existence and stability of stationary profiles of the lw scheme in this paper we study the behavior of difference schemes approximating solutions with shocks of scalar conservation laws when a difference scheme introduces artificial numerical diffusion for example the lax friedrichs scheme we experience smearing of the shocks whereas when a scheme introduces numerical dispersion for example the lax wendroff scheme we experience oscillations which decay exponentially fast on both sides of the shock in his dissertation gray jennings studied approximation by monotone schemes these contain artificial viscosity and are first order accurate they are known to be contractive in the sense of any lp norm jennings showed existence and l1 stability of traveling discrete smeared shocks for such schemes here we study similar questions for the lax wendroff scheme without artificial viscosity this is a nonmonotone second order accurate scheme we prove existence of a one parameter family of stationary profiles we also prove stability of these profiles for small perturbations in the sense of a suitably weighted l2 norm the proof relies on studying the linearized lax wendroff scheme

fractional factorial designs for factors with a prime number of quantitative levels a technique for single degree of freedom partitioning of canonical contrasts for prime level factorials with quantitative levels is reviewed the relationship between canonical contrasts and the polynomial contrasts of response function models is discussed aliasing of canonical contrasts in fractional factorials is examined and alias sets from principal fractions are shown to have a particularly simple structure second order response function designs built from single principal fractions or from sums of two or four different principal fractions are discussed the accommodation of nuisance trend effects in experiments with quantitative factor effects is exemplified tables of fractional factorial designs for factors with three or five quantitative levels are presented

construction of block designs using mathematical programming summary the construction of optimal or nearly optimal block designs using the a optimality criterion is formulated as a non linear 0 1 programme an approach which ignores the 0 1 constraint is suggested and its feasibility is examined by constructing block designs using the non linear programming computer package minos

circuits and efficiency in incomplete block designs summary this paper explains why numbers of circuits in the variety concurrence graph of a design provide an attractive measure of its efficiency it is conjectured that the search for designs with an optimal value of the harmonic mean efficiency factor can be restricted to those with minimal numbers of circuits of shorter lengths this conjecture is seen to be highly plausible to be a natural generalization of a conjecture that is already widely accepted and to offer significant savings in the construction of efficient designs

a distributed algorithm for solving a linear algebraic equation a distributed algorithm is described for solving a linear algebraic equation of the form ax b assuming the equation has at least one solution the equation is simultaneously solved by m agents assuming each agent knows only a subset of the rows of the partitioned matrix matrix a b the current estimates of the equation s solution generated by its neighbors and nothing more each agent recursively updates its estimate by utilizing the current estimates generated by each of its neighbors neighbor relations are characterized by a time dependent directed graph bbn t whose vertices correspond to agents and whose arcs depict neighbor relations it is shown that for any matrix a for which the equation has a solution and any sequence of repeatedly jointly strongly connected graphs bbn t t 1 2 ldots the algorithm causes all agents estimates to converge exponentially fast to the same solution to ax b it is also shown that under mild assumptions the neighbor graph sequence must actually be repeatedly jointly strongly connected if exponential convergence is to be assured a worst case convergence rate bound is derived for the case when ax b has a unique solution it is demonstrated that with minor modification the algorithm can track the solution to ax b even if a and b are changing with time provided the rates of change of a and b are sufficiently small it is also shown that in the absence of communication delays exponential convergence to a solution occurs even if the times at which each agent updates its estimates are not synchronized with the update times of its neighbors a modification of the algorithm is outlined which enables it to obtain a least squares solution to ax b in a distributed manner even if ax b does not have a solution

decay rate for perturbations of stationary discrete shocks for convex scalar conservation laws this paper is to study the decay rate for perturbations of stationary discrete shocks for the lax friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method if the summation of the initial perturbation over j is small and decays at the algebraic rate as j then the solution approaches the stationary discrete shock profiles at the corresponding rate as n this rate seems to be almost optimal compared with the rate in the continuous counterpart proofs are given by applying the weighted energy integration method to the integrated scheme of the original one the selection of the time dependent discrete weight function plays a crucial role in this procedure

construction of optimal block designs by computer this article describes an effective algorithm for constructing optimal or near optimal incomplete block designs with up to 100 treatments the algorithm is found to perform well when evaluated against 874 optimal or near optimal incomplete block designs in the literature examples that motivated the development of the algorithm are given

a robust criterion for experimental designs for serially correlated observations a new robust criterion for experimental designs is proposed for a given design the criterion is to minimize over all possible run orders the absolute value of the change of the variance function due to possible correlation between the observations the resulting design is robust against possible auto correlation among the observations in the sense that confidence interval coverage levels are maintained accurately applications are given for 2k factorial designs and one mixed level fractional experiment and robust runs are obtained computational strategies are also discussed and a simulated annealing algorithm is developed to search for robust designs

definitions and properties for m concurrence designs summary incomplete block designs can be regarded as being in some sense approximately partially balanced in this paper we show that parameters pjk corresponding to those used for partially balanced designs can be defined for certain designs with m distinct concurrences these parameters have properties analogous to those for m associate class partially balanced incomplete block pbib m designs and have proved useful in searching for optimal designs this leads to a new upper bound for the efficiency factor which for given pjk values is attained if a pbib 2 design exists some results on complement and dual designs are also given

the l 1 global decay to discrete shocks for scalar monotone schemes given a family of discrete shocks of a monotone scheme we prove that the discrete shock profile with rational shock speed is asymptotically stable with respect to the l1 topology 1 if u0 l1 then un n 1 0 as n under no restriction conditions of the initial data to the interval inf sup the asymptotic wave profile is uniquely identified from the above family by a mass parameter

the validity of the modified equation for nonlinear shock waves abstract the modified model equivalent equation is an important tool in designing and analyzing nonlinear difference schemes in this note the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case

the construction of trend free run orders of two level factorial designs abstract in experimental situations where a factorial design with all factors occurring at two levels is to be run in a time sequence the usual advice given to the experimenter is that the order of runs should be randomized before the experiment is performed however randomization may lead to an undesirable run order for example in a factory experiment there may be a certain learning process that occurs over time as a result of making level changes in the factors being studied or there may be equipment wear out in either case the observations obtained will be affected by uncontrollable variables that are highly correlated with the time or position in which they occur and randomization may lead to a run order in which the estimates of factor effects are adversely effected by the presence of the trend joiner and campbell 1976 gave some more specific examples as to when trend effects can occur in sequential experiments therefore it is important to consider systematic designs in which the estimat

existence and uniqueness of traveling waves and error estimates for godunov schemes of conservation laws the existence and uniqueness of the lipschitz continuous traveling wave of godunov s scheme for scalar conservation laws are proved the structure of the traveling waves is studied the approximation error of godunov s scheme on single shock solutions is shown to be o 1 x

time trends and factorial experiments when factorial experiments are carried out over a period of time the response may be subject to time trends this might happen for example with the steady buildup of deposits in a test engine this article shows how to arrange the runs in a factorial experiment in sequences so that the main effects and sometimes the two factor interactions are uncorrelated with linear or quadratic time trends this is achieved by using the principle of foldover designs trendfree sequences are obtained for both 2 n and 3 n factorials

trend robust two level factorial designs summary limiting the possible influence of time order effects may be an important consideration in designing a sequential experiment we consider the problem of finding trend robust run orders of two level factorials when the time effects are modelled via a first order autoregressive error model or via a time series model in both cases run orders are trend robust if the factors change level many times other run orders can be quite inefficient even if they are free of low degree polynomial trends we present a simple algorithm for constructing run orders of two level factorial designs with many level changes

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

on the stability of finite element methods for shock waves this paper we study the large time asymptotic stability of solutions for systems of nonlinear viscous conservation laws of the form 1 1 u t f u x u xx x 2 r i t 0 u 2 r i u delta 0 u 0 delta we treat systems which are strictly hyperbolic such systems possess a smooth travelling wave solution which is called a viscous p shock wave solution u x t oe x gamma oet x sigma1 oe x u sigma provided that the shock strength ffl j ju gamma u gamma j is small 19 the constant states u sigma and the wave speed oe are related by the rankine hugoniot condition 1 3a f u gamma gamma f u oe u gamma gamma u

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

nonlinear stability of discrete shocks for systems of conservation laws in this paper we study the asymptotic nonlinear stability of discrete shocks for the lax friedrichs scheme for approximating general m systems of nonlinear hyperbolic conservation laws it is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the lp norm for all p 1 provided that the sums of the initial perturbations equal zero these results should shed light on the convergence of the numerical solution constructed by the lax friedrichs scheme for the single shock solution of system of hyperbolic conservation laws if the riemann solution corresponding to the given far field states is a superposition of m single shocks from each characteristic family we show that the corresponding multiple discrete shocks are nonlinearly stable in l p p 2 these results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the lax friedrichs scheme

an investigation of the internal structure of shock profiles for shock capturing schemes the theoretical understanding of discrete shock transitions obtained by shock capturing schemes is very incomplete previous experimental studies indicate that discrete shock transitions obtained by shock capturing schemes can be modeled by continuous functions so called continuum shock profiles however the previous papers have focused on linear methods we have experimentally studied the trajectories of discrete shock profiles in phase space for a range of different high resolution shock capturing schemes including riemann solver based flux limiter methods high resolution central schemes and eno type methods in some cases no continuum profiles exists however in these cases the point values in the shock transitions remain bounded and appear to converge toward a stable limit cycle the possibility of such behavior was anticipated in bultelle grassin and serre 1998 but no specific examples or other evidence of this behavior have previously been given in other cases our results indicate that continuum shock profiles exist but are very complicated we also study phase space orbits with regard to post shock oscillations

convergence of sequential and asynchronous nonlinear paracontractions we establish the convergence of sequential and asynchronous iteration schemes for nonlinear paracontracting operators acting in finite dimensional spaces applications to the solution of linear systems of equations with convex constraints are outlined a first generalization of one of our convergence results to an infinite pool of asymptotically paracontracting operators is also presented

a distributed algorithm for computing a common fixed point of a finite family of paracontractions a distributed algorithm is described for finding a common fixed point of a family of m 1 nonlinear maps m i mathbb r n rightarrow mathbb r n assuming that each map is a paracontraction and that at least one such common fixed point exists the common fixed point is simultaneously computed by m agents assuming each agent i knows only m i the current estimates of the fixed point generated by its neighbors and nothing more each agent recursively updates its estimate of a fixed point by utilizing the current estimates generated by each of its neighbors neighbor relations are characterized by a time varying directed graph mathbb n t it is shown under suitably general conditions on mathbb n t that the algorithm causes all agent estimates to converge to the same common fixed point of the m nonlinear maps

nonresolvable incomplete block designs with few replicates summary tables are given showing incomplete block designs with up to 5 replicates for parameter values 10 v 60 2 r k 10 where r and k have a factor in common the designs are nonresolvable generalized cyclic incomplete block designs as defined by jarrett hall 1978 they give a general improvement in efficiency factor over the fractional cyclic incomplete block designs of john wolock david 1972 and provide a considerable extension to the tables of resolvable designs given by patterson williams hunter 1978

on the construction of trend free run orders of treatments summary in this paper we consider the problem of sequentially applying v treatments to n experimental units over time or space where there may be an unknown trend effect which can be expressed as a polynomial function of the order in which the observations are taken a method is given for constructing ordered applications of treatments to experimental units which produce easily computed and optimal estimates for treatment differences that are orthogonal to the unknown trend effect in this paper we consider experimental situations where v treatments are to be applied to n experimental units sequentially over space or time and where there may be an unknown time or spatial trend any sequential or ordered application of treatments to experimental units shall be called a run order or design and be denoted by d we assume that the treatments are to be applied to experimental units at equally spaced intervals and that the trend effect can be represented as a polynomial function of the positions in

generalized minimum aberration for asymmetrical fractional factorial designs by studying treatment contrasts and anova models we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs the criterion is independent of the choice of treatment contrasts and thus model free it works for symmetrical and asymmetrical designs regular and nonregular designs in particular it reduces to the minimum aberration criterion for regular designs and the minimum g 2 aberration criterion for two level nonregular designs in addition by exploring the connection between factorial design theory and coding theory we develop a complementary design theory for general symmetrical designs which covers many existing results as special cases

robust designs for serially correlated observations summary the presence of serial correlation affects the design strategy of a statistical experiment it is the object of this paper to construct robust and efficient designs under such conditions special consideration is given to the two level factorial designs and weighing designs

on the construction of trend resistant designs for comparing a set of test treatments with a set of controls abstract in this article we consider the problem of comparing a set of standard treatments to a set of test treatments where the treatments are to be applied to experimental units sequentially over time or space and where there may be an unknown time or spatial trend methods are given here for constructing run orders of treatments for those situations that are optimal and robust against trends that can be expressed as a polynomial function of the order in which the observations are taken

trend free block designs for varietal and factorial experiments some general results on the existence of trend free and partially trend free designs are given for both varietal and factorial experiments in particular trend free properties of cyclic and generalized cyclic designs are investigated it is shown that for factorial experiments certain designs which are not completely trend free are nevertheless trend free for estimating a subset of the main effect and interaction contrasts

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

distributed algorithms for computing a common fixed point of a group of nonexpansive operators this paper addresses the problem of seeking a common fixed point for a collection of nonexpansive operators over time varying multi agent networks in real hilbert spaces each operator is only privately and approximately known to each individual agent and all agents need to cooperate to solve this problem by local communications over time varying networks to handle this problem inspired by the centralized inexact krasnosel skii mann ikm iteration we propose a distributed algorithm called distributed inexact averaged operator algorithm d iao it is shown that the d iao algorithm can converge weakly to a common fixed point of the family of nonexpansive operators moreover under the linearly regular assumption it is proved that the d iao algorithm converges with a rate o gamma log 16 4k for some constant gamma in 0 1 where k is the iteration number the same converge speed can be ensured by a novel power regularity condition which is strictly weaker than linear regularity to reduce computational complexity another algorithm called d biao is developed and fully analyzed simulation examples are given to support the theoretical res

l 1 stability of stationary discrete shocks the nonlinear stability in the l sup p norm p ge 1 of stationary weak discrete shocks for the lax friedrichs scheme approximating general m times m systems of nonlinear hyperbolic conservation laws is proved provided that the summations of the initial perturbations equal zero the result is proved by using a both weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the lax friedrichs scheme 13 refs

convergence rates to the discrete travelling wave for relaxation schemes this paper is concerned with the asymptotic convergence of nu merical solutions toward discrete travelling waves for a class of relaxation nu merical schemes approximating the scalar conservation law it is shown that if the initial perturbations possess some algebraic decay in space then the nu merical solutions converge to the discrete travelling wave at a corresponding algebraic rate in time provided the sums of the initial perturbations for the u component equal zero a polynomially weighted l 2 norm on the perturba tion of the discrete travelling wave and a technical energy method are applied to obtain the asymptotic convergence rate

stable viscosity matrices for systems of conservation laws abstract a natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension u 1 f u x 0 u r m is studied these matrices are admissible in the sense that small amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system u t f u x v du x x as ifv 0 if d is in this class the class is determined by a linearized stability requirement the cauchy problem for the equation u 1 f u 0 u x vdu xx should be well posed in l 2 uniformly in v as v 0 previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion

nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws this paper is to study the asymptotic stability of stationary discrete shocks for the lax friedrichs scheme approximating nonconvex scalar conservation laws provided that the summations of the initial perturbations equal to zero the result is proved by using a weighted energy method based on the nonconvexity moreover the l 1 stability is also obtained the key points of our proofs are to choose a suitable weight function

equireplicate balanced block designs with unequal block sizes summary methods are given for the construction of equireplicate balanced block designs with unequal block sizes using group divisible designs balanced designs in which treatments are replicated 25 times or less are tabulated the plans of these designs can be readily obtained using existing published sources some of the designs given here are even smaller than those in balanced incomplete blocks

on the construction of trend resistant mixed level factorial run orders in this paper we consider experimental situations where treatments from a mixed level factorial design are to be applied to experimental units over space or time and where there may be an unknown trend effect which can be approximated by some polynomial function of the order in which the observations are obtained a method of constructing run orders of treatments for such situations is given which generally yields least squares estimators for main effects that have a higher degree of trend resistance than the least squares estimators of main effects that come from run orders obtainable by other methods of construction previously given in the literature

convergence rates to discrete shocks for nonconvex conservation laws this paper is concerned with polynomial decay rates of perturbations to stationary discrete shocks for the lax friedrichs scheme approximating non convex scalar conservation laws we assume that the discrete initial data tend to constant states as j rightarrow pm infty respectively and that the riemann problem for the corresponding hyperbolic equation admits a stationary shock wave if the summation of the initial perturbation over infty j is small and decays with an algebraic rate as j rightarrow infty then the perturbations to discrete shocks are shown to decay with the corresponding rate as n rightarrow infty the proof is given by applying weighted energy estimates a discrete weight function which depends on the space time variables for the decay rate and the state of the discrete shocks in order to treat the non convexity plays a crucial role

existence and asymptotic stability of relaxation discrete shock profiles kin this paper we study the asymptotic nonlinear stability of discrete shocks of the relaxing scheme for approximating the general system of nonlinear hyperbolic conservation laws the existence of discrete shocks is established by suitable manifold construction and it is shown that weak single discrete shocks for such a scheme are nonlinearly stable in l 2 provided that the sums of the initial perturbations equal zero these results should shed light on the convergence of the numerical solution constructed by the relaxing scheme for the single shock solution of the system of hyperbolic conservation laws these results are proved by using both a weighted norm estimate and a characteristic energy method based on the internal structures of the discrete shocks

on the structure of finite dimensional paracontractions abstract we give a characterization of paracontractions with respect to a strictly convex norm on c n as an application we give a characterization of linear mappings on m n which preserve paracontractions with respect to p norms for 1 p in both directions

on general balance in row column designs summary the purpose of this paper is to clarify the relationships between general balance in a row column design the commutivity of the information matrices of the row and column components and the concept of adjusted orthogonality the class of row column generalized cyclic incomplete block designs is defined and a characterization is given of the subclass having general balance

the decomposition of treatment degrees of freedom in quantitative factorial experiments summary in an experiment in which every treatment factor has the same number p of levels where p is prime there is a classical breakdown of the treatment degrees of freedom into components such as ab ab2 ab2 c each of p 1 degrees of freedom the disadvantages of this system are i the lack of canonical single degrees of freedom and ii the fact that the breakdown bears no relation to the contrasts typically of interest if all treatment factors are quantitative in this note we decompose the treatment degrees of freedom into single degrees of freedom and use these to show how appropriate choice of levels of quantitative factors enables quantitative contrasts to be completely unconfounded in classical designs

systematic row and column designs balanced for low order polynomial interactions between rows and columns systematic row and column designs intended to accommodate low order polynomial rows columns interaction effects are discussed latin square graeco latin square and quasi latin square designs of size 2 n 2 m and size 9 9 are examined by using plot pseudofactor methods latin square and graeco latin square designs of size 5 5 and 7 7 are examined by using a published technique for the design of quantitative factorial experiments with a prime number of factor levels a 6 6 latin square design is constructed by trial and error finally the control of positional effects by fitted quadratic response surfaces is discussed

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

linearized stability of extreme shock profiles for systems of conservation laws with viscosity abstract for a genuinely nonlinear hyperbolic system of conservation laws with added artificial viscosity we prove that traveling wave profiles for small amplitude extreme shocks the slowest and fastest are linearly stable to perturbations initial data chosen from certain spaces with weighted norm i e we show that the spectrum of the linearized equation lies strictly in the left half plane except for a simple eigenvalue at the origin due to phase translations of the profile the weight is used in components transverse to the profile where for an extreme shock the linearized equation is dominated by unidirectional convection