unbounded perturbation of the exponential dichotomy for evolution equations abstract in this paper we prove that the exponential dichotomy for evolution equations in banach spaces is not destroyed if we perturb the equation by small unbounded linear operator this is done by employing a skew product semiflow technique and a perturbation principle from linear operator theory finally we apply these results to partial parabolic equations and functional differential equations

a generalization of polyak s convergence result for subgradient optimization this paper generalizes a practical convergence result first presented by polyak this new result presents a theoretical justification for the step size which has been successfully used in several specialized algorithms which incorporate the subgradient optimization approach

some e optimal designs for the one way and two way elimination of heterogeneity summary in exploratory experiments aimed at providing as much information as possible on the effects of the treatments being studied and where heterogeneity needs to be eliminated in one or two directions use of an equally replicated block or row column design may mean wasting some of the available experimental units in this paper we prove the e optimality of several different types of block and row column designs that have unequally replicated treatments such unequally replicated designs can maximize the information on treat ment effects without wasting units block designs are used for experiments where it is important to eliminate heterogeneity in one direction those considered here have v treatments arranged in b blocks containing k experimental units each the structure of any such block design is determined by its v x b incidence matrix whose i j th entry gives the number of times treatment i occurs in block j in many experimental situations the position that an experimental unit occupies within a block can also affect observed responses when this happens row column designs can often be used to eliminate heterogeneity in two directions the row column designs considered here have bk experimental units arranged in a rectangular array of b columns and k rows such that each unit receives only one of the v treatments being studied we say that a block or row column design is equally replicated if each treatment is replicated the same number of times and otherwise unequally replicated this paper gives some optimal block and row column designs which can be used where equal replication is impossible if all the available experimental material is to be used let d denote an arbitrary row column design such as is described above observations ymnp obtained after applying the mth treatment to the unit occurring in the nth column and pth row are assumed to follow the usual three way additive model i e

an extension of some theorems of l barreira and c valls for the nonuniform exponential dichotomous evolution operators abstract the aim of this paper is to study the connection between the non uniform exponential dichotomy of a non uniform exponentially bounded strongly continuous evolution family and the admissibility of some function spaces thus there are extended recent results established by l barreira and c valls 2010 2011 in 10 and 11

decomposition tables for experiments ii two one randomizations we investigate structure for pairs of randomizations that do not follow each other in a chain these are unrandomized inclusive independent coincident or double randomizations this involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment we show how to establish the decomposition table giving the sources of variation their relationships and their degrees of freedom so that competing designs can be evaluated this leads to recommendations for when the different types of multiple randomization should be used

the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

stability radius and internal versus external stability in banach spaces an evolution semigroup approach in this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems these include autonomous and nonautonomous systems modeled with unbounded state space operators acting on banach spaces this approach allows one to apply the classical theory of strongly continuous semigroups to time varying systems in particular the complex stability radius may be expressed explicitly in terms of the generator of an evolution semigroup examples are given to show that classical formulas for the stability radius of an autonomous hilbert space system fail in more general settings upper and lower bounds on the stability radius are proven for banach space systems in addition it is shown that the theory of evolution semigroups allows for a straightforward operator theoretic analysis of internal stability as determined by classical frequency domain and input output operators even for nonautonomous banach space systems in particular for the nonautonomous setting internal stability is shown to be equivalent to input output stability for stabilizable and detectable systems for the autonomous setting an explicit formula for the norm of input output operator is given

existence and roughness of the exponential dichotomy for skew product semiflow in banach spaces abstract in this paper we introduce a concept of exponential dichotomy for skew product semiflow in infinite dimensional banach spaces which is an extension of the classic concept for evolution operators this concept is used to study the roughness property of the skew product semiflow also we introduce the concept of discrete skew product and give a necessary and sufficient condition for this discrete skew product to have a discrete dichotomy after that we give necessary and sufficient conditions for the existence of exponential dichotomy for skew product semiflow moreover we prove that the exponential dichotomy for skew product semiflow is not destroyed by small perturbation finally we apply these results to parabolic partial differential equations and functional differential equations

on the design of experiments under spatial correlation on considere tout d abord le cas ou les effets du traitement sont estimes par les moindres carres on considere ensuite le cas ou l analyse a utiliser est les moindres carres generalises utilisant une matrice de correlation connue

optimal design with many blocking factors designs for sets of experimental units with many blocking factors are studied it is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form in consequence a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest in a sense which is made precise in the paper this encompasses several previous results for optimal designs with more than one blocking factor and applications to many other situations are given

rectangular lattice designs efficiency factors and analysis rectangular lattice designs are shown to be generally balanced with respect to a particular decomposition of the treatment space efficiency factors are calculated and the analysis including recovery of interblock information is outlined the ideas are extended to rectangular lattice designs with an extra blocking factor

some minimum variance block designs for estimating treatment differences summary in this paper we consider experimental settings requiring usage of a block design in which v treatments are to be tested in b blocks of size k a block design is called mv optimal in such a setting if the maximal variance with which it estimates elementary treatment differences is minimal among all available designs mv optimal designs are particularly useful in exploratory experiments where as much information as possible is desired on the effects of all treatments being studied some sufficient conditions are derived which can be used to establish the mv optimality of certain types of generalized group divisible designs as defined in jacroux 1982 and some easy methods for constructing such mv optimal designs are given

simultaneous lotsizing and scheduling by combining local search with dual reoptimization abstract the contribution of this paper is twofold on the one hand the particular problem of integrating lotsizing and scheduling of several products on a single capacitated production line is modelled and solved taking into account sequence dependent setup times thereby continuous lotsizes meeting deterministic dynamic demands are to be determined and scheduled with the objective of minimizing inventory holding costs and sequence dependent setup costs on the other hand a new general algorithmic approach is presented a dual reoptimization algorithm is combined with a local search heuristic for solving a mixed integer programming problem this idea is applied to the above lotsizing and scheduling problem by embedding a dual network flow algorithm into threshold accepting and simulated annealing respectively computational tests show the effectiveness of the new solution method

reoptimization procedures for bounded variable primal simplex network algorithms abstract many algorithms and applications call for the use of a network subprogram which must be optimized numerous times with slight changes to the problem data bound and right hand side changes to an existing basis tree may yield an infeasible basic solution this report gives a sequence of steps that modify an existing basic solution to reflect such changes and streamline the reoptimization process

optimality of partial geometric designs we find a sufficient condition on the spectrum of a partial geometric design d such that when d satisfies this condition it is better with respect to all convex decreasing optimality criteria than all unequally replicated designs binary or not with the same parameters b v k as d combining this with existing results we obtain the following results i for any q ge 3 a linked block design with parameters b q2 v q2 q k q2 1 is optimal with respect to all convex decreasing optimality criteria in the unrestricted class of all connected designs with the same parameters ii a large class of strongly regular graph designs are optimal w r t all type 1 optimality criteria in the class of all binary designs with the given parameters for instance all connected singular group divisible gd designs with lambda 1 lambda 2 1 with one possible exception and many semiregular gd designs satisfy this optimality property specializing these general ideas to the a criterion we find a large class of linked block designs which are a optimal in the un restricted class we find an even larger class of regular partial geometric designs including for instance the complements of a large number of partial geometries which are a optimal among all binary designs

admissibility for nonuniform exponential contractions abstract we study the relation between the notions of nonuniform exponential stability and admissibility in particular using appropriate adapted norms which can be seen as lyapunov norms we show that if any of their associated l p spaces with p 1 is admissible for a given evolution process then this process is a nonuniform exponential contraction we also provide a collection of admissible banach spaces for any given nonuniform exponential contraction

optimality criteria for regression models based on predicted variance in the context of nonlinear regression models a new class of optimum design criteria is developed and illustrated this new class termed i l optimality is analogous to kiefer s k criterion but is based on predicted variance whereas kiefer s class is based on the eigenvalues of the information matrix i l optimal designs are invariant with respect to different parameterisations of the model and contain g and d optimality as special cases we provide a general equivalence theorem which is used to obtain and verify i l optimal designs the method is illustrated by various examples

new conditions for non uniform behaviour of linear cocycles over flows abstract we give a characterization of tempered exponential dichotomies for linear cocycles over flows in terms of the spectral properties of certain linear operators we consider noninvertible linear cocycles acting on infinite dimensional spaces and our approach avoids the use of lyapunov norms finally we apply obtained results to give new conditions for uniform exponential stability of linear cocycles

optimal two period repeated measurement designs with two or more treatments summary for two period repeated measurement designs for comparing t 2 treatments we discuss universally optimal designs when the number of subjects n is a multiple of t2 and some cases when n is a multiple of t we examine efficiencies of balanced designs and other symmetric designs relative to strongly balanced designs in addition efficiencies of the universally optimal designs obtained by hedayat zhao 1990 are examined under both fixed subject and random subject effect model assumptions

dual algorithms for pure network problems this paper reports the development of a new algorithmic implementation of the dual algorithm for the capacitated minimum cost network flow problem furthermore it introduces dual reoptimization procedures and compares primal and dual algorithms for the optimization and reoptimization of network problems the implementation makes use of cut sets for the efficient execution of the entering variable selection and the selection of the leaving variable is tied to the basis structure at an iteration empirical testing of the dual algorithm for optimization shows that it dominates the primal procedure for assignment problems with 400 nodes transportation problems with more than 600 nodes and transshipment problems with more than 1500 nodes computational testing with typical changes found in decomposition and relaxation procedures indicates the superiority of dual reoptimization over primal reoptimization for a sequence of parametric changes as would be typical in large scale programming techniques on the

optimal nested row column designs with specified components we consider nested row column designs where each of the row and column component designs is specified for the case that each of the component designs has second order balance we define such a nested row column design to be special if it is generally balanced with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components we show that if any special row column design exists then it is a optimal over all nested row column designs with the given components

optimal blocking of two level factorial designs summary blocking of two level factorial designs is considered for block sizes 2 and 4 using the method of fractional partial confounding a d and e optimal designs are obtained for block size 2 within the class of orthogonal designs for which main effects and two factor interactions are all orthogonal to each other before allowing for blocking a d and e optimal designs are obtained for block size 4 within the class of orthogonal designs with main effects orthogonal to blocks the designs obtained also have other favourable properties including orthogonal estimation of effects and orthogonality to superblocks

lp r x lq r x admissibility and exponential dichotomies of cocycles we analyze the existence of eventually no past exponential and ordinary dichotomies of an exponentially bounded strongly continuous cocycle t t r over a continuous semiflow our main tool is the lp r x lq r x admissibility condition i e there exist p q 1 p q 1 such that for each input f lp r x and there exists x x such that the output u x f r x u t x f t x 0t s t s f s ds belongs to lq r x we prove that the above admissibility condition implies that the output is bounded above by the input but nonuniformly with respect to requiring that the boundedness to be uniform with respect to we prove that the above admissibility condition assures the existence of a no past exponential dichotomy for t t r variants for ordinary dichotomy and also complete characterizations for the exponential dichotomy of cocycles are obtained it is worth to note that we involve a concept of a no past exponential dichotomy for cocycles weaker than the well known concept defined by sacker and sell 1994 33 our definition of exponential dichotomy follows partially the definition given in chow and leiva 1996 2 in the sense that we allow the unstable subspace to have infinite dimension the main difference is that we do not assume a priori that the cocycle is invertible on the unstable space actually we do not even assume that the unstable space is invariant under the cocycle thus we generalize some known results due to perron 1930 23 daleckij and krein 1974 6 massera and schaffer 1966 14 nguyen van minh rabiger and r schnaubelt 1998 18

network simplex algorithm for the general equal flow problem abstract in this paper the general equal flow problem is considered this is a minimum cost network flow problem with additional side constraints requiring the flow of arcs in some given sets of arcs to take on the same value this model can be applied to approach water resource system management problems or multiperiod logistic problems in general involving policy restrictions which require some arcs to carry the same amount of flow through the given study period although the bases of the general equal flow problem are no longer spanning trees it is possible to recognize a similar structure that allows us to take advantage of the practical computational capabilities of network models after characterizing the bases of the problem as good r 1 forests a simplex primal algorithm is developed that exploits the network structure of the problem and requires only slight modifications of the well known network simplex algorithm

some optimal designs for repeated measurements with autoregressive errors summary a number of individuals are observed at equally spaced time points different individuals behave independently but the observations on the same individual have the autocorrelation structure of a first order autoregressive process we are concerned with the optimal allocation of treatments assuming that at each time point a new selection must be made conditions for optimality are given for models without nuisance parameters and also with covariates and with block effects

the equal flow problem abstract this paper presents a new algorithm for the solution of a network problem with equal flow side constraints the solution technique is motivated by the desire to exploit the special structure of the side constraints and to maintain as much of the characteristics of pure network problems as possible the proposed algorithm makes use of lagrangean relaxation to obtain a lower bound and decomposition by right hand side allocation to obtain upper bounds the lagrangean dual serves not only to provide a lower bound used to assist in termination criteria for the upper bound but also allows an initial allocation of equal flows for the upper bound the algorithm has been tested on problems with up to 1500 nodes and 6000 arcs computational experience indicates that solutions whose objective function value is well within 1 of the optimum can be obtained in 1 65 of the mpsx time depending on the amount of imbalance inherent in the problem incumbent integer solutions which are within 99 99 feasible and well within 1 of the proven lower bound are obtained in a straightforward manner requiring on the average 30 of the mpsx time required to obtain a linear optimum

algorithms for the simple equal flow problem the minimum cost flow problem is to determine a least cost shipment of a commodity through a network g n a in order to satisfy demands at certain nodes from available supplies at other nodes in this paper we study a variant of the minimum cost flow problem where we are given a set math not displayed of arcs and require that each arc in r must carry the same amount of flow this problem which we call the simple equal flow problem arose while modeling a water resource system management in sardinia italy we consider the simple equal flow problem in a directed network with n nodes m arcs and where all arc capacities and node supplies are integer and bounded by u we develop several algorithms for the simple equal flow problem the network simplex algorithm the parametric simplex algorithm the combinatorial parametric algorithm the binary search algorithm and the capacity scaling algorithm the binary search algorithm solves the simple equal flow problem in o log nu applications of any minimum cost flow algorithm the capacity scaling algorithm solves it in o m m n log n log nu time which is almost the same time needed to solve the minimum cost flow problem by the capacity scaling algorithm these algorithms can be easily modified to obtain an integer solution of the simple equal flow problem

nested youden square designs summary youden square designs nested in two or three blocks are discussed these designs are useful in experimental settings with scarce materials involving many treatments

optimal additions to and deletions from two level orthogonal arrays summary consider the problem of selecting a two level factorial design it is well known that two level orthogonal arrays of strength 4 or more with e extra runs have various optimality properties including generalized cheng type 1 optimality when e 1 restricted cheng type 1 optimality when e 2 and e optimality when 3e5 more general schur optimality results are derived for more general values of e within the more restricted class of augmented two level orthogonal arrays similar results are derived for the class of orthogonal arrays with deletions examples are used to illustrate the results and in many cases the designs are confirmed to be optimal across all two level designs

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

optimum continuous block designs the incidence matrix of a block design is replaced by a normalized version n in which the entries are non negative numbers whose sum is unity the so called c matrix the information matrix for estimation of treatment contrasts is similarly replaced by the normalized analogue c n we study the set of ordered eigenvalues of all c n and give a complete specification for three treatments rows for any number of treatments we characterize the eigenvalues of an important subclass of designs for which the non zero entries in any given block are equal it is suggested that the natural ordering between designs is upper weak majorization of the eigenvalues using this we show how to improve a given n matrix and this leads to several optimality statements

resolvable designs with large blocks resolvable designs with two blocks per replicate are studied from an optimality perspective because in practice the number of replicates is typically less than the number of treatments arguments can be based on the dual of the information matrix and consequently in terms of block concurrences equalizing block concurrences for given block sizes is often but not always the best strategy sufficient conditions are established for various strong optimalities and a detailed study of e optimality offered including a characterization of the e optimal class optimal designs are found to correspond to balanced arrays and an affine like generalization

bayes d optimal and e optimal block designs summary bayes designs are considered for a two way analysis of variance model with a normal prior for treatments and blocks one of the treatments acting as a control the existence of an optimal allocation is proved for each bayesian optimality criterion i e each criterion defined on the posterior covariance matrix for the treatments under a special assumption on the treatment prior the structure of the optimal design is specified for the case of only one test treatment such a design is universally optimal bayes d and e optimal designs are found as special cases and results are compared with classical ones two examples are included

dichotomies for linear evolutionary equations in banach spaces abstract in this paper we present a characterization for the existence of an exponential dichotomy for a linear evolutionary system on a banach space the theory we present here applies to general time varying linear equations in banach spaces as a result it gives a description of the behavior of the nonlinear dynamics generated by certain nonlinear evolutionary equations in the vicinity of a compact invariant set in the case of dissipative systems our theory applies to the study of the flow in the vicinity of the global attractor the theory formulated here holds for linear evolutionary systems which are uniformly contracting and applies to the study of the linearization of nonlinear equations of the following type a parabolic pdes including systems of reaction diffusion equations and the navier stokes equations b hyperbolic pdes including the nonlinear wave equation and the nonlinear schrodinger equation with dissipation c retarded differential equations and d certain neutral differential delay equations

algorithms for network piecewise linear programs a comparative study abstract piecewise linear programming plp is an important area of mathematical programming and concerns the minimisation of a convex separable piecewise linear objective function subject to linear constraints in this paper a subarea of plp called network piecewise linear programming nplp is explored the paper presents four specialised algorithms for nplp strongly feasible primal simplex dual method out of kilter and strongly polynomial cost scaling and their relative efficiency is studied a statistically designed experiment is used to perform a computational comparison of the algorithms the response variable observed in the experiment is the cpu time to solve randomly generated network piecewise linear problems classified according to problem class transportation transshipment and circulation problem size extent of capacitation and number of breakpoints per arc results and conclusions on performance of the algorithms are reported

evolution semigroups translation algebras and exponential dichotomy of cocycles abstract we study the exponential dichotomy of an exponentially bounded strongly continuous cocycle over a continuous flow on a locally compact metric space acting on a banach space x our main tool is the associated evolution semigroup on c 0 x we prove that the cocycle has exponential dichotomy if and only if the evolution semigroup is hyperbolic if and only if the imaginary axis is contained in the resolvent set of the generator of the evolution semigroup to show the latter equivalence we establish the spectral mapping annular hull theorem for the evolution semigroup in addition dichotomy is characterized in terms of the hyperbolicity of a family of weighted shift operators defined on c 0 z x here we develop banach algebra techniques and study weighted translation algebras that contain the evolution operators these results imply that dichotomy persists under small perturbations of the cocycle and of the underlying compact metric space also exponential dichotomy follows from pointwise discrete dichotomies with uniform constants finally we extend to our situation the classical perron theorem which says that dichotomy is equivalent to the existence and uniqueness of bounded continuous mild solutions to the inhomogeneous equation

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

approximate model spaces for model robust experiment design optimal designs depend upon a prespecified model form a popular and effective model robust alternative is to design with respect to a set of models instead of just one however model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible here we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set we build our procedure on a restricted columnwise pairwise algorithm and explore its effectiveness for two model spaces in the literature for smaller full model spaces we find that the designs constructed with the new method compare favorably with robust designs that use the full model space with construction times reduced by orders of magnitude we also construct designs that heretofore have been unobtainable due to the size of their model spaces supplementary material available online

a mean squared error criterion for the design of experiments in estimating a response surface over a design region of interest mean squared error can arise both from sampling variance and bias introduced by model inadequacy the criterion adopted here for experimental design attempts to protect against bias resulting from a large class of deviations from the assumed model two algorithms are proposed for the construction of either approximate or exact designs and an example is given

schaffer spaces and exponential dichotomy for evolutionary processes a very general characterization of exponential dichotomy for evolutionary processes in terms of the admissibility of some pair of spaces which are translation invariant the so called schaffer spaces is given it includes as particular cases many interesting situations among which we note the results obtained by n van minh f rabiger and r schnaubelt and the authors concerning the connections between admissibility and dichotomy

optimal semi latin squares with side six and block size two an n x n k semi latin square is like an n n latin square except that there are k letters in each cell each of the nk letters occurs once in each row and once in each column designs for experiments are assessed according to the statistical concept of efficiency factor a high efficiency factor corresponds to low variances of within block estimators there are four widely used measures of the efficiency factor of a design for each any design which maximizes the value of the efficiency factor among a given class of designs is said to be optimal in that class previous theory gives optimal semi latin squares for various values of k for all values of n except for n 6 in this paper we therefore examine 6 x 6 2 semi latin squares we restrict attention to those semi latin squares whose quotient block designs are regular graph designs because a plausible and widely believed conjecture is that optimal regular graph designs are optimal overall for each of the four measures of efficiency factor we find the optimal 6 6 2 semi latin square among regular graph semi latin squares of that size

obtaining a good primal solution to the uncapacitated transportation problem abstract sharma and sharma european journal of operational research 122 3 2000 37 have given a new procedure to solve the dual of the well known uncapacitated transportation problem this is expected to enhance the performance of dual based optimizing algorithms for solving the transportation problems in this paper we give a heuristic that obtains a very good starting solution with a duality gap of less than 2 for the primal transportation problem in o n 3 time and this is expected to enhance the performance of network simplex algorithm that obtains the optimal solution and runs in o n 3 log n time empirical investigation revealed that our heuristic gave significantly better solutions than the well known vogel s approximation method that runs in o n 2 time

model robust response surface designs scaling two level factorials summary response surface methods use simple graduating functions to study the relationship between an experimental response variable and a set of continuous explanatory variables in designing a response surface study an experimenter must decide how far apart to set the levels of each factor i e how to scale the design a good choice should be sensitive to the fact that the graduating function is only an approximation to the true response function a bayesian model is proposed that makes explicit assumptions about the inadequacy of an assumed model and a design criterion based on the model leads to reasonable choices of scale for two level factorial designs the choice of scale is found to be insensitive to the prior distributions in the model

evolutionary semigroups and dichotomy of linear skew product flows on locally compact spaces with banach fibers abstract we study evolutionary semigroups generated by a strongly continuous semi cocycle over a locally compact metric space acting on banach fibers this setting simultaneously covers evolutionary semigroups arising from non autonomous abstract cauchy problems and c 0 semigroups and linear skew product flows the spectral mapping theorem for these semigroups is proved the hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew product flow to this end a banach algebra of weighted composition operators is studied the results are applied in the study of roughness of the dichotomy dichotomy and solutions of nonhomogeneous equations green s function for a linear skew product flow pointwise dichotomy versus global dichotomy and evolutionary semigroups along trajectories of the flow

a new dual based procedure for the transportation problem abstract we pose the transportation problem in a slightly different form to obtain a dual problem that has a special structure we exploit the structure of the dual problem to give a new heuristic that runs in o cn 2 time n is number of nodes in the network and c is a constant to improve the dual solution our heuristic obtained the optimal solution to several small sized transportation problems that we attempted and for large sized problems it obtained solutions that were within 82 of the optimal solution on average our approach gives good starting solutions for dual based approaches used for solving transportation problems and thus is expected to enhance their computational performance

a note on optimality in lattice square designs summary this note demonstrates that lattice square designs are a optimal within the class of lattice square designs if and only if they are m s optimal certain restricted lattice square designs are shown to be a optimal

criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations abstract we prove that the admissibility of any pair of vector valued schaffer function spaces satisfying a very general technical condition implies the existence of a no past exponential dichotomy for an exponentially bounded strongly continuous cocycle over a semiflow roughly speaking the class of schaffer function spaces consists in all function spaces which are invariant under the right shift and therefore our approach addresses most of the possible pairs of admissible spaces complete characterizations for the exponential dichotomy of cocycles are also obtained moreover we involve a concept of a no past exponential dichotomy for cocycles weaker than the classical concept defined by sacker and sell 1994 in 23 our definition of exponential dichotomy follows partially the definition given by chow and leiva 1996 in 4 in the sense that we allow the unstable subspace to have infinite dimension the main difference is that we do not assume a priori that the cocycle is invertible on the unstable space actually we do not even assume that the unstable space is invariant under the cocycle thus we generalize some known results due to o perron 1930 14 j daleckij and m krein 1974 7 j l massera and j j schaffer 1966 11 n van minh f rabiger and r schnaubelt 1998 26

construction and optimality of affine resolvable designs summary affine resolvable designs are constructed from orthogonal arrays and shown to be optimal among resolvable designs with respect to the usual criteria tables and text show how to construct such designs in up to seven replicates whenever the number of treatments properly divides the square of the block size data from experiments which use affine resolvable designs can be simply analysed by using pseudofactors in many experiments where an incomplete block design is used a resolvable design that is a design in which the blocks can be partitioned into sets containing each treatment once is desirable sometimes the blocks are naturally grouped into larger blocks contain ing each treatment exactly once an example from microbiology is an experiment in which jars of treated bacteria are placed in incubators so that the bacteria may multiply blocks are the shelves within the incubators and large blocks are the incubators use of a resolv able design ensures that the large blocks are orthogonal to treatments in other cases particularly in agricultural trials neighbouring blocks are grouped into large blocks for management purposes then a resolvable design not only keeps management effects ortho gonal to treatments it also gives some protection against the loss of a whole large block for all treatments are disadvantaged equally by such a loss the large blocks are often called replicates although somewhat ambiguously because their existence is independent of the treatment allocation suppose that a resolvable design is needed for v treatments in blocks of size k where v sk for some integer s greater than 1 and that r replicates are required for r 2 williams patterson john 1976 showed that an optimal resolvable design is equivalent to an optimal incomplete block design for s treatments in s blocks of size k thus optimality results about nonresolvable designs may be used to find the most efficient resolvable

incomplete block designs for comparing treatments wth a control general theory in this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control this class of designs is appropriate for comparing simultaneously p 2 test treatments with a control treatment the so called multiple comparisons with a control mcc problem when the observations are taken in incomplete blocks of common size k p 1 for this problem we propose a new general class of incomplete block designs that are balanced with respect to wrt test treatments we shall use the abbreviation btib to refer to such designs we study their structure and give some methods of construction a procedure for making exact joint confidence statements for this multiple comparisons problem is described by using a new concept of admissibility of designs it is shown how inferior designs can be eliminated from consideration and attention limited to a small class of btib designs that can be constructed from so called generator designs in the minimal complete class of such d

on the optimality of a class of designs with three concurrences abstract in the present paper we consider a class of unequally replicated designs having concurrence range 2 and spectrum of the form 1 2 v 3 3 now jacroux s some sufficient conditions for the type i optimality of block designs j statist plann inference 11 1985 385 396 proposition 2 4 says that a design with spectrum of the above form if satisfies some further conditions is type 1 optimal unfortunately this proposition does not apply to our designs since they have a poor status regarding e optimality yet we are able to prove the a optimality in the general class of these designs using majorisation technique a method of construction of an infinite series of our a optimal designs has also been given the first and only known infinite series of examples of designs satisfying jacroux s conditions appears to be the first one in section 4 1 of morgan and srivastav on the type 1 optimality of nearly balanced incomplete block designs with small concurrence range statist sinica 10 2000 1091 1116 hitherto referred to as ms in this paper we use majorisation technique to prove stronger optimality properties of the above mentioned designs of ms as well as to present simpler proof of another optimality result in ms

schaffer spaces and uniform exponential stability of linear skew product semiflows we study the exponential stability of linear skew product semiflows on locally compact metric space with banach fibers our main tool is the admissibility of a pair of the so called schaffer spaces this characterization is a very general one it includes as particular cases many interesting situations among them we can mention some results due to clark datko latushkin van minh montgomery smith randolph rabiger schnaubelt

representing inverses in pure network flow optimization abstract a basis for a pure network flow problem always exhibits special structure whose exploitation has led to the development of extremely efficient network optimization software the backbone of these programs is a data structure which represents the basis as a tree and is used to perform the linear algebraic steps required for optimization we demonstrate that the basis inverse also possesses a special structure which we call the inverse tree we develop a data structure to represent the inverse tree and we show that it obeys a symmetric relationship with the basis tree data structure the predecessor function of the inverse tree is the preorder link function of the basis tree and vice versa we develop efficient computational procedures for exploiting these results and show that using the inverse tree requires computation of the same order as the basis tree

computer aided blocking of factorial and response surface designs we consider the problem of blocking response surface and factorial designs when block sizes are prespecified often rendering standard approaches inapplicable a generalization of harville s 1974

a dynamic network flow problem with uncertain arc capacities formulation and problem structure we consider a dynamic network flow problem where the arc capacities are random variables this gives a multistage stochastic linear program we describe the randomness using a multi scenario approach because of the multilayered structure there are several ways to decompose the linear program we classify different decomposition schemes and we develop a scheme calledcompath decomposition which is derived from path decomposition for network flows we give a polynomial time algorithm to find a cheapest compath that can solve the subproblems resulting from compath decomposition finally compath decomposition is extended to multicommodity flow problems

exact two sample permutation tests based on the randomized play the winner rule in comparing two treatments in a clinical trial the randomized play the winner rule tends to assign more study subjects to the better treatment it is applicable when patients have delayed responses to treatments it is not deterministic and is less vulnerable to experimental bias than other adaptive designs in this paper an efficient algorithm is provided to construct exact permutation tests for testing the equality of the two treatments with the randomized play the winner rule the test procedure is illustrated with a real life example the example shows that the design used in the trial should not be ignored in the analysis