive noise i e noise which is concentrated on a small subset of the domain of definition of g it is well known that tikhonov type regularization with an mathbf l 1 data fidelity term yields significantly more accurate results than tikhonov regularization with classical mathbf l 2 data fidelity terms for this type of noise the purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy our error estimates significantly improve previous error estimates for tikhonov regularization with mathbf l 1 fidelity term in the case of impulsive noise we present numerical results which are in good agreement with the predictions of our analysis

ball algorithms for constructing solutions of nonlinear operator equations abstract in the most general setting we extend the previous theory of the region contraction algorithm developed recently by several authors for solving nonlinear operator equations it is demonstrated that the extended algorithm still possesses properties such as generating error bounds automatically providing a computational test for the existence of solutions and being globally convergent under nominal conditions as example of applications we specialize the extended theory in particular to nonlinear operator equations of monotone type

coincidence points by generalized mann iterates with applications in hilbert spaces this paper deals with the construction of the coincidence points by the generalized mann iterates and their applications in hilbert spaces our results generalize and improve a number of recent results

approximation of common fixed points for finite families of total asymptotically nonexpansive mappings abstract let e be a real banach space k a closed convex nonempty subset of e let t 1 t 2 t m k k be m total asymptotically nonexpansive mappings an iterative sequence for approximation of common fixed points assuming existence of t 1 t 2 t m is constructed necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given furthermore in the case that e is uniformly convex a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established

second order sufficient conditions for error bounds in banach spaces recently huang and ng presented second order sufficient conditions for error bounds of continuous and ga teaux differentiable functions in banach spaces wu and ye dropped the assumption of huang and ng on ga teaux differentiability but required the space to be a hilbert space we carry on this research in two directions first we extend wu and ye s result to some non hilbert spaces second same as huang and ng we work on banach spaces but provide different second order sufficient conditions that may allow the function to be non ga teaux differentiable

higher order convergence rates for bregman iterated variational regularization of inverse problems we study the convergence of variationally regularized solutions to linear ill posed operator equations in banach spaces as the noise in the right hand side tends to 0 the rate of this convergence is determined by abstract smoothness conditions on the solution called source conditions for non quadratic data fidelity or penalty terms such source conditions are often formulated in the form of variational inequalities such variational source conditions vscs as well as other formulations of such conditions in banach spaces have the disadvantage of yielding only low order convergence rates a first step towards higher order vscs has been taken by grasmair j inverse ill posed probl 21 3 379 394 2013 https doi org 10 1515 jip 2013 0002 who obtained convergence rates up to the saturation of tikhonov regularization for even higher order convergence rates iterated versions of variational regularization have to be considered in this paper we introduce vscs of arbitrarily high order which lead to optimal convergence rates in hilbert spaces for bregman iterated variational regularization in banach spaces with general data fidelity and penalty terms we derive convergence rates under third order vsc these results are further discussed for entropy regularization with elliptic pseudodifferential operators where the vscs are interpreted in terms of besov spaces and the optimality of the rates can be demonstrated our theoretical results are confirmed in numerical experiments

characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations abstract in the present paper sufficient and necessary conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations are established for the sufficiency part and a specific error estimation is also given

on the rate of convergence of iterated bregman projections and of the alternating algorithm abstract we study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth banach spaces for banach spaces which are convex and smooth of power type we exhibit a condition which implies linear convergence of this method we show these convergence results for iterates of bregman projections onto closed linear subspaces using an intimate connection between the metric projection onto a closed linear subspace and the bregman projection onto its annihilator we deduce the convergence rate results for the alternating algorithm from the corresponding results for the iterated bregman projection method

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

asymptotic behavior of the solutions of non autonomous systems in banach spaces abstract in this paper we study the weak and strong convergence of the integral solution of the following nonlinear evolution inclusion u t a t u t f t t 0 u 0 x 0 where a t t 0 is a family of m accretive operators and f is a multi function which extends some results in this area