strong convergence theorems for a countable family of quasi ϕ asymptotically nonexpansive nonself mappings abstract the purpose of this article is to introduce a class of quasi asymptotically nonexpansive nonself mappings and to study the strong convergence under a limit condition only in the framework of banach spaces as an application we utilize our results to study the approximation problem of solution to a system of equilibrium problems the results presented in the paper improve and extend the corresponding results announced by some authors recently

finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms abstract in this paper a finite difference scheme is presented for the generalized time fractional telegraph equation gtfte defined using generalized fractional derivative gfd terms introduced recently the generalization of fractional derivatives is done by introducing scale and weight functions and for their particular choices gfd reduces to caputo and riemann liouville derivatives we present the solution behaviour of the gtfte by changing the weight and scale functions in gfd the convergence and the stability of the finite difference scheme fds are also presented and for the numerical simulation of the fds we consider examples which validate our numerical method

the poincare series of the module of derivations of affine monomial curves abstract let a be a graded k algebra and m be a finitely generated a module the poincare series p m a z is the formal power series i dim k tor i a k m z i we study the poincare series of der k k s the module of derivations of a numerical semigroup ring k s and we relate it to the poincare series of k over k s and to the type of s we then use this in order to determine the poincare series of der k k s or at least its rationality for some classes of examples we finally give an example of a non rational p der k k s k s z

a new explicit method for the diffusion convention equation abstract we consider here the finite difference approximation to the diffusion convection equation from which new explicit formulation are obtained which are asymmetric these explicit schemes can then be used to develop a new class of methods called group explicit as introduced in 2 theoretical aspects of the stability consistency convergence and truncation errors of this new class of methods is briefly discussed and numerical evidence presented to confirm our recomendations

hybrid approximation of solutions of nonlinear operator equations and application to equation of hammerstein type in this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of inverse strongly monotone mappings in a 2 uniformly convex and uniformly smooth real banach space our results extend improve and generalize the results of several authors which are announced recently application of our theorem to solution of equations of hammerstein type is of independent interest

classification of the tor algebras of codimension four almost complete intersections let r m k be a local ring in which 2 is a unit assume that every element of k has a square root in k we classify the algebras tor r r j k as j varies over all grade four almost complete intersection ideals in r the analogous classification has already been found when j varies over all grade four gorenstein ideals 21 and when j varies over all ideals of grade at most three 5 30 the present paper makes use of the classification in 21 of the tor algebras of codimension four gorenstein rings as well as the usually nonminimal dg algebra resolution of a codimension four almost complete intersection which is produced in 25 and 26

on the generic free resolutions the problem we discuss in this paper is to find the arithmetic structure of finite free resolutions it started with hilbert s characterisation of ideals of projective dimension 1 with gcd 1 in a polynomial ring he proved that such ideals are given by n x n minors of an n x n 1 matrix this result was then generalized by several authors notably by burch b the hilbert burch theorem has since found many important applications to deformation theory and algebraic geometry in their paper buchsbaum and eisenbud be1 generalized the hilbertburch theorem they proved several structure theorems concerning various factorizations of the minors of the maps involved for resolutions of arbitrary length hochster h has shown that buchsbaum eisenbud structure theorems are enough to give the full structure of resolutions of length 2 he found in this case the universal pair r if i e a ring r and a resolution 5 over it such that for each resolution g with the same dimensions of modules over the ring s there exists a unique map r s such that g for s he proved that r is noetherian normal and cohenmacaulay if we not have the uniqueness in the above definition we speak of the generic pair r f if r f is a universal generic pair and r is noetherian we speak of the universal noetherian generic noetherian pair

a modified halpern type iteration algorithm for totally quasi ϕ asymptotically nonexpansive mappings with applications abstract the purpose of this article is to modify the halpern type iteration algorithm for total quasi asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of banach spaces the results presented in the paper improve and extend the corresponding results of x l qin y j cho s m kang h y zhou convergence of a modified halpern type iterative algorithm for quasi nonexpansive mappings appl math lett 22 2009 1051 1055 z m wang y f su d x wang y c dong a modified halpern type iteration algorithm for a family of hemi relative nonexpansive mappings and systems of equilibrium problems in banach spaces j comput appl math 235 2011 2364 2371 y f su h k xu x zhang strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications nonlinear anal 73 2010 3890 3906 c martinez yanes h k xu strong convergence of the cq method for fixed point iteration processes nonlinear anal 64 2006 2400 2411 and others

on the structure of free resolutions of length 3 the sources of structure theory of finite free resolutions go back to hilbert in his famous paper on invariant theory he proved that every ideal of projective dimension 1 over a polynomial ring is determinantal this theorem was then extended by burch to arbitrary commutative rings there are various motivations for extending this results one of them is a variety of applications of the hilbert burch theorem in deformation theory and algebraic geometry cf for example s another reason comes from serre s conjecture one would like to understand in terms of resolutions why the lifting property of grothendieck does not hold in 1974 buchsbaum and eisenbud in bel introduced so called structure theorems various factorisations which occur for acyclic complexes of arbitrary length then hochster in h generalized the hilbert burch theorem to arbitrary free complexes of length 2 his results were then improved in br pw still the structure of complexes of length bigger than 2 is not understood the first steps in this direction are the results of b and the construction of a generic ring for complexes of length 3 of type 1 rz 1 1 given in pw in this paper i construct a ring which i believe is the generic ring for complexes of length 3 the construction involves new structure theorems and a new idea the notion of defects of structure theorems the paper is organized as follows section 1 is introductory i give there the background from representation theory and the cohomology groups of a lie algebra section 2 contains the proof of the new structure theorems we need the construction of the generic ring r and of the defect lie algebra l in section 3 i show that genericity of r follows from vanising of the homology of a certain family of complexes over u l the enveloping algebra of l in section 4 i apply the results of section 2 to study multi

strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications the purpose of this paper is by using the hybrid iterative method to prove some strong convergence theorems for approximating a common element of the set of solutions to a system of generalized mixed equilibrium problems and the set of common fixed points for two countable families of closed and asymptotically relatively nonexpansive mappings in banach space the results presented in the paper improve and extend the corresponding results of su et al y f su h k xu x zhang strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications nonlinear anal 73 2010 3890 3906 li and su h y li y f su strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems nonlinear anal 72 2 2010 847 855 chang et al s s chang h w joseph lee chi kin chan a new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in banach spaces with applications nonlinear anal tma 73 2010 2260 2270 kang et al j kang y su x zhang hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications nonlinear anal hs 4 4 2010 755 765 matsushita and takahashi s matsushita w takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 tan et al j f tan s s chang m liu j i liu strong convergence theorems of a hybrid projection algorithm for a family of quasi asymptotically nonexpansive mappings opuscula math 30 3 2010 341 348 takahashia and zembayashi w takahashi k zembayashi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 and wattanawitoon and kumam k wattanawitoon p kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid systems 3 2009 11 20 and others

on the variety of complexes publisher summary this chapter focuses on the characteristic free study of the buchsbaum eisenbud varieties of complexes in detail with the use of young diagrams and young tableaux to give an explicit basis for buchsbaum and eisenbud have studied the varieties of complexes from the point of view of resolutions and have proven the results for the variety w k 1 a young tableau is a filling of the boxes of a young diagram with integers out of 1 2 and is called the shape of the young tableau the chapter presents a proposition that states that ach element in can be written as a linear combination of standard multitableaux

strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces abstract in this paper we introduce two iterative sequences 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 a banach space then we study the strong and weak convergence of the sequences

a new difference scheme with high accuracy and absolute stability for solving convection diffusion equations in this paper we use a semi discrete and a pade approximation method to propose a new difference scheme for solving convection diffusion problems the truncation error of the difference scheme is o h email protected 5 it is shown through analysis that the scheme is unconditionally stable numerical experiments are conducted to test its high accuracy and to compare it with crank nicolson method

a compact fourth order l stable scheme for reaction diffusion systems with nonsmooth data exponential time differencing runge kutta etdrk schemes based on diagonal pade approximations for the numerical solution of reaction diffusion systems containing nonsmooth data have the disadvantage of producing poor numerical results when the time steps are too large relative to the spatial steps on the other hand methods based on sub diagonal pade approximations do not suffer from this bottleneck in this paper we present a novel modified version of cox and matthews fourth order etdrk scheme based on sub diagonal pade approximation to matrix exponential functions in combination with compact fourth order finite difference scheme in space for direct integration of reaction diffusion problems with nonsmooth data for an efficient implementation of the scheme a partial fraction splitting technique is utilized in which it is required to solve several backward euler type linear systems at each time step moreover the design of the algorithm offers parallel implementation so we implement the proposed algorithm in parallel on two processors utilizing matlabmpi a parallel message passing version of matlab and obtain that the parallel version is computationally more efficient than the existing schemes considered in this paper we investigate the amplification factor of the scheme and plot its boundaries of stability regions which give an indication of the stability of the scheme calculation of the local truncation error and an empirical convergence analysis demonstrates the fourth order accuracy of the proposed scheme accuracy computational efficiency and reliability of the new scheme are demonstrated with numerical examples and comparing it with existing schemes

the resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring abstract let k be a field for each pair of positive integers n n we resolve q r x n y n z n as a module over the ring r k x y z x n y n z n write n in the form n a n r for integers a and r with r between 0 and n 1 if n does not divide n and the characteristic of k is fixed then the value of a determines whether q has finite or infinite projective dimension if q has infinite projective dimension then value of r together with the parity of a determines the periodic part of the infinite resolution when q has infinite projective dimension we give an explicit presentation for the module of first syzygies of q this presentation is quite complicated we also give an explicit presentation for the module of second syzygies for q this presentation is remarkably uncomplicated we use linkage to find an explicit generating set for the grade three gorenstein ideal x n y n z n x n y n z n in the polynomial ring k x y z the question does q have finite projective dimension is intimately connected to the question does k x y z x a y a z a have the weak lefschetz property the second question is connected to the enumeration of plane partitions when the field k has positive characteristic we investigate three questions about the frobenius powers f t q of q when does there exist a pair n n so that q has infinite projective dimension and f q has finite projective dimension is the tail of the resolution of the frobenius power f t q eventually a periodic function of t up to shift in particular we exhibit a situation where the tail of the resolution of f t q after shifting is periodic as a function of t with an arbitrarily large period can one use socle degrees to predict that the tail of the resolution of f t q is a shift of the tail of the resolution of q

strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a hilbert space abstract we introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space and then obtain that the sequence converges strongly to a common element of two sets using this result we prove three new strong convergence theorems in fixed point problems variational inequalities and equilibrium problems

approximation theorems for total quasi ϕ asymptotically nonexpansive mappings with applications abstract the purpose of this article is to prove some approximation theorems of common fixed points for countable families of total quasi asymptotically nonexpansive mappings which contain several kinds of mappings as its special cases in banach spaces in order to get the approximation theorems the hybrid algorithms are presented and are used to approximate the common fixed points using this result we also discuss the problem of strong convergence concerning the maximal monotone operators in a banach space the results of this article extend and improve the results of matsushita and takahashi s matsushita w takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theor 134 2005 257 266 plubtieng and ungchittrakool s plubtieng k ungchittrakool hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in banach spaces j approx theor 149 2007 103 115 li su h y li y f su strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems nonlinear anal 72 2 2010 847 855 su xu and zhang y f su h k xu x zhang strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications nonlinear anal 73 2010 3890 3960 wang et al z m wang y f su d x wang y c dong a modified halpern type iteration algorithm for a family of hemi relative nonexpansive mappings and systems of equilibrium problems in banach spaces j comput appl math 235 2011 2364 2371 chang et al s s chang h w joseph lee chi kin chan a new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in banach spaces with applications nonlinear anal 73 2010 2260 2270 chang et al s s chang c k chan h w joseph lee modified block iterative algorithm for quasi asymptotically nonexpansive mappings and equilibrium problem in banach spaces appl math comput 217 2011 7520 7530 ofoedu and malonza e u ofoedu d m malonza hybrid approximation of solutions of nonlinear operator equations and application to equation of hammerstein type appl math comput 217 2011 6019 6030 and yao et al y h yao y c liou s m kang strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings appl math comput 208 2009 211 218

strong convergence theorems for bregman totally quasi asymptotically nonexpansive mappings in reflexive banach spaces the purpose of this article is by using the shrinking projection method introduced by takahashi kubota and takeuchi to propose an iteration algorithm for bregman total quasi f asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of reflexive banach spaces as applications we apply our results to a system of equilibrium problems and zero point problem of maximal monotone mappings in reflexive banach spaces the results presented in the paper improve and extend the corresponding results of reich and sabach 2010 12 suantai et al 2012 13 nilsrakoo and saejung 2011 11 qin et al 2009 5 wang et al 2011 6 su et al 2010 7 martinez yanes and xu 2006 3 and others

poincare series of modules over local rings of small embedding codepth or small linking number abstract let s n k be a commutative noetherian local ring and m be a finitely generated s module then the poincare series of m is rational if any of the following holds edim s depth s 3 edim s depth s 4 and s is gorenstein s is one link from a complete intersection s is two links from a complete intersection and s is gorenstein to prove this result we assume without loss of generality that s r i with r m regular local and the key to the argument is to produce a factorization of the canonical map r s as a composition of a complete intersection r c with a golod map c s this is accomplished by invoking a theorem of avramov and backelin once one has existence of a dg algebra structure on a minimal r free resolution of s together with detailed knowledge of the structure of the induced homology algebra tor r s k h k s linkage theory provides the main technical tool for this analysis

a fourth order method of the convection diffusion equations with neumann boundary conditions abstract in this paper we have developed a fourth order compact finite difference scheme for solving the convection diffusion equation with neumann boundary conditions firstly we apply the compact finite difference scheme of fourth order to discrete spatial derivatives at the interior points then we present a new compact finite difference scheme for the boundary points which is also fourth order accurate finally we use a pade approximation method for the resulting linear system of ordinary differential equations the presented scheme has fifth order accuracy in the time direction and fourth order accuracy in the space direction it is shown through analysis that the scheme is unconditionally stable numerical results show that the compact finite difference scheme gives an efficient method for solving the convection diffusion equations with neumann boundary conditions

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

restrictive taylor s approximation for solving convection diffusion equation in this paper we shall develop a new explicit method for solve the convection diffusion equation which will exhibit several advantageous features highly accurate fast and with good results whatever the exact solution is too large the stability region is discussed the error upper bound is proved the obtained results for a test problem compared with the exact solution and its douglas approximation it proves the mentioned advantages

weighted finite difference techniques for the one dimensional advection diffusion equation various numerical techniques will be developed and compared for solving the one dimensional advection diffusion equation with constant coefficient these techniques are based on the two level finite difference approximations the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the new methods are more accurate and are more efficient than the conventional techniques these schemes are free of numerical diffusion the results of a numerical experiment are presented and the accuracy and central processor cpu time needed are discussed and compared

a structure theorem for type 3 grade 3 perfect ideals abstract in 1977 buchsbaum and eisenbud gave a complete characterization of grade 3 perfect ideals i of type 1 i e gorenstein in a noetherian local ring r exploiting the fact that a minimal free resolution for r i has a structure of associative commutative differential graded algebra they also studied successfully the structure of grade 3 almost complete intersections ideals in 1981 and 1982 kustin and miller studied the structure of gorenstein ideals of grade 4 but they introduced a new variable to the problem they defined the concept of defect of an ideal and they found that for grade 4 gorenstein ideals the structures vary in part according to the value of d i the defect of i later in 1984 ann brown in her ph d thesis gave a structure theorem for grade 3 perfect ideals of type 2 and defect positive she also proved that for grade 3 perfect ideals of type 2 d i can be either 0 or 1 the purpose of this paper is to give a structure theorem for grade 3 perfect ideals of type 3 and defect 2 or greater furthermore this structure theorem permits us to establish that for grade 3 type 3 perfect ideals d i can be either 0 or 1 or 2 or 4

extended one step time integration schemes for convection diffusion equations abstract we first describe a one parameter family of unconditionally stable third order time integration schemes for the convection diffusion equation u t cu x vu xx based on the extended trapezoidal formulas of usmani and agarwal 1 interestingly there exists a method that is fourth order as well as unconditionally stable we then describe a one parameter family of unconditionally stable fourth order time integration schemes based on the extended simpson rules of chawla et al 2 again there exists a method that is fifth order as well as unconditionally stable the stability and accuracy of the obtained methods are tested and compared with the widely used method of crank nicolson by considering three problems of practical interest

strong convergence theorems of total quasi φ asymptotically nonexpansive semi groups in banach spaces the purpose of this article is first to introduce the concept of total quasi f asymptotically nonexpansive semigroups which contains many kinds of semi groups as its special cases and then to modify the halpern mann type iteration algorithm for this kind of semi groups to have the strong convergence under a limit condition only in the framework of banach spaces the results presented in the paper improve and extend the corresponding recent results announced by many authors

on the finite difference approximation to the convection diffusion equation abstract in this paper the system of ordinary differential equations arisen from discretizing the convection diffusion equation with respect to the space variable to compute its approximate solution along a time level is considered this system involves in computing e k a y for some vector y where k is the time step size and a is a large tridiagonal toeplitz matrix the common ways to compute an approximate solution of the convection diffusion equation are based on replacing e k a y by an its approximation we give an explicit expression for the exact value of e k a y and then the numerical results of our method with that of some well known methods are compared

a compact finite volume method and its extrapolation for elliptic equations with third boundary conditions a fourth order compact finite volume method is constructed for one and two dimensional elliptic equations with third boundary conditions in this paper taking two point boundary value problem of third kind as an example we derive some useful high accuracy post processing formulas to recover the numerical derivatives at the nodes or midpoints of the elements we also improve the accuracy of the compact finite volume scheme from order 4 to 6 based on richardson extrapolation by rigorously proving the scheme has error asymptotic expansion numerical examples verify the correctness of the theoretical analysis and also show the effectiveness of the scheme as well as its post processing formulas and extrapolation

schur functors and schur complexes the study of schur functors has a relatively long history its main impetus derived from representation theory originally in characteristic zero over the years however with the development of modular representations and algebraic geometry over fields of positive characteristic the need for a theory of universal polynomial functors increased and since the mid 1960s approaches to a characteristic free treatment of schur functors have been developing see for instance the recent book of green 1 l in which the treatments by carter and lusztig 6 higman 12 and towber 20 among others are discussed our own interest in such a treatment was awakened by the work of lascoux 141 on resolutions of determinantal ideals although his thesis treated only the characteristic zero case it suggested that a general and elementary theory of schur functors could be developed using only the rudiments of multilinear algebra involving the hopf algebra structures of the symmetric exterior and divided power algebras moreover this elementary development admitted of a natural generalization to the idea of schur complexes whose usefulness was demonstrated for instance in our construction of a universal minimal

a new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in banach spaces with applications abstract the purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a banach space as applications we utilize our results to obtain some new results for finding a solution of an equilibrium problem a fixed point problem and a common zero point problem for maximal monotone mappings in banach spaces

high order unconditionally stable difference schemes for the riesz space fractional telegraph equation in this paper a class of unconditionally stable difference schemes based on the pade approximation is presented for the riesz space fractional telegraph equation firstly we introduce a new variable to transform the original differential equation to an equivalent differential equation system then we apply a second order fractional central difference scheme to discretize the riesz space fractional operator finally we use 1 1 2 2 and 3 3 pade approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations matrix analysis is used to show the unconditional stability of the proposed algorithms two examples with known exact solutions are chosen to assess the proposed difference schemes numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space fractional hyperbolic equation