algebraic reflexivity of sets of bounded operators on vector valued lipschitz functions abstract in this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued lipschitz functions we also derive a representation for the generalized bi circular projections on these spaces

representations versus numberings on the relationship of two computability notions abstract this paper gives an answer to weihrauch s computability springer berlin 1987 question whether and if not always when an effective map between the computable elements of two represented sets can be extended to a partial computable map between the represented sets examples are known showing that this is not possible in general a condition is introduced and for countably based topological t 0 spaces it is shown that exactly the partial effective maps meeting the requirement are extendable for total effective maps the extra condition is satisfied in the standard cases of effectively given separable metric spaces and continuous directed complete partial orders in which the extendability is already known in the first case a similar result holds also for partial effective maps but not in the second

the c 3 theorem and a d 2 algorithm for large scale stochastic mixed integer programming set convexification this paper considers the two stage stochastic integer programming problem with an emphasis on instances in which integer variables appear in the second stage drawing heavily on the theory of disjunctive programming we characterize convexifications of the second stage problem and develop a decomposition based algorithm for the solution of such problems in particular we verify that problems with fixed recourse are characterized by scenario dependent second stage convexifications that have a great deal in common we refer to this characterization as the c3 common cut coefficients theorem based on the c3 theorem we develop a decomposition algorithm which we refer to as disjunctive decomposition d2 in this new class of algorithms we work with master and subproblems that result from convexifications of two coupled disjunctive programs we show that when the second stage consists of 0 1 milp problems we can obtain accurate second stage objective function estimates after finitely many steps this result implies the convergence of the d2 algorithm

homomorphisms between algebras of lipschitz functions with the values in function algebras abstract we give a characterization of algebra homomorphisms and isomorphisms between banach algebras of lipschitz functions with the values in unital commutative c algebras we prove that such homomorphisms are composition operators of the form and preserve some properties

a finite branch and bound algorithm for two stage stochastic integer programs this paper addresses a general class of two stage stochastic programs with integer recourse and discrete distributions we exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm the proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature

algebraic reflexivity of some subsets of the isometry group let x be a compact first countable space in this paper we show that the set of isometries of c x that are involutions is algebraically reflexive as a consequence of a recent work of botelho and jamison this leads to the conclusion that the set of generalized bi circular projections on c x is also algebraically reflexive we also consider these questions for the space c x e where e is a uniformly convex banach space

algebraic reflexivity of the isometry group of some spaces of lipschitz functions abstract we show that the isometry groups of lip x d and lip x d with 0 1 for a compact metric space x d are algebraically reflexive we also prove that the sets of isometric reflections and generalized bi circular projections on such spaces are algebraically reflexive in order to achieve this we characterize generalized bi circular projections on these spaces

dynamical systems measures and fractals via domain theory abstract we introduce domain theory in dynamical systems iterated function systems fractals and measure theory for a discrete dynamical system given by the action of a continuous map f x x on a metric space x we study the extended dynamical systems vx vf ux uf and lx lf where v u and l are respectively the vietoris hyperspace the upper hyperspace and the lower hyperspace functors we show that if x f is chaotic then so is ux uf when x is locally compact ux is a continuous bounded complete dcpo if x is second countable as well then ux will be continuous and can be given an effective structure we show how strange attractors attractors of iterated function systems fractals and julia sets are obtained effectively as fixed points of deterministic functions on ux or fixed points of non deterministic functions on cux where c is the convex plotkin power domain we also show that the set m x of finite borel measures on x can be embedded in pux where p is the probabilistic power domain this provides an effective framework for measure theory we then prove that the invariant measure of an hyperbolic iterated function system with probabilities can he obtained as the unique fixed point of an associated continuous function on pux

readies and failures in the algebra of communicating processes readiness and failure semantics are studied in the setting of algebra of communicating processes acp a model of process graphs modulo readiness equivalence respectively failure equivalence is constructed and an equational axiom system is presented which is complete for this graph model an explicit representation of the graph model is given the failure model whose elements are failure sets furthermore a characterisation of failure equivalence is obtained as the maximal congruence which is consistent with trace semantics by suitably restricting the communication format in acp this result is shown to carry over to subsets of hoare s communicating sequential processes csp and milner s calculus of communicating systems ccs also the characterisation implies a full abstraction result for the failure model in the above we restrict ourselves to finite processes without tau steps at the end of the paper a comment is made on the situation for infinite processes with tau steps notably w

the complexity of computing the number of strings of given length in context free languages abstract computing the number of strings of given length contained in a language is related to classical problems of combinatorics formal languages and computational complexity here we study the complexity of this problem in the case of context free languages it is shown that for unambiguous context free languages such a computation is easy and can be carried out by efficient parallel algorithms on the contrary for some context free languages of ambiguity degree two the problem becomes intractable these results are related to other classical subjects concerning counting problems exponential time recognizable languages and sparse sets

local isometries of function spaces abstract we show that for a large class of function spaces any isometry that coincides locally with a surjective isometry must be automatically surjective this class includes finite codimensional subspaces of c left x right and spaces c left x e right of e valued continuous functions for finite dimensional or uniformly convex and algebraically reflexive e

stochastic programming with integer variables including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design starting from mean risk approaches with different risk measures we identify corresponding two and multi stage stochastic integer programs that are large scale block structured mixed integer linear programs if the underlying probability distributions are discrete we highlight the role of mixed integer value functions for structure and stability of stochastic integer programs when applied to the block structures in stochastic integer programming well known algorithmic principles such as branch and bound lagrangian relaxation or cutting plane methods open up new directions of research we review existing results in the field and indicate departure points for their extension

analytic models and ambiguity of context free languages we establish that several classical context free languages are inherently ambiguous by proving that their counting generating functions when considered as analytic functions exhibit some characteristic form of transcendental behaviour to that purpose we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages in particular the paper contains a general density theorem for unambiguous context free languages

solving the asymmetric travelling salesman problem with time windows by branch and cut many optimization problems have several equivalent mathematical models it is often not apparent which of these models is most suitable for practical computation in particular when a certain application with a specific range of instance sizes is in focus our paper addresses the asymmetric travelling salesman problem with time windows atsp tw from such a point of view the real world application we aim at is the control of a stacker crane in a warehouse we have implemented codes based on three alternative integer programming formulations of the atsp tw and more than ten heuristics computational results for real world instances with up to 233 nodes are reported showing that a new model presented in a companion paper outperforms the other two models we considered at least for our special application and that the heuristics provide acceptable solutions

a binary decision diagram based algorithm for solving a class of binary two stage stochastic programs we consider a special class of two stage stochastic integer programming problems with binary variables appearing in both stages the class of problems we consider constrains the second stage variables to belong to the intersection of sets corresponding to first stage binary variables that equal one our approach seeks to uncover strong dual formulations to the second stage problems by transforming them into dynamic programming dp problems parameterized by first stage variables we demonstrate how these dps can be formed by use of binary decision diagrams which then yield traditional benders inequalities that can be strengthened based on observations regarding the structure of the underlying dps we demonstrate the efficacy of our approach on a set of stochastic traveling salesman problems

decomposition algorithms with parametric gomory cuts for two stage stochastic integer programs we consider a class of two stage stochastic integer programs with binary variables in the rst stage and general integer variables in the second stage we develop decomposition algorithms akin to the l shaped or benders methods by utilizing gomory cuts to obtain iteratively tighter approximations of the second stage integer programs we show that the proposed methodology is exible in that it allows several modes of implementation all of which lead to nitely convergent algorithms we illustrate our algorithms using examples from the literature we report computational results using the stochastic server location problem instances which suggest that our decomposition based approach scales better with increases in the number of scenarios than a state of the art solver which was used to solve the deterministic equivalent formulation

on 2 local isometries on continuous vector valued function spaces article history received 24 july 2008 available online 24 december 2008 submitted by j d m wright a not necessarily linear mapping from a banach space x to a banach space y is said to be a 2 local isometry if for any pair x y of elements of x t here is as urjective linear isometry t x y such that tx x and ty y we show that under certain conditions on locally compact hausdorff spaces q k and a banach space e e very 2 local isometry on c0 q e to c0 k e is linear and surjective we also show that every 2 local isometry on p is linear and surjective for 1 p p 2 but this fails for the hilbert space 2

sparse sets in np p exptime versus nexptime this paper investigates the structural properties of sets in np p and shows that the computational difficulty of lower density sets in np depends explicitly on the relations between higher deterministic and nondeterministic time bounded complexity classes the paper exploits the recently discovered upward separation method which shows for example that there exist sparse sets in np p if and only if exptime nexptime in addition the paper uses relativization techniques to determine logical possibilities limitations of these proof techniques and exhibits one of the first natural structural differences between relativized np and conp

decomposition with branch and cut approaches for two stage stochastic mixed integer programming decomposition has proved to be one of the more effective tools for the solution of large scale problems especially those arising in stochastic programming a decomposition method with wide applicability is benders decomposition which has been applied to both stochastic programming as well as integer programming problems however this method of decomposition relies on convexity of the value function of linear programming subproblems this paper is devoted to a class of problems in which the second stage subproblem s may impose integer restrictions on some variables the value function of such integer subproblem s is not convex and new approaches must be designed in this paper we discuss alternative decomposition methods in which the second stage integer subproblems are solved using branch and cut methods one of the main advantages of our decomposition scheme is that stochastic mixed integer programming smip problems can be solved by dividing a large problem into smaller mip subproblems that can be solved in parallel this paper lays the foundation for such decomposition methods for two stage stochastic mixed integer programs

l shaped decomposition of two stage stochastic programs with integer recourse we consider two stage stochastic programming problems with integer recourse the l shaped method of stochastic linear programming is generalized to these problems by using generalized benders decomposition nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques finite convergence of the method is established when gomory s fractional cutting plane algorithm or a branch and bound algorithm is applied

computation by while programs on topological partial algebras the language of while programs is a fundamental model for imperative programming on any data type it leads to a generalisation of the theory of computable functions on the natural numbers to the theory of computable functions on any many sorted algebra the language is used to express many algorithms in scientific computing where while programs are applied to continuous data in the theory of data continuous data types are modelled by topological many sorted algebras we study both exact and approximate computations by while programs and while programs with arrays over topological many sorted algebras with partial operations first we establish that partial operations are necessary in order to compute a wide range of continuous functions we prove basic continuity properties of our abstract computability any partial function computable over a partial topological algebra by a while array program is continuous any set semicomputable or computable over a partial topological algebra by a while array program is open or clopen respectively secondly we contrast exact and approximate computations the class of functions that can be computed exactly can be quite limited we show that on connected total algebras the while and while array computable functions are precisely those that are explicitly definable by terms we show that for certain general classes of topological algebras the total functions that can be approximated by while programs are precisely those that can be effectively approximated by terms this property we call generalised weierstrass approximation an application of this result is that a function on the set r of reals is computable in the sense of computable analysis if and only if it is while program approximable on a simple algebra based on r

ranking and formal power series abstract we prove that the ranking problem for unambiguous context free languages is nc 1 reducible to the value problem for algebraic formal power series in noncommuting variables in the particular case of regular languages we show that the problem of ranking is nc 1 reducible to the problem of counting the number of strings of given length in suitable regular languages as a consequence ranking problems for regular languages are nc 1 reducible to integer division and hence computable by log space uniform boolean circuits of polynomial size and depth o log n log log n or by p uniform boolean circuits of polynomial size and depth o log n

embedding metric spaces into cpo s abstract we show that metric spaces with polish topology mp can be represented very well by bounded complete algebraic cpo s with continuous weight and distance cwd an operator cwd mp is defined such that 1 and 2 hold 1 1 d can be embedded topologically into d such that a partial function on d is metrically continuous if it can be extended to a total continuous function on d 2 2 every m mp is isometric to some d therefore the continuous cpo functions are exactly adequate for describing the continuous functions on the corresponding metric spaces the approach could be refined in order to study computability on metric spaces with polish topology examples of application are the euclidean space the space of total functions on the natural numbers baire space and spaces of infinite trees

concrete models of computation for topological algebras a concrete model of computation for a topological algebra is based on a representation of the algebra made from functions on the natural numbers the functions computable in a concrete model are computable in the representation in the classical sense of the chruch turing thesis moreover the functions turn out to be continuous in the topology of the algebra in this paper we consider different concrete models for computing in topological algebras and prove their mutual equivalence in certain commonly occurring circumstances for topological algebras the concrete models we use are effective representation by algebraic domains stoltenberg hansen and tucker effective representation by continuous domains edelat effective representation by type two recursion on baire space weihrauch and for metric and normed algebras we use effective metric spaces moschovakis and computability structures pour el and richards the result are evidence that computability theory for topological algebras is a stable theory independent of the specific models of computation just as classical computability theory for discrete algebras is stable

local isometries on spaces of continuous functions let x and y be banach spaces and s a subset of the space of linear continuous operators from x to y we say that an operator t belongs locally to s if for every x x there is s s possibly depending on x such that tx sx pointwise should be better than locally but we have followed tradition if each operator that belongs locally to s belongs in fact to s we say that s is algebraically reflexive when y x and s iso x is the group of isometries of x we say that t is a local isometry of x in this paper isometry means linear surjective isometry similarly a local automorphism of a banach algebra is an operator which agrees at every point with some automorphism also we will consider approximate local isometries and automorphisms these are operators having with the following property given x x and e 0 there is an isometry respectively an automorphism s of x such that tx sx e the study of local isometries and automorphisms of banach algebras spurred a considerable interest in recent years see the bibliography of the dissertation 16 in this paper we deal with local isometries and automorphisms of the algebras c0 l as usual we write c0 l or c k 0 l for the banach algebra of all continuous k valued functions on the locally compact space l vanishing at infinity where k is either c or r if l is compact the subscript will be omitted by the banach stone theorem if t is local isometry of c0 l then for each f there are a homeomorphism of l and a continuous unitary u l k such that tf u f

2 local automorphisms of operator algebras abstract a not necessarily continuous linear or multiplicative function from an algebra a into itself is called a 2 local automorphism if agrees with an automorphism of a at each pair of points in a in this paper we study when a 2 local automorphism of a c algebra or a standard operator algebra on a locally convex space is an automorphism

domain representations of partial functions with applications to spatial objects and constructive volume geometry a partial spatial object is a partial map from space to data data types of partial spatial objects are modelled by topological algebras of partial maps and are the foundation for a high level approach to volume graphics called constructive volume geometry cvg where space and data are subspaces of n dimensional euclidean space we investigate the computability of partial spatial object data types in general and in volume graphics using the theory of effective domain representations for topological algebras the basic mathematical problem considered is to classify which partial functions between topological spaces can be represented by total continuous functions between given domain representations of the spaces we prove theorems about partial functions on regular hausdorff spaces and their domain representations and apply the results to partial spatial objects and cvg algebras

logarithmic depth circuits for algebraic functions this paper describes circuits for computation of a large class of algebraic functions on polynomials power series and integers for which it has been a long standing open problem to compute in depth less than omega log n 2 algebraic circuits assume unit cost for elemental addition and multiplication this paper describes o log n depth algebraic circuits which given as input the coefficients of n degree polynomials over an appropriate ring compute the product of n o 1 polynomials the symmetric functions as well as division and interpolation of real polynomials also described are o log n depth algebraic circuits which are given as input the first n coefficients of a power series over an appropriate ring compute the product of n o 1 power series as well as division reciprocal and reversion of real power series furthermore this paper describes boolean circuits of depth o log n log log n which given n bit binary numbers compute the product of n numbers and integ

theory of representations abstract an approach for a simple general and unified theory of effectivity on sets with cardinality not greater than that of the continuum is presented a standard theory of effectivity on f f n n has been developed in a previous paper by representations f m this theory is extended to other sets m topological and recursion theoretical properties of representations are studied where the final topology of a representation plays an essential role it is shown that for any separable t0 space an up to equivalence unique admissible representation can be defined which reflects the topological properties correctly

solving stochastic programs with integer recourse by enumeration a framework using gro bner basis reductions in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

an optimal algorithm for the traveling salesman problem with time windows this paper presents the development of new elimination tests which greatly enhance the performance of a relatively well established dynamic programming approach and its application to the minimization of the total traveling cost for the traveling salesman problem with time windows the tests take advantage of the time window constraints to significantly reduce the state space and the number of state transitions these reductions are performed both a priori and during the execution of the algorithm the approach does not experience problems stemming from increasing problem size wider or overlapping time windows or an increasing number of states nearly as rapidly as other methods our computational results indicate that the algorithm was successful in solving problems with up to 200 nodes and fairly wide time windows when the density of the nodes in the geographical region was kept constant as the problem size was increased the algorithm was capable of solving problems with up to 800 nodes for these problems the cpu time increased linearly with problem size these problem sizes are much larger than those of problems previously reported in the literature

the parallel complexity of abelian permutation group problems we classify abelian permutation group problems with respect to their parallel complexity for such groups specified by generating permutations we show that testing membership computing order and testing isomorphism are nc 1 equivalent to and therefore have essentially the same parallel complexity as determining solvability of a system of linear equations modulo a product of small prime powers we show that intersecting two such groups is nc 1 equivalent to computing setwise stabilizers we show that each of these problems is nc 1 reducible to the problem of computing a generator relator presentation then we prove that the aforementioned problems belong to nc 3 thus identifying several natural set recognition problems in nc which may lie outside nc 2 finally we prove that nc 4 contains the problem of computing the cyclic decomposition of an abelian permutation group background results include an nc 1 solution to the problem of computing the product of n integers modulo a lce

log depth circuits for division and related problems we present optimal depth boolean circuits depth o log n for integer division powering and multiple products we also show that these three problems are of equivalent uniform depth and space complexity in addition we describe an algorithm for testing divisibility that is optimal for both depth and space

solving stochastic programs with integer recourse by enumeration a framework using grobner basis in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

outer approximation for integer nonlinear programs via decision diagrams as an alternative to traditional integer programming ip decision diagrams dds provide a new solution technology for discrete problems exploiting their combinatorial structure and dynamic programming representation while the literature mainly focuses on the competitive aspects of dds as a stand alone solver we investigate their complementary role by introducing ip techniques that can be derived from dds and used in conjunction with ip to enhance the overall performance this perspective allows for studying problems with more general structure than those typically modeled via recursive formulations in particular we develop linear programming and subgradient type methods to generate valid inequalities for the convex hull of the feasible region described by dds for convex ips these cutting planes dominate the so called linearized cuts used in the outer approximation framework these cutting planes can also be derived for nonconvex ips which leads to a generalization of the outer approximation framework computational experiments show significant optimality gap improvement for integer nonlinear programs over the traditional cutting plane methods employed in the state of the art solvers

bfc a branch and fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0 1 programs we present a framework for solving some types of 0 1 multi stage scheduling planning problems under uncertainty in the objective function coe cients and the right hand side a scenario analysis scheme with full recourse is used the solution o ered for each scenario group at each stage takes into account all scenarios but without subordinating to any of them the constraints are modelled by a splitting variables representation via scenarios so a 0 1 model for each scenario is consid ered plus the non anticipativity constraints that equate the 0 1 variables from the same group of scenarios in each stage the mathematical representation of the model is very amenable for the proposed framework to deal with the 0 1 character of the variables a branch and fix coordi nation approach is introduced for coordinating the selection of the branching nodes and branching variables in the scenario subproblems to be jointly optimized some computational experience is reported for di erent types of problems

algebraic languages and polyominoes enumeration abstract in this paper the use of algebraic languages theory in solving an open problem in combinatorics is shown by constructing a bijection between convex polyominoes and words of an algebraic language and by solving the corresponding algebraic system we prove that the number of convex polyominoes with perimeter 2n 8 is 2n 11 4 n 4 2n 1 2n n

two stage stochastic hierarchical multiple risk problems models and algorithms in this paper we consider a class of two stage stochastic risk management problems which may be stated as follows a decision maker determines a set of binary first stage decisions after which a random event from a finite set of possible outcomes is realized depending on the realization of this outcome a set of continuous second stage decisions must then be made that attempt to minimize some risk function we consider a hierarchy of multiple risk levels along with associated penalties for each possible scenario the overall objective function thus depends on the cost of the first stage decisions plus the expected second stage risk penalties we develop a mixed integer 0 1 programming model and adopt an automatic convexification procedure using the reformulation linearization technique to recast the problem into a form that is amenable to applying benders partitioning approach as a principal computational expedient we show how the reformulated higher dimensional benders subproblems can be efficiently solved via certain reduced sized linear programs in the original variable space in addition we explore several key ingredients in our proposed procedure to enhance the tightness of the prescribed benders cuts and the efficiency with which they are generated finally we demonstrate the computational efficacy of our approaches on a set of realistic test problems

on approximate and algebraic computability over the real numbers abstract we consider algebraic and approximate computations of partial real functions r d r algebraic computability is defined by means of parameter free finite algorithmic procedures the notion of approximate computability is a straightforward generalization of the ko friedman approach based on oracle turing machines to functions with not necessarily recursively open domains the main results of the paper give characterizations of approximate computability by means of the passing sets of finite algorithmic procedures i e characterizations from the algebraic point of view some consequences and also modifications of the concepts are discussed finally two variants of arithmetical hierarchies over the reals are considered and used to classify and mutually compare the domains graphs and ranges of algebraically resp approximately computable real functions

an exact algorithm for solving large scale two stage stochastic mixed integer problems some theoretical and experimental aspects abstract we present an algorithmic framework so called bfc tsmip for solving two stage stochastic mixed 0 1 problems the constraints in the deterministic equivalent model have 0 1 variables and continuous variables at any stage the approach uses the twin node family tnf concept within an adaptation of the algorithmic framework so called branch and fix coordination for satisfying the nonanticipativity constraints for the first stage 0 1 variables jointly we solve the mixed 0 1 submodels defined at each tnf integer set for satisfying the nonanticipativity constraints for the first stage continuous variables in these submodels the only integer variables are the second stage 0 1 variables a numerical example and some theoretical and computational results are presented to show the performance of the proposed approach

simple integer recourse models convexity and convex approximations we consider the objective function of a simple recourse problem with fixed technology matrix and integer second stage variables separability due to the simple recourse structure allows to study a one dimensional version instead based on an explicit formula for the objective function we derive a complete description of the class of probability density functions such that the objective function is convex this result is also stated in terms of random variables next we present a class of convex approximations of the objective function which are obtained by perturbing the distributions of the right hand side parameters we derive a uniform bound on the absolute error of the approximation finally we give a representation of convex simple integer recourse problems as continuous simple recourse problems so that they can be solved by existing special purpose algorithms

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

unifying computers and dynamical systems using the theory of synchronous concurrent algorithms a synchronous concurrent algorithm sca is a parallel deterministic algorithm based on a network of modules and channels computing and communicating data in parallel and synchronised by a global clock with discrete time many types of algorithms computer architectures and mathematical models of physical and biological systems are examples of scas for example conventional digital hardware is made from components that are scas and many computational models possess the essential features of scas including systolic arrays neural networks cellular automata and coupled map lattices in this paper we formalise the general concept of an sca equipped with a global clock in order to analyse precisely i specifications of their spatio temporal behaviour and ii the senses in which the algorithms are correct we start the mathematical study of sca computation specification and correctness using methods based on computation on many sorted topological algebras and equational logic we show that specifications can be given equationally and hence that the correctness of scas can be reduced to the validity of equations in certain computable algebras since the idea of an sca is general our methods and results apply to each of the particular classes of algorithms and dynamical systems above

convex approximations for complete integer recourse models we consider convex approximations of the expected value function of a two stage integer recourse problem the convex approximations are obtained by perturbing the distribution of the random right hand side vector it is shown that the approximation is optimal for the class of problems with totally unimodular recourse matrices for problems not in this class the result is a convex lower bound that is strictly better than the one obtained from the lp relaxation

recursive characterization of computable real valued functions and relations abstract corresponding to the definition of recursive functions we introduce a class of recursive relations in metric spaces such that each relation is generated from a class of basic relations by a finite number of applications of some specified operators we prove that our class of recursive relations essentially coincides with our class of densely computable relations defined via turing machines in the special case of the real numbers our subclass of recursive functions coincides with the classical class of computable real valued functions defined via turing machines by grzegorczyk lacombe and others

the characterization of nonexpansive grammars by rational power series given a reduced cycle free context free grammar g p y1 the following statements are equivalent i g is nonexpansive ii the structure generating functions of the grammars gi p yi yi are rational furthermore a helpful theorem for proving certain context free languages to be inherently ambiguous is given

a branch and price algorithm for multistage stochastic integer programming with application to stochastic batch sizing problems in this paper we present a branch and price method to solve special structured multistage stochastic integer programming problems we validate our method on two different versions of a multistage stochastic batch sizing problem sbsp one version adopts a recourse formulation and the other is based on probabilistic constraints our algorithmic approach is applicable to both formulations our computational results suggest that both classes of problems can be solved using relatively few nodes of a branch and price tree the success of our approach calls for extensions in methodology as well as applications

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

experimental computation of real numbers by newtonian machines following a methodology we have proposed for analysing the nature of experimental computation we prove that there is a 3 dimensional newtonian machine which given any point x 2 0 1 can generate an infinite sequence pn qn for n 1 2 of rational number interval approximations that converges to x as n 1 the machine is a system for scattering and collecting particles the theorem implies that every point x 2 0 1 is computable by a simple newtonian kinematic system that is bounded in space and mass and for which the calculation of the n th approximation of x takes place in o n time with o n energy we describe a set of variants of the scatter machine which explain why our machine is non deterministic