a lindelof group with non lindelof square we show that the lindelof property of a topological group is not inherited by its square thus solving an old problem from 2 our construction introduces a new method to this area of mathematics and is of independent interest as it may have some further applications our method builds on ideas of 11 and techniques from 20 and give us also an optimal result about the partition properties on 1 1

antidiamond principles and topological applications we investigate some combinatorial statements that are strong enough to imply that fails hence the name antidiamonds yet most of them are also compatible with ch we prove that these axioms have many consequences in set theoretic topology including the consistency modulo large cardinals of a yes answer to a problem on linearly lindelof spaces posed by arhangel ski and buzyakova 1998

resonant suppression of turing patterns by periodic illumination we study the resonant behavior of turing pattern suppression in a model of the chlorine dioxide iodine malonic acid reaction with periodic illumination the results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system the resonance in turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force square wave on off periodic forcing is more effective in suppressing turing patterns than sinusoidal forcing we compare the dynamics of periodically forced turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns

first countable countably compact spaces and the continuum hypothesis we build a model of zfc ch in which every first countable countably compact space is either compact or contains a homeomorphic copy of 1 with the order topology the majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals our results generalize saharon shelah s iteration theorems appearing in chapters v and viii of proper and improper forcing 1998 as well as eisworth and roitman s 1999 iteration theorem we close the paper with a zfc example constructed using shelah s club guessing sequences that shows similar results do not hold for closed pre images of 2

a solution to the l space problem received by the editors january 8 2005 2000 mathematics subject classification primary 54d20 54d65 03e02 03e75 secondary 54f15

min max and min max regret versions of combinatorial optimization problems a survey abstract min max and min max regret criteria are commonly used to define robust solutions after motivating the use of these criteria we present general results then we survey complexity results for the min max and min max regret versions of some combinatorial optimization problems shortest path spanning tree assignment min cut min s t cut knapsack since most of these problems are np hard we also investigate the approximability of these problems furthermore we present algorithms to solve these problems to optimality

spatially periodic modulated rayleigh benard convection two dimensional thermal convection in a fluid layer between two rigid walls at different mean temperatures is investigated the top container boundary is undulated and the temperatures at the top and bottom boundaries are spatially periodic modulated with modulation wavelengths large compared to the thickness of the fluid layer the continuous translational invariance in the fluid layer is broken by these spatial modulations consequently phase differences between two periodic modulations give rise to an interesting drifting pattern with the drift direction depending on the sign of the relative phase between the modulations at distinguished ratios between the modulation wave numbers and relative phases the onset of convection changes as function of the modulation amplitudes from a stationary into an oscillatory one we call this phenomenon hopf bifurcation by frustrated drifts possible experiments are described in detail where this phenomenon can be expected textcopyright 1996 the american physical society

spatial synchronization of regular optical patterns we investigate an extended nonlinear optical experiment exhibiting the spontaneous formation of hexagonal patterns out of a stationary bifurcation the system is exposed to a two dimensional spatially periodic forcing namely static hexagonal patterns under variation of their spatial periodicity parameters are the strength of the forcing and the distance to pattern forming threshold the system response is quantitatively characterized with different methods we observe several locking regimes where the system is entrained by the forcing most of the locking regimes can be related to resonances between the different critical wave numbers and the forcing wave number or its spatial harmonics one particular locking appears to result from two of these simple resonances in a kind of generalized order m n synchronization the width of the locking regimes increases with forcing strength apparently representing a spatial analog of arnold tongues

the two stage assembly scheduling problem complexity and approximation this paper introduces a new two stage assembly scheduling problem there are m machines at the first stage each of which produces a component of a job when all m components are available a single assembly machine at the second stage completes the job the objective is to schedule jobs on the machines so that the makespan is minimized we show that the search for an optimal solution may be restricted to permutation schedules the problem is proved to be np hard in the strong sense even when m 2 a schedule associated with an arbitrary permutation of jobs is shown to provide a worst case ratio bound of two and a heuristic with a worst case ratio bound of 2 1 m is presented the compact vector summation technique is applied for finding approximation solutions with worst case absolute performance guarantees

malykhin s problem abstract we construct a model of zfc where every separable frechet topological group is metrizable this solves a 1978 problem of v i malykhin

short shop schedules we consider the open shop job shop and flow shop scheduling problems with integral processing times we give polynomial time algorithms to determine if an instance has a schedule of length at most 3 and show that deciding if there is a schedule of length at most 4 is x1d4a9 x1d4ab complete the latter result implies that unless x1d4ab x1d4a9 x1d4ab there does not exist a polynomial time approximation algorithm for any of these problems that constructs a schedule with length guaranteed to be strictly less than 5 4 times the optimal length this work constitutes the first nontrivial theoretical evidence that shop scheduling problems are hard to solve even approximately

ch with no ostaszewski spaces this is the published version also available here http dx doi org 10 1090 s0002 9947 99 02407 1 first published in trans amer math soc in 1999 published by the american mathematical society

a five element basis for the uncountable linear orders in this paper i will show that it is relatively consistent with the usual axioms of mathematics zfc together with a strong form of the axiom of infinity the existence of a supercompact cardinal that the class of uncountable linear orders has a five element basis in fact such a basis follows from the proper forcing axiom a strong form of the baire category theorem the elements are x o1 o 1 c c where x is any suborder of the reals of cardinality 1 and c is any countryman line this confirms a longstanding conjecture of shelah

stripe hexagon competition in forced pattern forming systems with broken up down symmetry we investigate the response of two dimensional pattern forming systems with a broken up down symmetry such as chemical reactions to spatially resonant forcing and propose related experiments the nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a 1 2 and 1 1 ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system both sets of coupled amplitude equations are derived by a perturbative method from the lengyel epstein model describing a chemical reaction showing turing patterns which gives us the opportunity to relate the generic response scenarios to a specific pattern forming system the nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence stability and coexistence is determined whereas without modulations hexagonal patterns are always preferred near onset of pattern formation single mode solutions stripes are favored close to threshold for modulation amplitudes beyond some critical value hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude furthermore depending on the modulation amplitude the transition between stripes and distorted hexagons is either subcritical or supercritical

sidewall forcing of hexagonal turing patterns rhombic patterns abstract rhombic arrays were obtained by sidewall forcing during turing pattern formation in numerical simulations locking between the frequency of forcing and the wave length between blobs was obtained in accordance with the farey sequence this locking appears as a perfect rhombic array oriented in the direction of the imposed forcing for a constant forcing in duration and amplitude the following scheme of bifurcation was observed parallel stripes rhombic array domains of hexagons and rhombi separated by penta hepta defects symmetry considerations based on a non uniform stretching along the x axis were used to describe these transitions unstable varicose vein stripes were observed to evolve during the temporal evolution arrays

on the approximability of robust spanning tree problems in this paper the minimum spanning tree problem with uncertain edge costs is discussed in order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution the min max min max regret and 2 stage min max versions of the problem are discussed the complexity and approximability of all these problems are explored it is proved that the min max and min max regret versions with nonnegative edge costs are hard to approximate within o log 1 en for any e 0 unless the problems in np have quasi polynomial time algorithms similarly the 2 stage min max problem cannot be approximated within o logn unless the problems in np have quasi polynomial time algorithms in this paper randomized lp based approximation algorithms with performance bound of o log 2n for min max and 2 stage min max problems are also proposed

long wave instability in optical parametric oscillators abstract we show that the full dynamical equations for optical parametric oscillators in a large aspect ratio cavity for the case of long wave instability is reduced to a ginzburg landau equation near the instability threshold this equation enables us to introduce the concept of optical vortices in 2 medium a criterion of supercritical and subcritical instability is given as well as a condition of the benjamin feir instability

linear sigma additivity and some applications we show that countable increasing unions preserve a large family of well studied covering properties which are not necessarily additive using this together with infinite combinatorial methods and simple forcing theoretic methods we explain several phenomena settle problems of just miller scheepers and szeptycki 1996 gruenhage and szeptycki 2005 tsaban and zdomskyy 2008 and tsaban 2006 2007 and construct topological groups with very strong combinatorial properties

normality in x2 for compact x in 1977 the second author announced the following consistent neg ative answer to a question of katetov assuming ma gh there is a compact nonmetric space x such that x1 is hereditarily normal we give the details of this example and construct another example assuming ch we show that both examples can be constructed so that x2 a is perfectly normal we also construct in zfc a compact nonperfectly normal x such that x2 a is nor mal in his classical paper k katetov showed that if x and y are infinite compact spaces and x x y is hereditarily normal then x and y are per fectly normal by sneider s theorem that a compact space with a gvdiagonal is metrizable s katetov concludes that if x is compact and x3 is heredi tarily normal then x is metrizable he asked if the same conclusion could be obtained assuming only that x2 is hereditarily normal in 1977 the second au thor obtained a counterexample assuming martin s axiom plus the negation of the continuum hypothesis ma ch this result was announced in ny and an outline of the proof appeared there although with many details omitted a complete proof appears in this paper for the first time we also construct a necessarily different as will be seen counterexample assuming ch since any counterexample must be perfectly normal it is probably not sur prising that our examples are related to alexandrov s double arrow space d 0 1 x 0 1 with the lexicographic order topology for it is in some sense the only known example in zfc of a compact perfectly normal nonmetrizable space see gi for a discussion of this the double arrow space has also been called the split interval because one can think of obtaining it by splitting each x 0 1 into two points x and x and putting the order topology on these points where x is declared to be less than x and otherwise the order is the natural one inherited by 0 1 now if a c 0 1 let d a be the same as above but with only the points of a split of course d a is just the quotient space of d obtained by identifying x with x for all x a if a is uncountable then d a is a compact perfectly normal nonmetrizable space

min max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty abstract we consider the min max regret version of a single machine scheduling problem to determine which jobs are processed by outsourcing under processing time uncertainty the performance measure is expressed as the total cost for processing some jobs in house and outsourcing the rest processing time uncertainty is described through two types of scenarios either an interval scenario or a discrete scenario the objective is to minimize the maximum deviation from optimality over all scenarios we show that when the cost for in house jobs is expressed as the makespan the problem with an interval scenario is polynomially solvable while the one with a discrete scenario is np hard thus for the discrete scenario case we develop a 2 approximation algorithm and investigate when the problem is polynomially solvable since the problem minimizing the total completion time as a performance measure for in house jobs is known to be np hard for both scenarios we consider the problem with a special structure for the processing time uncertainty and develop a polynomial time algorithm for both scenarios

zero subspaces of polynomials on l1 γ abstract we provide two examples of complex homogeneous quadratic polynomials p on banach spaces of the form l 1 the first polynomial p has both separable and nonseparable maximal zero subspaces the second polynomial p has the property that while the index set is not countable all zero subspaces of p are separable

space periodically driven codimension two bifurcations an amplitude equation is derived for a one dimensional extended dynamical system undergoing a codimension two bifurcation subjected to a weak near resonant spatially periodic forcing it is proved that in some appropriate limit the dynamics is of the propagative phase type and it is governed by the time dependent sine gordon equation with weak dissipation

complementation and decompositions in some weakly lindelof banach spaces abstract let denote an uncountable set we consider the questions if a banach space x of the form c k of a given class 1 has a complemented copy of c 0 or 2 for every c 0 x has a complemented c 0 e for an uncountable e or 3 has a decomposition x a b where both a and b are nonseparable the results concern a superclass of the class of nonmetrizable eberlein compacts namely k s such that c k is lindelof in the weak topology and we restrict our attention to k s scattered of countable height we show that the answers to all these questions for these c k s depend on additional combinatorial axioms which are independent of zfc ch if we assume the p ideal dichotomy for every c 0 c k there is a complemented c 0 e for an uncountable e which yields the positive answer to the remaining questions if we assume then we construct a nonseparable weakly lindelof c k for k of height 1 where every operator is of the form c i s for c r and s with separable range and conclude from this that there are no decompositions as above which yields the negative answer to all the above questions since in the case of a scattered compact k the weak topology on c k and the pointwise convergence topology coincide on bounded sets and so the lindelof properties of these two topologies are equivalent many results concern also the space c p k

makespan minimization in open shops a polynomial time approximation scheme in this paper we demonstrate the existence of a polynomial time approximation scheme for makespan minimization in the open shop scheduling problem with an arbitrary fixed numberm of machines for the variant of the problem where the number of machines is part of the input it is known that the existence of an approximation scheme would implyp np hence our result draws a precise separating line between approximable cases i e withm fixed and non approximable cases i e withm part of the input of this shop problem 1998 the mathematical programming society inc published by elsevier science b v

a c_0 saturated banach space with no long unconditional basic sequences we present a banach space mathfrak x with a schauder basis of length omega 1 which is saturated by copies of c 0 and such that for every closed decomposition of a closed subspace x x 0 oplus x 1 either x 0 or x 1 has to be separable this can be considered as the non separable counterpart of the notion of hereditarily indecomposable space indeed the subspaces of mathfrak x have few operators in the sense that every bounded operator t x rightarrow mathfrak x from a subspace x of mathfrak x into mathfrak x is the sum of a multiple of the inclusion and a omega 1 singular operator i e an operator s which is not an isomorphism on any non separable subspace of x we also show that while mathfrak x is not distortable being c 0 saturated it is arbitrarily omega 1 distortable in the sense that for every lambda 1 there is an equivalent norm cdot on mathfrak x such that for every non separable subspace x of mathfrak x there are x y in s x such that cdot cdot ge la

spatial forcing of spontaneous optical patterns a nonlinear optical system which spontaneously forms hexagonal patterns is exposed to a weak spatially modulated forcing as forcing stationary hexagonal patterns are used under variation of their transverse wave number in the experiment we observe a locking when the forcing wave number is close to one of the critical wave numbers of the unforced system outside the locking regimes forcing provokes spatiotemporal disorder the system response is characterized quantitatively with respect to its dynamics and to its spatial order

effects of parametric disorder on a stationary bifurcation abstract effects of a frozen random contribution to the control parameter are investigated in terms of the complex ginzburg landau equation with real coefficients the threshold of the bifurcation from the homogeneous basic state is reduced by a random contribution even with a vanishing spatial mean value as shown by three different approaches by a perturbation calculation by a self consistent iteration method and by a fully numerical solution of the linear part of the ginzburg landau equation for arbitrary random contributions the nonlinear stationary solutions are numerically determined and in the limit of small random amplitudes analytical expressions are derived in terms of two different perturbation expansions which cover already several related trends beyond threshold for instance the spatial modulations of the solutions increase with the noise amplitude but decrease with increasing distance from threshold

front explosion in a resonantly forced complex ginzburg landau system abstract periodically forced oscillatory reaction diffusion systems near the hopf bifurcation can be modeled by the resonantly forced complex ginzburg landau equation in the 3 1 resonant locking regime this equation has three stable fixed points corresponding to the phase locked states in the underlying reaction diffusion system phase fronts separate spatial domains containing the phase locked states when the ginzburg landau equation parameters lie in the benjamin feir unstable regime the phase fronts have a turbulent internal spatio temporal structure as the forcing intensity is changed the intrinsic width of a front grows until at a critical value the front explodes and the turbulent interfacial zone expands to fill the entire domain the scaling properties of this transition are explored and it is shown that front width and spatial and temporal correlations diverge as the critical forcing intensity is approached these results are compared with similar behavior seen in a coupled map model with period 3 local dynamics the prospects for observation of these phenomena in experiments on periodically forced reaction diffusion systems are discussed

transition from oscillatory to excitable regime in a system forced at three times its natural frequency the effect of a temporal modulation at three times the critical frequency on a hopf bifurcation is studied in the framework of amplitude equations we consider a complex ginzburg landau equation with an extra quadratic term resulting from the strong coupling between the external field and the unstable modes we show that by increasing the intensity of the forcing one passes from an oscillatory regime to an excitable one with three equivalent frequency locked states in the oscillatory regime topological defects are one armed phase spirals while in the excitable regime they correspond to three armed excitable amplitude spirals analytical results show that the transition between these two regimes occurs at a critical value of the forcing intensity the transition between phase and amplitude spirals is confirmed by numerical analysis and it might be observed in periodically forced reaction diffusion systems

linear subsets of nonlinear sets in topological vector spaces for the last decade there has been a generalized trend in mathematics on the search for large algebraic structures linear spaces closed subspaces or infinitely generated algebras composed of mathematical objects enjoying certain special properties this trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis operator theory summability theory polynomials in banach spaces hypercyclicity and chaos and general functional analysis this expository paper is devoted to providing an account on the advances and on the state of the art of this trend nowadays known as lineability and spaceability

transforming rectangles into squares with applications to strong colorings abstract it is proved that every singular cardinal admits a function rts 2 2 that transforms rectangles into squares namely for every cofinal subsets a b of there exists a cofinal subset c such that rts a b c c as a corollary we get that for every uncountable cardinal the classical negative partition relation 2 coincides with the following syntactically stronger statement there exists a function f 2 such that for every positive integer n every family a n of size of mutually disjoint sets and every coloring d n n there exist a b a with max a min b such that c a i b j d i j for all i j n

effects of an almost resonant spatial thermal modulation in the rayleigh benard problem quasiperiodic behaviour the authors consider the effect of prescribed spatially periodic temperatures at the bounding walls of a 2d boussinesq fluid on 1d pattern forming transitions they determine the normal form equation for the slowly varying pattern amplitude quasiperiodic behaviour is found when one takes into account the deviation of the external wavelength modulation from the critical value for the onset of classical rayleigh benard convection

approximating a two machine flow shop scheduling under discrete scenario uncertainty abstract this paper deals with the two machine permutation flow shop problem with uncertain data whose deterministic counterpart is known to be polynomially solvable in this paper it is assumed that job processing times are uncertain and they are specified as a discrete scenario set for this uncertainty representation the min max and min max regret criteria are adopted the min max regret version of the problem is known to be weakly np hard even for two processing time scenarios in this paper it is shown that the min max and min max regret versions of the problem are strongly np hard even for two scenarios furthermore the min max version admits a polynomial time approximation scheme if the number of scenarios is constant and it is approximable with performance ratio of 2 and not 4 3 approximable for any 0 unless p np if the number of scenarios is a part of the input on the other hand the min max regret version is not at all approximable even for two scenarios

a vector sum theorem and its application to improving flow shop guarantees we prove that if a closed polygonal path in rd consists of a finite number of line segments of at most unit length then it is possible to transpose the segments in such a way that the new polygonal path is contained in a ball of radius frac 3 2 d using this result we give a near optimal algorithm for the np complete flow shop problem the error of the algorithm cannot exceed a constant depending on the maximal execution time and the number of machines but not depending on the number of jobs our theorems improve earlier results of the same type by belov and stolin

minimizing makespan in a class of reentrant shops we study the problem of scheduling a chain reentrant shop in which each job goes for its processing first to a machine called the primary machine then to a number of other machines in a fixed sequence and finally back to the primary machine for its last operation the problem is to schedule the jobs so as to minimize the makespan this problem is unary np hard for a general number of machines we focus in particular on the two machine case that is also at least binary np hard we prove some properties that identify a specific class of optimal schedules and then use these properties in designing an approximation algorithm and a branch and bound type optimization algorithm the approximation algorithm of which we present three versions has a worst case performance guarantee of 3 2 along with an excellent empirical performance the optimization algorithm solves large instances quickly finally we identify a few well solvable special cases and present a pseudo polynomial algorithm for the case in which the first and the last operations of any job on the primary machine are identical

the flow shop problem with no idle constraints a review and approximation the makespan minimization problem in flow shops with no idle constraints on machines is considered the latter means that each machine once started must process all its operations without intermediate idle time until all those operations are completed the problem is known to be strongly np hard already for three machines while being based on a geometrical approach we propose several polynomial time heuristics for the general case and for special cases of 3 and 4 machines which provide asymptotically optimal solutions for the increasing number of jobs a comprehensive review of relevant results is also presented

a class of banach spaces with few non strictly singular operators we construct a family x of reflexive banach spaces with long countable as well as uncountable transfinite bases but with no unconditional basic sequences the method we introduce to achieve this allows us to considerably control the structure of subspaces of the resulting spaces as well as to precisely describe the corresponding spaces on non strictly singular operators for example for every pair of countable ordinals we are able to decompose every bounded linear operator from x to x as the sum of a diagonal operator and an strictly singular operator we also show that every finite dimensional subspace of any member x of our class can be moved by and 4 isomorphism to essentially any region of any other member x or our class finally we find subspaces x of x such that the operator space l x x is quite rich but any bounded operator t from x into x is a strictly singular pertubation of a scalar multiple of the identity

higher souslin trees and the gch revisited abstract it is proved that for every uncountable cardinal gch entails the existence of a cf complete souslin tree in particular if gch holds and there are no 2 souslin trees then 2 is weakly compact in godel s constructible universe improving gregory s 1976 lower bound furthermore it follows that if gch holds and there are no 2 and 3 souslin trees then the axiom of determinacy holds in l r

selective covering properties of product spaces ii spaces we study productive properties of spaces and their relation to other classic and modern selective covering properties among other things we prove the following results 1 solving a problem of f jordan we show that for every unbounded tower set x r of cardinality 1 the space cp x is productively frechet urysohn in particular the set x is productively 2 solving problems of scheepers and weiss and proving a conjecture of babinkostova scheepers we prove that assuming the continuum hypothesis there are spaces whose product is not even menger 3 solving a problem of scheepers tall we show that the properties and gerlits nagy are preserved by cohen forcing moreover every hurewicz space that remains hurewicz in a cohen extension must be rothberger and thus we apply our results to solve a large number of additional problems and use arhangel skiuo duality to obtain results concerning local properties of function spaces and countable topo logical groups

a banach space with a countable infinite number of complex structures abstract we give examples of real banach spaces with exactly infinite countably many complex structures and with 1 many complex structures

approximability of flow shop scheduling shop scheduling problems are notorious for their intractability both in theory and practice in this paper we construct a polynomial approximation scheme for the flow shop scheduling problem with an arbitrary fixed number of machines for the three common shop models open flow and job this result is the only known approximation scheme since none of the three models can be approximated arbitrarily closely in the general case unless p np the result demonstrates the approximability gap between the models in which the number of machines is fixed and those in which it is part of the input of the instance the result can be extended to flow shops with job release dates and delivery times and to flow shops with a fixed number of stages where the number of machines at any stage is fixed 1998 the mathematical programming society inc published by elsevier science b v

concurrent flowshop scheduling to minimize makespan abstract this paper considers the concurrent flowshop scheduling problem with the makespan objective function in this problem each job consists of several components each of which is processed on a dedicated flowshop equivalently each component requires a series of consecutive operations in a prespecified order as in the standard serial flowshop we assume that each component has the same number of indexed operations and that these operations must be processed in the same order for each component we first show that this problem is strongly np hard and then using compact vector summation techniques we construct schedules using a quadratic time heuristic with an absolute performance guarantee independent of the number of jobs this makes our schedules asymptotically optimal as the number of jobs becomes very large

translational and nontranslational motion of perturbed turing patterns when the front and rear boundaries of a turing pattern with nonzero flux boundary conditions move synchronously several modes of motion of the pattern are found traveling boundaries can be obtained experimentally by illuminating a turing unstable system through a moving mask consisting of a single dark stripe with a light intensity sufficient to suppress pattern formation all structured moving patterns belong to two general types smooth translation at low mask velocity v x and nontranslational hopping at intermediate v x at high v x turing patterns are unable to form and an unstructured striped image of the mask is seen when the mask width exceeds the turing wavelength bistability between different types of moving patterns can occur as v x is varied

partitioning pairs of countable ordinals on montre que les paires d ordinaux denombrables peuvent etre colorees avec une infinite non denombrable de couleurs de telle sorte que tout ensemble non denombrable contienne des paires de chaque couleur

synchronization and control of coupled ginzburg landau equations using local coupling in this paper we discuss the properties of a recently introduced coupling scheme for spatially extended systems based on local spatially averaged coupling signals see z tasev et al int j bifurcation chaos appl sci eng to be published and l junge et al int j bifurcation chaos appl sci eng 9 2265 1999 using the ginzburg landau model we performed an extensive numerical examination of this coupling scheme i e a complete scan through the relevant coupling parameters furthermore we demonstrate suppression and control of spatiotemporal chaos e g stabilizing the homogeneous steady state and spatially localized control as an application all model parameters of the ginzburg landau equation are estimated given only the local information of the system

minimizing the makespan in the 3 machine assembly type flowshop scheduling problem this paper considers minimizing the makespan in the 3 machine assembly type flowshop scheduling problem after problem formulation we present a proof to show that the general version of this problem is strongly np complete we then discuss a few polynomially solvable cases of the problem and present the solution algorithms next a branch and bound solution scheme is suggested finally three heuristics to find approximate solutions to the general problem are proposed and their error bounds are analyzed

if all normal moore spaces are metrizable then there is an inner model with a measurable cardinal this is the published version also available here http www dx doi org 10 1090 s0002 9947 1982 0664048 8 first published in trans amer math soc in 1982 published by the american mathematical society

pattern formation in diffusive advective coupled map lattices we investigate pattern formation and evolution in coupled map lattices when advection is incorporated inaddition to the usual diffusive term all patterns may be suitably grouped into ve classes three periodic supporting static patterns and traveling waves and two nonperiodic relative frequencies are determined as afunction of all model parameters diffusion advection local nonlinearity and lattice size advection plays animportant role in coupled map lattices being capable of considerably altering pattern evolution for instance advection may induce synchronization making chaotic patterns evolve periodically as a byproduct we de scribe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of travelingwaves doi 10 1103 physreve 69 066206 pacs number s 89 75 kd 05 45 xt 05 45 rai introduction

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

open block scheduling in optical communication networks in this paper the process of data transmission in star coupled optical communication networks is modelled as a shop type scheduling problem where channels wavelengths are treated as machines we formulate an open block problem with the minimum makespan objective o b cmax in which a relation of a new type between the operations of each job is introduced any two operations of a job have identical processing times and may be processed either simultaneously in a common block or alternatively at disjoint time intervals we show that the problem is polynomially solvable for 4 machines np hard for 6 machines and strongly np hard for a variable number of machines for the case of a variable number of machines we present a polynomial time 2 approximation algorithm and prove that there is no polynomial time approximation algorithm with 11 10 unless p np for the case when the number of machines is fixed we show that the problem admits a linear time ptas in addition we show that the two machine problem with release dates is np hard in the strong sense

empirical bifurcation analysis of optical pattern formation the experimental characterization of pattern forming bifurcations is difficult since the unstable solutions are generally not accessible in experiments in nonlinear optics a novel control scheme allows one to select and stabilize generic patterns and thus to track these solutions in parameter space this fourier space scheme is applied to a single feedback system and the amplitudes of roll square and hexagon patterns are determined experimentally even though the bifurcation is imperfect the coefficients of a prototype amplitude equation are recovered the coefficients show satisfactory agreement with theory and with numerical simulations which are performed for comparison the simulations also clarify the origin of the imperfect bifurcation in the experiment boundaries and speckles appear to have an unexpected strong influence

controlling and synchronizing space time chaos control and synchronization of continuous space extended systems is realized by means of a finite number of local tiny perturbations the perturbations are selected by an adaptive technique and they are able to restore each of the independent unstable patterns present within a space time chaotic regime as well as to synchronize two space time chaotic states the effectiveness of the method and the robustness against external noise is demonstrated for the amplitude and phase turbulent regimes of the one dimensional complex ginzburg landau equation the problem of the minimum number of local perturbations necessary to achieve control is discussed as compared with the number of independent spatial correlation lengths s1063 651x 99 00806 5 pacs number s 05 45 2a in the last decade control and synchronization of chaos have attracted the attention of the scientific community in both cases a chaotic dynamics is conveniently disturbed by means of an external perturbation usually small as compared with the unperturbed dynamics in order to force the appearence of a goal behavior g t compatible with the natural evolution of the system in the former case the goal dynamics corresponds to one unstable periodic orbit embedded within the chaotic attractor 1 in the latter case it corresponds to compensating for the difference of the same system due to different initial conditions since the first proposals for control 2 and synchronization 3 of chaos many other approaches have been sug

the minmax regret permutation flow shop problem with two jobs abstract we consider the makespan minimizing permutation flow shop problem with 2 jobs and m machines and uncertain processing times of operations for each operation an uncertainty interval is given and it is assumed that the processing time of each operation can take on any value from the corresponding uncertainty interval regardless of the values taken by processing times of other operations for the problem of finding a minmax regret solution we present an o m algorithm

forcing axioms and the continuum hypothesis woodin has demonstrated that in the presence of large cardinals there is a single model of zfc which is maximal for 2 sentences over the structure h 2 ns 1 in the sense that its h 2 ns 1 satisfies every 2 sentence for which h 2 ns 1 can be forced by set forcing in this paper we answer a question of woodin by showing that there are two 2 sentences over the structure h 2 1 which can each be forced to hold along with the continuum hypothesis but whose conjunction implies 2 aleph 0 2 aleph 1 in the process we establish that there are two preservation theorems for not introducing new real numbers by a countable support iterated forcing which cannot be subsumed into a single preservation theorem

multiphase patterns in periodically forced oscillatory systems periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency we study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency the 4 1 resonance these systems possess four coexisting stable states corresponding to uniform oscillations with successive phase shifts of pi 2 using an amplitude equation approach near a hopf bifurcation to uniform oscillations we study front solutions connecting different phase states these solutions divide into two groups pi fronts separating states with a phase shift of pi and pi 2 fronts separating states with a phase shift of pi 2 we find a type of front instability where a stationary pi front open quotes decomposes close quotes into a pair of traveling pi 2 fronts as the forcing strength is decreased the instability is degenerate for an amplitude equation with cubic nonlinearities at the instability point a continuous family of pair solutions exists consisting of pi 2 fronts separated by distances ranging from zero to infinity quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability we conjecture the existence of similar instabilities in higher 2n 1 resonances n 3 4 hor ellipsis where stationarymore pi fronts decompose into ital n traveling pi n fronts the instabilities designate transitions from stationary two phase patterns to traveling 2n phase patterns as an example we demonstrate with a numerical solution the collapse of a four phase spiral wave into a stationary two phase pattern as the forcing strength within the 4 1 resonance is increased copyright ital 1999 ital the american physical society less

katetov s problem in 1948 miroslav katetov showed that if the cube x 3 of a compact space x satisfies the separation axiom t 5 then x must be metrizable he asked whether x 3 can be replaced by x 2 in this metrization result in this note we prove the consistency of this implication

wavenumber locking and pattern formation in spatially forced systems we study wavenumber locking and pattern formation resulting from weak spatially periodic one dimensional forcing of two dimensional systems we consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes forcing at close to twice the pattern wavenumber selects stabilizes or creates resonant stripes locked at half the forcing wavenumber if the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns when the unforced system supports traveling waves resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves

two phase resonant patterns in forced oscillatory systems boundaries mechanisms and forms we use the forced complex ginzburg landau cgl equation to study resonance in oscillatory systems periodically forced at approximately twice the natural oscillation frequency the cgl equation has both resonant spatially uniform solutions and resonant two phase standing wave pattern solutions such as stripes or labyrinths the spatially uniform solutions form a tongueshaped region in the parameter plane of the forcing amplitude and frequency but the parameter range of resonant standing wave patterns does not coincide with the tongue of spatially uniform oscillations on one side of the tongue the boundary of resonant patterns is inside the tongue and is formed by the nonequilibrium ising bloch bifurcation and the instability to traveling waves on the other side of the tongue the resonant patterns extend outside the tongue forming a parameter region in which standing wave patterns are resonant but uniform oscillations are not the standing wave patterns in that region appear similar to those inside the tongue but the mechanism of their formation is different the formation mechanism is studied using a weakly nonlinear analysis near a hopf turing bifurcation the analysis also gives the existence and stability regions of the standing wave patterns outside the resonant tongue the analysis is supported by numerical solutions of the forced complex ginzburg landau equation 2004 elsevier b v all rights reserved

pointwise convergence of partial functions the gerlits nagy problem abstract for a set x r let b x r x denote the space of borel real valued functions on x with the topology inherited from the tychonoff product r x assume that for each countable a b x each f in the closure of a is in the closure of a under pointwise limits of sequences of partial functions we show that in this case b x is countably frechet urysohn that is each point in the closure of a countable set is a limit of a sequence of elements of that set this solves a problem of arnold miller the continuous version of this problem is equivalent to a notorious open problem of gerlits and nagy answering a question of salvador hernandez we show that the same result holds for the space of all baire class 1 functions on x we conjecture that in the general context the answer to the continuous version of this problem is negative but we identify a nontrivial context where the problem has a positive solution the proofs establish new local to global correspondences and use methods of infinite combinatorial topology including a new fusion result of francis jordan

the three machine proportionate open shop and mixed shop minimum makespan problems abstract we first consider the ordinary np hard three machine proportionate open shop minimum makespan o 3 prpt c max problem and show that it is solvable in o n log n time when certain conditions on the total machine load are met when these conditions are not met we derive an approximate solution by implementing the optimal solution for the o 3 prpt c max problem when the two longest jobs are of equal length in that case both absolute and ratio worst case bounds are derived we also consider the more general mixed shop problem m 3 prpt c max in which a given job subset must be processed as in a flow shop while the remaining jobs can be processed as in the o 3 prpt c max problem we show that our open shop solution techniques can be implemented to derive exact and approximate solutions for the m 3 prpt c max problem finally we discuss the applicability of our open shop results to the proportionate open shop problem with unequal machine speeds

a travelling salesman approach to solve the f no idle cmax problem this paper investigates the f no idle cmax problem where machines work continuously without idle time intervals the idle characteristic is a very strong constraint and it affects seriously the value of cmax criterion we treat here only the permutation flow shop configuration for machine no idle problems with the objective to minimise the makespan based on the idea that this problem can be modelled as a travelling salesman problem an adaptation of the well known nearest insertion rule is proposed to solve it a computational study shows the result quality

generalized synchronization of spatiotemporal chemical chaos we report the synchronization of two spatially extended chemical systems in one spatial dimension under appropriate parameter conditions the model systems exhibit a transition to turbulence via backfiring of pulses by implementing continuous control to the underlying partial differential equations synchronization is achieved not only for identical systems but also for systems operating under unequal parameter values exhibiting different dynamical behavior using this technique spatiotemporal chaos turbulence can be suppressed maintained or even enhanced depending on the dynamical behavior of the drive system this could possibly be of relevance to biological systems where in certain situations the emergence of chaos is undesirable while under different circumstances the loss of the chaotic dynamics is undesirable epileptic seizures

regressive partition relations for infinite cardinals the regressive partition relation which turns out to be important in incompleteness phenomena is completely characterized in the transfinite case this work is related to schmerl si whose characterizations we complete regressive functions arise naturally in the study of infinite cardinals from fodor s well known lemma to contexts involving large cardinals for example the n subtle cardinals of baumgartner b2 in kanamori and mcaloon km a regressive function version of the theorem of erd6s and rado er on canonical partitions was miniaturized and shown to be independent of peano arithmetic this result in turn reverberated to the infinite context to raise new questions here we completely characterize the corresponding partition symbol for infinite cardinals in contrast to the erdos rado theorem for the ordinary partition symbol we show that these partition relations actually provide a characterization of cardinals in the finite mahlo hierarchy thus just as with the finite miniaturization an elementary combinatorial property leads to a necessary transcendence our work confirms some speculations in mcaloon m where an infinitary analogue of the paris harrington partition relation is considered after we had already established some characterizations we became aware of the close relationship of this work to the results of schmerl s the third author then saw how to sharpen the characterization of schmerl s property as well as ours and this paper is written so as to approach these optimal results most directly the sharpening uses ideas of todorcevic t who noted that our 3 4 for n 0 can be derived directly from his work in 1 we begin the study of our partition symbol and establish the straightforward positive results about mahlo cardinals in 2 we develop some technical formulations and lemmata finally we apply this work in 3 to establish the optimal results on the necessity of mahlo cardinals we discuss the connections with schmerl s at the end we would like to thank jim schmerl for several expository suggestions particularly for providing the statement of 3 3 1 preliminaries we first formulate the regressive partition symbol let x be a set of ordinals and n a natural number if f is a function with domain xi n we write f ao an 1 for f ao an 1 with the understanding that ao k n 1 such a function is called regressive if f a0o an i ao received by the editors december 26 1985 1980 mathematics subject classification 1985 revision primary 03e05 secondary 03e55

symmetry breaking hopf bifurcation in anisotropic systems abstract symmetry breaking hopf bifurcation from a spatially uniform steady state of a spatially extended anisotropic system is considered this work is motivated by the experimental observation of a hopf bifurcation to oblique traveling rolls in electrohydrodynamic convection in planarly aligned nematic liquid crystals symmetry forces four traveling rolls to lose stability simultaneously four coupled complex ordinary differential equations describing the nonlinear interaction of the traveling rolls are analyzed using methods of equivariant bifurcation theory six branches of periodic solutions always bifurcate from the trivial state at the hopf bifurcation these correspond to traveling and standing wave patterns in an open region of coefficient space there is a primary bifurcation to a quasiperiodic standing wave solution the hopf bifurcation can also lead directly to an aperiodic attractor in the form of an asymptotically stable structurally stable heteroclinic cycle the theory is applied to a model for the transition from normal to oblique traveling rolls

forcing axioms and stationary sets is stationary in general if x is any class of posets the forcing axioms xfa and xfa are obtained by replacing semi proper ly by 9 e x in the above definitions sometimes we denote these axioms by fa x and fa x thus for example fa ccc is the familiar martin s axiom man the notion of semi proper as an extension of a previous notion of proper was defined and extensively studied by shelah in shl j these forcing notions generalize ccc and countably closed forcing and can be iterated without collapsing n spfa is implicit in shl as an obvious strengthening of the proper forcing axiom pfa previously formulated and proved consistent by baumgartner see bal del pfa had settled many combinatorial questions on the uncountable and spfa was not

on the complexity of a class of combinatorial optimization problems with uncertainty we consider a robust minmax regret version of the problem of selecting p elements of minimum total weight out of a set of m elements with uncertainty in weights of the elements we present a polynomial algorithm with the order of complexity o min p m p 2m for the case where uncertainty is represented by means of interval estimates for the weights we show that the problem is np hard in the case of an arbitrary finite set of possible scenarios even if there are only two possible scenarios this is the first known example of a robust combinatorial optimization problem that is np hard in the case of scenario represented uncertainty but is polynomially solvable in the case of the interval representation of uncertainty

vector summation in banach space and polynomial algorithms for flow shops and open shops we consider the flow shop and the open shop problems with m machines and n jobs m is the total processing time of the most loaded machine t is the maximum operation length two functions are defined m is the minimum number such that the optimum of any flow shop is at most m m t m is the minimum number for which the inequality m m t ensures that the optimum of the open shop is equal to m upper and lower bounds for functions m and m are derived and two polynomial algorithms are suggested the first one delivers an optimal schedule of an open shop provided m m t for some function m m the second one computes a near optimal approximation schedule of a flow shop both algorithms are based on a vector summation algorithm in m dimensional banach space