ramification of local fields with imperfect residue fields we define two decreasing filtrations by ramification groups on the absolute galois group of a complete discrete valuation field whose residue field may not be perfect in the classical case where the residue field is perfect we recover the classical upper numbering filtration the definition uses rigid geometry and log structures we also establish some of their properties

on labeled birooted tree languages with an aim to developing expressive language theoretical tools applicable to inverse semigroup languages that is subsets of inverse semigroups this paper explores the language theory of finite labeled birooted trees munn s birooted trees extended with vertex labeling to this purpose we define a notion of finite state birooted tree automata that simply extends finite state word automata semantics this notion is shown to capture the class of languages that are definable in monadic second order logic and upward closed with respect to the natural order then we derive from these automata the notion of quasi recognizable languages that is languages recognizable by means of adequate premorphisms into finite adequately ordered monoids this notion is shown to capture finite boolean combinations of languages as above a class that contains classical regular languages of finite mono rooted trees this contrasts with the known collapse of classical algebraic tools when applied to inverse semigroups

universal groups for point sets and tilings abstract we study the universal groups of inverse semigroups associated with point sets and with tilings we focus our attention on two classes of examples the first class consists of point sets which are obtained by a cut and projection scheme so called model sets here we introduce another inverse semigroup which is given in terms of the defining data of the projection scheme and related to the model set by the empire congruence the second class is given by one dimensional tilings

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

mann and ishikawa iterations with errors for asymptotically nonexpansive mappings abstract in a recent paper rhoades 1 presented some generalizations of schu 2 on the convergence of the mann and ishikawa iterations of asymptotically nonexpansive mappings in uniformly convex banach spaces we continue the study on the ishikawa and mann iteration process with errors and prove that if x is a uniformly convex banach space o e x closed bounded and convex and t e e is an asymptotically nonexpansive mapping then the ishikawa and mann iteration process with errors converges strongly to some fixed point of t

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

on the swan conductor in positive characteristic let x be a proper smooth surface over an algebraically closed field of positive characteristic and u be a complement of a simple normal crossing divisor for a smooth l adic sheaf on u deligne proved a formula calculating the euler characteristic of by local invariants kato gave another formula for the euler characteristic in case where is of rank 1 using class field theory in this paper we show that local terms of these formulas coincide admitting certain conjectures for vanishing cycles

on a mann type implicit iteration process for continuous pseudo contractive mappings abstract let k be a nonempty closed convex subset of a banach space e t k k a continuous pseudo contractive mapping suppose that n is a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the mann type implicit iteration process x n given by x n n x n 1 1 n t x n n 0 strongly and weakly converges to a fixed point of t respectively

on ramification in transcendental extensions of local fields abstract let l k be an extension of complete discrete valuation fields and assume that the residue field of k is perfect and of positive characteristic the residue field of l is not assumed to be perfect in this paper we prove a formula for the swan conductor of the image of a character h 1 k q z in h 1 l q z for sufficiently ramified further we define generalizations l k ab and l k as of the classical function and prove a formula for l k ab t for sufficiently large t r

semigroups and ordered categories i the reduced case abstract we investigate the relationship which exists between certain classes of ordered small categories introduced by charles ehresmann in the course of his work on local structures and the class of u semiabundant semigroups first studied by el qallali and by de barros u semiabundant semigroups embrace both the abundant and the regular semigroups the former have been studied by fountain and his students in a number of papers the latter constitute a well known and wellinvestigated branch of semigroup theory one consequence of the ideas presented in this paper is that the work of nambooripad on inductive groupoids and regular semigroups should not be seen as sui generis but as belonging to the general framework of the theory of ordered small categories

simpler is also better in approximating fixed points in this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified krasnoselskij iteration process which is much simpler to use than the other iteration schemes that have been defined

iterative algorithms for a new class of extended general nonconvex set valued variational inequalities abstract some new classes of extended general nonconvex set valued variational inequalities and the extended general wiener hopf inclusions are introduced by the projection technique equivalence between the extended general nonconvex set valued variational inequalities and the fixed point problems as well as the extended general nonconvex wiener hopf inclusions is proved then by using this equivalent formulation we discuss the existence of solutions of the extended general nonconvex set valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set valued variational inequalities we also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set valued variational inequalities the results presented in this paper extend and improve some known results from the literature

inverse monoids trees and context free languages this paper is concerned with a study of inverse monoids presented by a set x subject to relations of the form e i f i i i where e i and f i are dyck words i e idempotents of the free inverse monoid on x some general results of stephen are used to reduce the word problem for such a presentation to the membership problem for a certain subtree of the cayley graph of the free group on x in the finitely presented case the word problem is solved by using rabin s theorem on the second order monadic logic of the infinite binary tree some connections with the theory of rational subsets of the free group and the theory of context free languages are explored

a perturbed iterative procedure for multivalued pseudo contractive mappings and multivalued accretive mappings in banach spaces abstract the main purpose of this paper is to introduce and study a new perturbed iteration method for multivalued mappings some strong convergence theorems of perturbed iteration sequences for multivalued pseudo contractive mappings and strongly accretive mappings are obtained

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

generalized set valued variational inclusions in q uniformly smooth banach spaces abstract in this paper a class of generalized set valued variational inclusions in banach spaces are introduced and studied which include many variational inclusions studied by others in recent years by using some new and innovative techniques several existence theorems for the generalized set valued variational inclusions in q uniformly smooth banach spaces are established and some perturbed iterative algorithms for solving this kind of set valued variational inclusions are suggested and analyzed our results improve and generalize many known algorithms and results

the local structure of tilings and their integer group of coinvariants the local structure of a tiling is described in terms of a multiplicative structure on its pattern classes the groupoid associated to the tiling is derived from this structure and its integer group of coinvariants is defined this group furnishes part of the k0 group of the groupoid c algebra for tilings which reduce to decorations of the group itself as well as the image of its state is computed for substitution tilings in case the substitution is locally invertible and v primitive this yields in particular the set of possible gap labels predicted by k theory for schrodinger operators describing the particle motion in such a tiling

stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces in this paper we introduce the new iterative sequences with errors approximating the common fixed point for a couple of quasi contractive mappings and show the stability of the iterative procedures with errors in q uniformly smooth banach spaces our results extend improve and unify the corresponding results of chidume osilike liu and others

the equivalence of the convergence of four kinds of iterations for a finite family of uniformly asymptotically o pseudocontractive mappings in this paper we prove the equivalences of the strong convergence each other the modified mann iterative process with errors the modified ishikawa iterative process with errors the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically o pseudocontractive mappings in arbitrary real banach space the results presented in this paper generalize and improve the corresponding results of roades soltuz and huang

inverse monoids decidability and complexity of algebraic questions this paper investigates the word problem for inverse monoids generated by a set c subject to relations of the form e f where e and f are both idempotents in the free inverse monoid generated by c it is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a ram as well as in deterministic logarithmic space which solves an open problem of margolis and meakin for the uniform word problem where the presentation is part of the input exptime completeness is shown for the cayley graphs of these monoids it is shown that the first order theory with regular path predicates is decidable regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language as a corollary the decidability of the generalized word problem is deduced

stability of iterative procedures with errors for approximating common fixed points of a couple of q contractive like mappings in banach spaces abstract recently agarwal cho li and huang r p agarwal y j cho j li n j huang stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces j math anal appl 272 2002 435 447 introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi contractive mappings and showed the stability of these iterative procedures with errors in banach spaces in this paper we introduce a new concept of a couple of q contractive like mappings q 1 in a banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q contractive like mappings the results established in this paper improve extend and unify the corresponding ones of agarwal cho li and huang r p agarwal y j cho j li n j huang stability of iterative procedures with errors approximating common fixed points for a couple of quasi contractive mappings in q uniformly smooth banach spaces j math anal appl 272 2002 435 447 chidume c e chidume approximation of fixed points of quasi contractive mappings in l p spaces indian j pure appl math 22 1991 273 386 chidume and osilike c e chidume m o osilike fixed points iterations for quasi contractive maps in uniformly smooth banach spaces bull korean math soc 30 1993 201 212 liu q h liu on naimpally and singh s open questions j math anal appl 124 1987 157 164 q h liu a convergence theorem of the sequence of ishikawa iterates for quasi contractive mappings j math anal appl 146 1990 301 305 osilike m o osilike a stable iteration procedure for quasi contractive maps indian j pure appl math 27 1996 25 34 m o osilike stability of the ishikawa iteration method for quasi contractive maps indian j pure appl math 28 1997 1251 1265 and many others in the literature

recognisability for algebras of infinite trees we develop an algebraic language theory for languages of infinite trees we define a class of algebras called w hyperclones and we show that a language of infinite trees is regular if and only if it is recognised by a finitary path continuous w hyperclone

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

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

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

global existence and mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations abstract this paper deals with the first order nonlinear neutral delay differential equation d dt x t p t x t f t x 1 t x 2 t x n t 0 t t 0 where 0 p c t 0 r f c t 0 r n r and l c t 0 r with limt l t for l 1 2 n by using the banach fixed point theorem we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p construct some mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions seven examples are presented to illuminate the results obtained in this paper

strong convergence of viscosity approximation methods for finding zeros of accretive operators in banach spaces abstract in this paper we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in banach spaces then we establish strong convergence theorems for the composite iterative scheme the main theorems improve and generalize the recent corresponding results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 as well as aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 benavides et al t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 chen and zhu r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory and appl 2006 2006 1 10 and kamimura and takahashi s kamimura w takahashi approximation solutions of maximal monotone operators in hilberts spaces j approx theory 106 2000 226 240

a general iterative scheme for k strictly pseudo contractive mappings and optimization problems in this paper we introduce a new general iterative scheme for finding fixed points of a strictly pseudo contractive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a fixed point of the mapping which is a solution of a certain optimization problem related to a strongly positive bounded linear operator additional results of the main result are also obtained