projection methods isotone projection cones and the complementarity problem one studies some iterative methods for solving complementarity problems explicit or implicit in hilbert spaces the iterative methods presented are based on the fixed point theory on the coincidence equations on convex cones and on some properties of projection operators onto a special cone named the isotone projection cone the ordering defined by the cone is essential for the complementarity theory the idea is to use systematically the ordering in the iterative methods for solving complementarity problems in this sense one shows that the isotone projection cone is a good instrument

iterative methods for linear complementarity problems with upperbounds on primary variables this paper is concerned with iterative methods for the linear complementarity problem lcp of findingx and y in rn such thatc dx y 0 b x 0 andxt c dx y yt b x 0 whenb 0 this is the lcp m q withm l 0d t which is in turn equivalent to a linear variational inequality over a rectangle this type of problem arises for example from quadratic programming qp problems with upper and lower bounds ifd is symmetric and from multicommodity market equilibrium problems with institutional price controls imposed ifd is not necessarily symmetric iterative methods for the lcp m q with symmetricm are well developed and studied using qp applications for nonsymmetric cases withm being either an h matrix with positive diagonals or a z matrix there exists a robust iterative method with guaranteed convergence this paper extends this algorithm so that the lcp m q withm l 0d t which is neither symmetric nor an h matrix with positive diagonals nor a z matrix can be processed when onlyd notm satisfies such properties the case whered is nonsymmetric is explicitly discussed

associated primes of local cohomology of flat extensions with regular fibers and σ finite d modules abstract in this manuscript we study the following question raised by mel hochster let r m k be a local ring and s be a flat extension with regular closed fiber is v m s ass s h i i s finite for every ideal i s and i n we prove that the answer is positive when s is either a polynomial or a power series ring over r and dim r i r 1 in addition we analyze when this question can be reduced to the case where s is a power series ring over r an important tool for our proof is the use of finite d modules which are not necessarily finitely generated as d modules but whose associated primes are finite we give examples of this class of d modules and applications to local cohomology

iterative methods for a class of complementarity problems abstract in this paper we propose and study an algorithm for a new class of complementarity problems of finding u r n such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a nonlinear transformation from r n into itself it is proved that the approximate solution obtained from the iterative scheme converges to the exact solution several special cases are also discussed

theory of one tape linear time turing machines a theory of one tape two way one head off line linear time turing machines is essentially different from its polynomial time counterpart since these machines are closely related to finite state automata this paper discusses structural complexity issues of one tape turing machines of various types deterministic nondeterministic reversible alternating probabilistic counting and quantum turing machines that halt in linear time where the running time of a machine is defined as the length of any longest computation path we explore structural properties of one tape linear time turing machines and clarify how the machines resources affect their computational patterns and power

on the discreteness and rationality of f jumping coefficients abstract we prove that the f jumping coefficients of a principal ideal of an excellent regular local ring of characteristic p 0 are all rational and form a discrete subset of r

strong f regularity and generating morphisms of local cohomology modules abstract we establish a criterion for the strong f regularity of a non gorenstein cohen macaulay reduced complete local ring of dimension at least 2 and prime characteristic p we also describe an explicit generating morphism in the sense of lyubeznik for the top local cohomology module with support in certain ideals arising from an n n 1 matrix x of indeterminates for a perfect field k of characteristic p 5 these results led us to derive a simple new proof of the well known fact that the generic determinantal ring over k given by the maximal minors of x is strongly f regular

the quasi complementarity problem abstract variational inequality techniques are used to suggest a unified and general iterative algorithm for computing the approximate solution of a new class of complementarity problems the convergence properties of this algorithm are also discussed

generalized complementarity problems for fuzzy mappings in this paper we introduce a new class of generalized complementarity problems for the fuzzy mappings and construct a new iterative algorithm we also discuss the existence of solutions for the generalized complementarity problems and the convergence of iterative sequence

on the structure of logspace probabilistic complexity classes we investigate hierarchical properties and logspace reductions of languages recognized by logspace probabilistic turing machines arthur merlin games and games against nature with logspace probabilistic verifiers each logspace complexity class is decomposed into a hierarchy based on corresponding two way multihead finite state automata and we eventually prove the separation of the hierarchy levels even for languages over a single letter alphabet furthermore we show efficient reductions of each logspace complexity class to or between low levels of its corresponding hierarchy we find probabilistic and probabilistic plus nondeterministic variants of savitch s maze threading problem which are logspace complete for pl the class of languages recognized by logspace probabilistic turing machines and respectively ppp the class of languages recognized by polynomial time deterministic turing machines and which can be recognized by one way non sensing two head or one way one head one counter finite state automata with probabilistic and both probabilistic and nondeterministic states respectively

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic let r k x 1 dots x n be a ring of polynomials over a field k of characteristic p 0 there is an algorithm due to lyubeznik for deciding the vanishing of local cohomology modules h i i r where i subset r is an ideal this algorithm has not been implemented because its complexity grows very rapidly with the growth of p which makes it impractical in this paper we produce a modification of this algorithm that consumes a modest amount of memory

on the nonlinear complementarity problem abstract we consider and study an algorithm for a new class of complementarity problems of finding u such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a diagonally nonlinear mapping from r n into itself furthermore it is proved that the approximate solution obtained by the iterative scheme converges to the exact solution special cases are also discussed

space efficient deterministic simulation of probabilistic automata given a description of a probabilistic automaton one head probabilistic finite state automaton or probabilistic turing machine and an input string x of length n we ask how much space does a deterministic turing machine need in order to decide the acceptance of the input string by that automaton the question is interesting even in the case of one head one way probabilistic finite state automata 1pfa s we call rational stochastic languages ss rat the class of languages recognized by 1pfa s whose transition probabilities and cutpoints i e recognition thresholds are rational numbers the class ss rat contains context sensitive languages that are not context free but on the other hand there are context free languages not included in ss rat our main results are as follows begin itemize item the proper inclusion of ss rat in zlo which is optimal i e ss rat not subset dspace o log n the previous upper bounds were dspace n obtained by p d dieu in 1972 and linebreak 4 dspace log n log log n obtained by h jung in 1984 item probabilistic turing machines with space bound f n in o log n can be deterministically simulated in space o min c f n log n log n f n log log n where c is a constant depending on the simulated probabilistic turing machine the best previously known simulation uses o log n f n log log n space obtained by h jung in 1984 end itemize to obtain these results we develop and use two space efficient but also parallel time efficient techniques which are of independent interest begin itemize item a technique to compare deterministically using only o log n space large numbers given in terms of their values modulo a sequence of primes p1 p2 cdots pn in o na where a is some arbitrary constant item a technique to compare deterministically a threshold with entries of the inverse of a given banded matrix end itemize

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

monotone iterative methods for nonlinear equations involving a noninvertible linear part we study monotone iterative methods for the numerical solution of a class of nonlinear elliptic boundary value problems by applying a theorem of ortega and rheinboldt this generalizes the work of earlier authors to the case of nonlinear perturbations of linear problems with a nontrivial kernel

newton s method for linear complementarity problems this paper presents an iterative newton type method for solving a class of linear complementarity problems this class was discovered by mangasarian who had established that these problems can be solved as linear programs cottle and pang characterized solutions of the problems in terms of least elements of certain polyhedral sets the algorithms developed in this paper are shown to converge to the least element solutions some applications and computational results are also discussed

generic vanishing in characteristic p 0 and the characterization of ordinary abelian varieties we prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of kawamata s theorems a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the albanese map when the frobenius stable kodaira dimension is zero

a motivic conjecture of milne let k be an algebraically closed field of characteristic p 0 let w k be the ring of witt vectors with coefficients ink we prove a motivic conjecture of milne that relates thecohomology with zp coefficients to the crystalline cohomology with integral coefficients in the wider context ofp divisible groups endowed with families of crystalline tensors over a finite discrete valuation ring extension of w k the result extends work of faltings as a main new tool we construct global deformations of p divisible groups endowed with crystalline tensors over certain regular formally smooth schemes over w k

f thresholds of hypersurfaces for every 0 that is f finite i e such that the frobenius morphism f r r is finite if a is an ideal in r and if is a nonnegative real number then the corresponding test ideal is denoted by a in this context we say that is an f jumping exponent or an f threshold if a 6 a for every the following is our main result about f jumping exponents in positive characteristic theorem 1 1 if r is an f finite regular ring and if a f is a principal ideal then the f jumping exponents of a are rational and they form a discrete set the discreteness and the rationality of f jumping numbers has been proved in bms for every ideal when the ring r is essentially of finite type over an f finite field we mention also that for r k x y with k a finite field the above result has been proved in ha using a completely different approach we stress that the difficulty in attacking this result does notcome from the fact that there is no available resolution of singularities in positive characteristic even

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities