lattice ordered algebras that are subdirect products of valuation domains an f ring i e a lattice ordered ring that is a subdirect product of totally ordered rings a is called an sv ring if a p is a valuation domain for every prime ideal p of a if m is a maximal t ideal of a then the rank of a at m is the number of minimal prime ideals of a contained in m rank of a is the sup of the ranks of a at each of its maximal ideals if the latter is a positive integer then a is said to have finite rank and if a c x is the ring of all real valued continuous functions on a tychonoff space the rank of x is defined to be the rank of the f ring c x and x is called an sv space if c x is an sv ring x has finite rank k iff k is the maximal number of pairwise disjoint cozero sets with a point common to all of their closures in general f rings these two concepts are unrelated but if a is uniformly complete in particular if a c x then if a is an sv ring then it has finite rank showing that this latter holds makes use of the theory of finite valued lattice ordered abelian groups these two kinds of rings are investigated with an emphasis on the uniformly complete case fairly powerful machinery seems to have to be used and even then we do not know if there is a compact space x of finite rank that fails to be an sv space

averaging operators and positive contractive projections abstract the main topic of the present paper is a generalization of two theorems about positive contractive projections on c 0 x due to seever and kelley resp to the more general structure of algebras the theorems in question are the following if a is an archimedean semiprime algebra with the stone condition then every positive contractive projection t in a satisfies the identity t a tb t ta tb for all a b a seever furthermore t is averaging if and only if the range of t is a subalgebra kelley both theorems hold in particular for an archimedean unital algebra in contrast to the original proofs of seever and kelley in the c 0 x case our proofs are purely algebraic and order theoretical

totally real immersions of surfaces first published in transactions of the american mathematical society in volume 362 and issue 1 published by the american mathematical society

matrix algebras with multiplicative decomposition property we consider the multiplicative decomposition property the multiplicative analogue of the riesz decomposition property for entry wise ordered matrix algebras over the reals we characterize for which matrix pairs such a decomposition exists and use this result to present necessary and sufficient conditions for a matrix algebra to enjoy the decomposition property by all its positive matrix pairs thus we describe all matrix algebras with the decomposition property

conditional expectations on riesz spaces abstract conditional expectations operators acting on riesz spaces are shown to commute with a class of principal band projections using the above commutation property conditional expectation operators on riesz spaces are shown to be averaging operators here the theory of f algebras is used when defining multiplication on the riesz spaces this leads to the extension of these conditional expectation operators to their so called natural domains i e maximal domains for which the operators are both averaging operators and conditional expectations the natural domain is in many aspects analogous to l 1

on dantzig wolfe decomposition in integer programming and ways to perform branching in a branch and price algorithm dantzig wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound the reformulation gives rise to an integer master problem whose typically large number of variables is dealt with implicitly by using an integer programming column generation procedure also known as branch and price algorithm there is a large class of integer programs that are well suited for this solution technique in this paper we propose to base the dantzig wolfe decomposition of an integer program on the discretization of the integer polyhedron associated with a subsystem of constraints as opposed to its convexification this allows us to formulate the integrality restriction directly on the master variables and sets a theoretical framework for dealing with specific issues such as branching or the introduction of cutting planes in the master we discuss specific branching schemes and their effect on the structure of the column generation subproblem we give theoretical bounds on the complexity of the separation process and the extent of the modifications to the column generation subproblem our computational tests on the cutting stock problem and a generalisation the cutting strip problem show that in practice all fractional solutions can be eliminated using branching rules that preserve the tractability of the subproblem but there is a trade off between branching efficiency and subproblem tractability

extensions of positive projections and averaging operators abstract the main topic of the first section of this paper is the following theorem let e be a dedekind complete riesz space vector lattice and let a be a vector subspace of it which majorizes e if t is a positive projection on a then t can be extended to a positive projection on the whole of e in the second section we are concerned with a generalization of two theorems about contractive projections due to seever and kelley respectively for c0 x and huijsmans and de pagter for the more general case of an archimedean semiprime f algebra with the stone condition the theorems in question are the following if a is a majorizing sub algebra of an archimedean semiprime f algebra e then every positive contractive projection t in a satisfies the identity t a tb t ta tb for all a b a seever furthermore t is averaging if and only if the range of t is a subalgebra kelley moreover if there exists a riesz norm on a then both theorems hold without the assumption a majorizes e

u algebras and the hahn banach extension theorem an archimedean unital f algebra a is called a u algebra if for every a a there exists an invertible element u a such that a u a characterisations of a u algebra are established as an application an extension theorem of hahn banach type on modules over a u algebra and over the complexification of a dedekind complete unital f algebra is given

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

lp spaces with respect to conditional expectation on riesz spaces recently labuschagne and watson introduced the space l2 t for a conditional expectation t with natural domain a riesz space l1 t the main purpose of this paper is to carry on with this process by introducing and investigate the spaces lp t with p 1

polynomial diffeomorphisms of ii stable manifolds and recurrence f x y y y ax c the diffeomorphisms in this class have complicated dynamics in particular they have periodic points of infinitely many periods and positive topological entropy see fm s we can distinguish between these classes by considering the growth of the degrees of iterates of the diffeomorphism define deg f to be the maximum of the degrees of the coordinate functions this quantity is not a conjugacy invariant of f hence not a dynamical invariant we can construct a conjugacy invariant which we call the dynamical degree as follows

dynamics of transcendental henon maps the dynamics of transcendental functions in the complex plane has received a significant amount of attention in particular much is known about the description of fatou components besides the types of periodic fatou components that can occur for polynomials there also exist so called baker domains periodic components where all orbits converge to infinity as well as wandering domains in trying to find analogues of these one dimensional results it is not clear which higher dimensional transcendental maps to consider in this paper we find inspiration from the extensive work on the dynamics of complex henon maps we introduce the family of transcendental henon maps and study their dynamics emphasizing the description of fatou components we prove that the classification of the recurrent invariant fatou components is similar to that of polynomial henon maps and we give examples of baker domains and wandering domains

global constraints for round robin tournament scheduling abstract in the presence of side constraints and optimization criteria round robin tournament problems are hard combinatorial problems commonly tackled with tree search and branch and bound optimization recent results indicate that constraint based tree search has crucial advantages over integer programming based tree search for this problem domain by exploiting global constraint propagation algorithms during search in this paper we analyze arc consistent propagation algorithms for the global constraints all different and one factor in the domain of round robin tournaments the best propagation algorithms allow us to compute all feasible perfectly mirrored pattern sets with minimal breaks for intermural tournaments of realistic size and to improve known lower bounds for intramural tournaments balanced with respect to carry over effects

a simulated annealing and hill climbing algorithm for the traveling tournament problem abstract the traveling tournament problem ttp e easton g nemhauser m trick the traveling tournament problem description and benchmarks in proceedings of the 7th international conference on principles and practice of constraint programming cp 2001 2001 pp 580 584 m trick challenge traveling tournament problems 2004 schedules a double round robin tournament to minimize the total distance traveled by competing teams it involves issues of feasibility and optimality and is a challenge to constraint and integer programming in this work we divide the search space and use simulated annealing sa to search a timetable space and hill climbing to explore a team assignment space the sa component mutates timetables using conditional local jumps to find timetables which lead to better schedules while hill climbing is enhanced by pre computation and dynamic cost updating to provide fast and efficient search computational experiments using this hybrid approach on benchmark sets give results comparable to or better than current best known solutions

towards understanding the pierce birkhoff conjecture via mv algebras our main issue was to understand the connection between ukasiewicz logic with product and the pierce birkhoff conjecture and to express it in a mathematical way to do this we define the class of fmv algebras which are mv algebras endowed with an internal binary product and with a scalar product with scalars from 0 1 the proper quasi variety generated by 0 1 with both products interpreted as the real product provides the desired framework the normal form theorem of its corresponding logical system can be seen as a local version of the pierce birkhoff conjecture

logic based benders decomposition benders decomposition uses a strategy of learning from one s mistakes the aim of this paper is to extend this strategy to a much larger class of problems the key is to generalize the linear programming dual used in the classical method to an inference dual solution of the inference dual takes the form of a logical deduction that yields benders cuts the dual is therefore very different from other generalized duals that have been proposed the approach is illustrated by working out the details for propositional satisfiability and 0 1 programming problems computational tests are carried out for the latter but the most promising contribution of logic based benders may be to provide a framework for combining optimization and constraint programming methods

on orthomorphisms quasi orthomorphisms and quasi multipliers in this paper we introduce a new concept namely that of a quasi orthomorphism on a vector lattice which generalizes the notion of an orthomorphism we consider quasi multipliers on l algebras and establish the relationship between quasi orthomorphisms and quasi multipliers we prove that for certain banach algebras the quasi orthomorphisms qorth a form a dedekind complete banach f algebra with a multiplicative identity we conclude with a kakutani type representation theorem for qorth a

scheduling double round robin tournaments with divisional play using constraint programming abstract we study a tournament format that extends a traditional double round robin format with divisional single round robin tournaments elitserien the top swedish handball league uses such a format for its league schedule we present a constraint programming model that characterizes the general double round robin plus divisional single round robin format this integrated model allows scheduling to be performed in a single step as opposed to common multistep approaches that decompose scheduling into smaller problems and possibly miss optimal solutions in addition to general constraints we introduce elitserien specific requirements for its tournament these general and league specific constraints allow us to identify implicit and symmetry breaking properties that reduce the time to solution from hours to seconds a scalability study of the number of teams shows that our approach is reasonably fast for even larger league sizes the experimental evaluation of the integrated approach takes considerably less computational effort to schedule elitserien than does the previous decomposed approach

the isometry groups of manifolds and the automorphism groups of domains we prove that every compact lie group can be realized as the full automorphism group of a strictly pseudoconvex domain and as the full isometry group of a compact connected smooth riemannian manifold

a benders approach for the constrained minimum break problem this paper presents a hybrid ip cp algorithm for designing a double round robin schedule with a minimal number of breaks both mirrored and non mirrored schedules with and without place constraints are considered the algorithm uses benders cuts to obtain feasible home away pattern sets in few iterations and this approach leads to significant reductions in computation time for hard instances furthermore the algorithm is capable of solving a number of previously unsolved benchmark problems for the traveling tournament problem with constant distances

the order bidual of lattice ordered algebras abstract the main topic of the present paper is a systematic investigation of the second order dual a of an archimedean algebra a with point separating order dual a it is shown that in the case that a has a unit element the equality a a n holds where a n is the collection of all order continuous linear functionals on a it turns out that in general a n equipped with the arens multiplication is an algebra again necessary and sufficient conditions are derived for a n to be semiprime and for a n to have a unit element with respect to this multiplication

a branching scheme for finding cost minimal round robin tournaments abstract single round robin tournaments are a well known class of sports leagues schedules we consider leagues with a set t of n teams where n is even costs are associated to each possible match the goal is to find the minimum cost tournament among those having the minimum number of breaks we pick up structural properties of home away pattern sets having the minimum number of breaks a branching idea using these properties is developed in order to guide branching steps on the first levels of a branch and bound tree in order to avoid nodes corresponding to infeasible subproblems

an approximation algorithm for the bipartite traveling tournament problem the bipartite traveling tournament problem bttp is an np complete scheduling problem whose solution is a double round robin inter league tournament with minimum total travel distance the 2n team bttp is a variant of the well known traveling salesman problem tsp albeit much harder as it involves the simultaneous coordination of 2n teams playing a sequence of home and away games under fixed constraints rather than a single entity passing through the locations corresponding to the teams home venues as the bttp requires a distance optimal schedule linking venues in close proximity we provide an approximation algorithm for the bttp based on an approximate solution to the corresponding tsp we prove that our polynomial time algorithm generates a 2n team inter league tournament schedule whose total distance is at most 1 2c 3 3 c 3n times the total distance of the optimal bttp solution where c is the approximation factor of the tsp in practice the actual approximation factor is far better we provide a specific example by generating a nearly optimal inter league tournament for the 30 team national basketball association with total travel distance just 1 06 times the trivial theoretical lower bound

a note on symmetry reduction for circular traveling tournament problems abstract the traveling tournament problem ttp consists of finding a distance minimal double round robin tournament where the number of consecutive breaks is bounded easton et al 2001 introduced the so called circular ttp instances where venues of teams are located on a circle the distance between neighboring venues is one so that the distance between any pair of teams is the distance on the circle it is empirically proved that these instances are very hard to solve due to the inherent symmetry this note presents new ideas to cut off essentially identical parts of the solution space enumerative solution approaches e g relying on branch and bound benefit from this reduction we exemplify this benefit by modifying the dfs algorithm of uthus et al 2009 and show that speedups can approximate factor 4n

a new branch and price algorithm for the traveling tournament problem abstract the traveling tournament problem ttp consists of finding a distance minimal double round robin tournament where the number of consecutive breaks is bounded for solving the problem exactly we propose a new branch and price approach the starting point is a new compact formulation for the ttp the corresponding extensive formulation resulting from a dantzig wolfe decomposition is identical to one given by easton k nemhauser g trick m 2003 solving the traveling tournament problem a combined interger programming and constraint programming approach in burke e de causmaecker p eds practice and theory of automated timetabling iv volume 2740 of lecture notes in computer science springer verlag berlin heidelberg pp 100 109 who suggest to solve the tour generation subproblem by constraint programming in contrast to their approach our method explicitly utilizes the network structure of the compact formulation first the column generation subproblem is a shortest path problem with additional resource and task elementarity constraints we show that this problem can be reformulated as an ordinary shortest path problem over an expanded network and thus be solved much faster an exact variable elimination procedure then allows the reduction of the expanded networks while still guaranteeing optimality second the compact formulation gives rise to supplemental branching rules which are needed since existing rules do not ensure integrality in all cases third non repeater constraints are added dynamically to the master problem only when violated the result is a fast exact algorithm which improves many lower bounds of knowingly hard ttp instances from the literature for some instances solutions are proven optimal for the first time

orthogonal decompositions in hilbert a modules abstract pre hilbert a modules are a natural generalization of inner product spaces in which the scalars are allowed to be from an arbitrary algebra in this perspective submodules are the generalization of vector subspaces the notion of orthogonality generalizes in an obvious way too in this paper we focus on f algebras a that are either of l or of l 0 type we provide necessary and sufficient topological conditions for a submodule to be orthogonally complemented then we present four applications of our results the most important ones are doob s and kunita watanabe s decompositions for conditionally square integrable processes they are obtained as orthogonal decomposition results carried out in an opportune pre hilbert a module second we show that a version of stricker s lemma can be also derived as a corollary of our results finally we provide a version of the koopman von neumann decomposition theorem for a specific pre hilbert module which is useful in ergodic theory

complexity of the traveling tournament problem we consider the complexity of the traveling tournament problem which is a well known benchmark problem in tournament timetabling the problem was supposed to be computationally hard ever since its proposal in 2001 recently the first np completeness proof has been given for the variant of the problem were no constraints on the number of consecutive home games or away games of a team are considered the complexity of the original traveling tournament problem including these constraints however is still open in this paper we show that this variant of the problem is strongly np complete when the upper bound on the maximal number of consecutive away games is set to 3

a multi round generalization of the traveling tournament problem and its application to japanese baseball abstract in a double round robin tournament involving n teams every team plays 2 n 1 games with one home game and one away game against each of the other n 1 teams given a symmetric n by n matrix representing the distances between each pair of home cities the traveling tournament problem ttp seeks to construct an optimal schedule that minimizes the sum total of distances traveled by the n teams as they move from city to city subject to several natural constraints to ensure balance and fairness in the ttp the number of rounds is set at r 2 in this paper we generalize the ttp to multiple rounds r 2 k for any k 1 and present an algorithm that converts the problem to finding the shortest path in a directed graph enabling us to apply dijkstra s algorithm to generate the optimal multi round schedule we apply our shortest path algorithm to optimize the league schedules for nippon professional baseball npb in japan where two leagues of n 6 teams play 40 sets of three intra league games over r 8 rounds our optimal schedules for the pacific and central leagues achieve a 25 reduction in total traveling distance compared to the 2010 npb schedule implying the potential for considerable savings in terms of time money and greenhouse gas emissions

hilbert a modules abstract we consider real pre hilbert modules h on archimedean f algebras a with unit e we provide conditions on a and h such that a riesz representation theorem for bounded continuous a linear operators holds