model order reduction for nonlinear dynamical systems based on trajectory piecewise linear approximations in this paper we analyze and expand a recently developed approach to model order reduction mor for nonlinear dynamical systems based on trajectory piecewise linear tpwl approximations error estimates are given for solutions computed with tpwl reduced order models and problems of preserving stability and passivity are examined since the tpwl method has limited a priori guarantees on global accuracy its effectiveness is demonstrated on a range of examples including a micromachined switch two nonlinear electronic circuits and shock propagation modeled by burgers equation

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

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

construction of some balanced incomplete block designs with nested rows and columns par i j qac ij as j j a 1 where a a constant integer independent of the pair i j chosen satisfies the relationship a v 1 r p 1 q 1 ar ij ac ij and a i j denote respectively the numbers of rows within sets columns within sets and sets in which the pair occurs together these variance balanced binary designs introduced and discussed by singh dey 1979 with parameters v b r p q and a are abbreviated as bibrc v b r p q a note that 1 1 is an alternative version of their condition 4 3 agarwal prasad 1982 1983 and cheng 1986 gave further methods of construction of these designs cheng 1986 considered the case of k v in these designs and called them balanced complete block designs with nested rows and columns with parameters v b r p q and a and abbreviated as bcbrc v b r p q a he has equivalently used the condition

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

the construction of exact d optimum experimental designs with application to blocking response surface designs summary the properties of optimum designs are investigated when there are both qualitative and quantitative factors algorithms for the construction of exact designs are described which are of general applicability the case when the qualitative factors represent blocking variables is given special treatment a modified algorithm provides the opportunity to divide the experimental trials into blocks of specified sizes examples are given of second order models in the quantitative factors divided into two or three blocks of a variety of sizes use of the adjustment algorithm to improve such designs generated from a list of candidate points is demonstrated

finite element analysis of post buckling dynamics in plates part i an asymptotic approach abstract various static and dynamic aspects of post buckled thin plates including the transition of buckled patterns post buckling dynamics secondary bifurcation and dynamic snapping mode jumping phenomenon are investigated systematically using asymptotical and non stationary finite element methods in part i the secondary dynamic instability and the local post secondary buckling behavior of thin rectangular plates under generalized mechanical and thermal loading is investigated using an asymptotic numerical method which combines koiter s nonlinear instability theory with the finite element technique a dynamic multi mode reduction method similar to its static single mode counterpart liapunov schmidt reduction is developed in this perturbation approach post secondary buckling equilibrium branches are obtained by solving the reduced low dimensional parametric equations and their stability properties are determined directly by checking the eigenvalues of the resulting jacobian matrix typical post secondary buckling forms transcritical supercritical and subcritical bifurcations are observed according to different combinations of boundary conditions and load types geometric imperfection analysis shows that not only the secondary bifurcation load but also changes in the fundamental post secondary buckling behavior are affected the post buckling dynamics and the global analysis of mode jumping of the plates are addressed in part ii

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

optimal designs for diallel crosses with specific combining abilities optimal designs for diallel crosses are considered when in addition to the block effects and general combining abilities the model also includes specific combining abilities it is seen that partially balanced incomplete block designs with the triangular association scheme play a key role in this context

a note on design when response has an exponential family distribution summary some simple design problems are considered when responses have an exponential family distribution with the difference between treatment groups in the canonical parameter being the objective of study it is shown that normal theory conclusions apply to a possibly surprising extent the loss from randomizing followed by subsequent stratification is the equivalent of one observation per stratum for binary data heterogeneity has to be quite large before failure to stratify induces serious loss whereas unnecessary use of a matched pair design is fully efficient asymptotically

optimum biased coin designs for sequential treatment allocation with covariate information randomized optimum designs of biased coin type are compared with other strategies for the sequential allocation of two or more treatments in a clinical trial the emphasis is on the variance of estimated treatment contrasts this variance which depends on the design strategy employed may be interpreted as the number of patients on whom information is lost simulations provide clear plots of the evolution of this loss during the course of the clinical trial

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

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

dimensional model reduction in non linear finite element dynamics of solids and structures a general approach to the dimensional reduction of non linear finite element models of solid dynamics is presented for the newmark implicit time discretization the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments to deal with this it is shown how the problem can be formulated in an approximation ritz basis of much smaller dimension similarly the explicit newmark algorithm can be also written in a reduced dimension basis and the computation time savings in that case follow from an increase in the stable time step length in addition the empirical eigenvectors are proposed as the basis in which to expand the incremental problem this basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense because of this global time viewpoint the basis need not be updated as with reduced bases computed from a linearization of the full finite element model if the dynamics of a finite element model is expressed in terms of a small number of basis vectors the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved at the same time numerical experiments indicate that by using reduced models substantial savings can be achieved even in the pre asymptotic range furthermore the algorithm parallelizes very efficiently the method we present is expected to become a useful tool in applications requiring a large number of repeated non linear solid dynamics simulations such as convergence studies design optimization and design of controllers of mechanical systems

reduction method for finite element nonlinear dynamic analysis of shells doi 10 2514 1 j051003theprojectionoftheequationsofmotiononasuitablemodalbasiscandrasticallyreducethenumberofdegreesoffreedom of a nonlinear dynamic nite element analysis a reduction method based on enriching a set of vibrationmodeswithsecond ordermodescalculatedviaaperturbationtechniqueispresented thesesecond ordermodesarereadily calculated via the solution of corresponding linear problems the results indicate that the second ordermodes are displacement elds that are essential for an appropriate representation of the nonlinear behavior of thestructure problems exhibiting strong geometrical nonlinearities under relatively high dynamic loads aresuccessfully handled by forming the reduction basis with vibration modes and their corresponding second ordermodes calculated at two different static equilibrium con gurations

optimal partial diallel crosses even in the absence of blocks each cross in a partial diallel cross design can be formally identified with a block of size two and thus the design itself can be identified with a binary block design we show that unblocked partial diallel crosses so linked with a certain class of group divisible designs are uniquely e optimal in general and also uniquely d and a optimal in the saturated case further results on e optimality applicable even when the number of parental lines does not admit a factorisation are also derived the issue of optimal or efficient blocking of partial diallel crosses is discussed

explicit time reversible adaptive step size control adaptive step size control is difficult to combine with geometric numerical integration as classical step size control is based on past information only time symmetry is destroyed and with it the qualitative properties of the method in this paper we develop completely explicit reversible symmetry preserving adaptive step size selection algorithms for geometric numerical integrators such as the stormer verlet method a new step density controller is proposed and analyzed using backward error analysis and reversible perturbation theory for integrable reversible systems we show that the resulting adaptive method nearly preserves all action variables and in particular the total energy for hamiltonian systems it has the same excellent long term behavior as that obtained when constant steps are used with variable steps however both accuracy and efficiency are greatly improved

projection based reduction of fluid structure interaction systems using monolithic space time modes abstract the focus of this work is the development of reduced models for engineering applications in complex bidirectional fluid structure interaction in the simultaneous solution procedure velocity variables are used for both fluid and solid and the whole set of model equations is discretized by a stabilized time discontinuous space time finite element method flexible structures are modeled using a three dimensional continuum approach in a total lagrangian setting considering large displacements and rotations in the flow domain the incompressible navier stokes equations describe the newtonian fluid a continuous finite element mesh is applied to the entire spatial domain and the discretized model equations are assembled in a single set of algebraic equations considering the two field problem as a whole the continuous fluid structure mesh with identical orders of approximation for both solid and fluid in space and time automatically yields conservation of mass momentum and energy at the fluid structure interface a mesh moving scheme is used to adapt the nodal coordinates of the fluid space time finite element mesh to the structural deformation the computational approach for strongly coupled fluid structure interaction is used to create suitable reduced models of generic nonlinear problems reduction is performed with monolithic projection based space time modes ensuring strong coupling of fluid and structure in the reduced model the contribution discusses results using proper orthogonal decomposition pod for determination of monolithic space time modes in the reduction of fluid structure systems

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

evaluation of geometrically nonlinear reduced order models with nonlinear normal modes several reduced order modeling strategies have been developed to create low order models of geometrically nonlinear structures from detailed finite element models allowing one to compute the dynamic response of the structure at a dramatically reduced cost however the parameters of these reduced order models are estimated by applying a series of static loads to the finite element model and the quality of the reduced order model can be highly sensitive to the amplitudes of the static load cases used and to the type number of modes used in the basis this paper proposes to combine reduced order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced order model can be assessed hence the second contribution of this

doubly quasi consistent parallel explicit peer methods with built in global error estimation recently kulikov presented the idea of double quasi consistency which facilitates global error estimation and control considerably more precisely a local error control implemented in such methods plays a part of global error control at the same time however kulikov studied only nordsieck formulas and proved that there exists no doubly quasi consistent scheme among those methods here we prove that the class of doubly quasi consistent formulas is not empty and present the first example of such sort this scheme belongs to the family of superconvergent explicit two step peer methods constructed by weiner schmitt podhaisky and jebens we present a sample of s stage doubly quasi consistent parallel explicit peer methods of order s 1 when s 3 the notion of embedded formulas is utilized to evaluate efficiently the local error of the constructed doubly quasi consistent peer method and hence its global error at the same time numerical examples of this paper confirm clearly that the usual local error control implemented in doubly quasi consistent numerical integration techniques is capable of producing numerical solutions for user supplied accuracy conditions in automatic mode

constant coefficient linear multistep methods with step density control in linear multistep methods with variable step size the method s coefficients are functions of the step size ratios the coefficients therefore need to be recomputed on every step to retain the method s proper order of convergence an alternative approach is to use step density control to make the method adaptive if the step size sequence is smooth the method can use constant coefficients without losing its order of convergence the paper introduces this new adaptive technique and demonstrates its feasibility with a few test problems the technique works in perfect agreement with theory for a given step density function for practical use however the density must be generated with data computed from the numerical solution we introduce a local error tracking controller which automatically adapts the density to computed data and demonstrate in computational experiments that the technique works well at least up to fourth order methods

system identification guided basis selection for reduced order nonlinear response analysis reduced order nonlinear simulation is often times the only computationally efficient means of calculating the extended time response of large and complex structures under severe dynamic loading this is because the structure may respond in a geometrically nonlinear manner making the computational expense of direct numerical integration in physical degrees of freedom prohibitive as for any type of modal reduction scheme the quality of the reduced order solution is dictated by the modal basis selection the techniques for modal basis selection currently employed for nonlinear simulation are ad hoc and are strongly influenced by the analyst s subjective judgment this work develops a reliable and rigorous procedure through which an efficient modal basis can be chosen the method employs proper orthogonal decomposition to identify nonlinear system dynamics and the modal assurance criterion to relate proper orthogonal modes to the normal modes that are eventually used as the basis functions the method is successfully applied to the analysis of a planar beam and a shallow arch over a wide range of nonlinear dynamic response regimes the error associated with the reduced order simulation is quantified and related to the computational cost

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

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

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

on quasi consistent integration by nordsieck methods in this paper we study advantages of numerical integration by quasi consistent nordsieck formulas all quasi consistent numerical methods possess at least one important property for practical use which has not attracted attention yet i e the global error of a quasi consistent method has the same order as its local error this means that the usual local error control will produce a numerical solution for the prescribed accuracy requirement if the principal term of the local error dominates strongly over remaining terms in other words the global error control can be as cheap as the local error control in the methods under discussion here we apply the above mentioned idea to nordsieck adams moulton methods which are known to be quasi consistent moreover some nordsieck adams moulton methods are even super quasi consistent the latter property means that their propagation matrices annihilate two leading terms in the defect expansion of such methods in turn this can impose a strong relation between the local and global errors of the numerical solution and allow the global error to be controlled effectively by a local error control we also introduce implicitly extended nordsieck methods such that in some sense they form pairs of embedded formulas with their source nordsieck methods this facilitates the local error control in quasi consistent nordsieck schemes numerical examples presented in this paper confirm clearly the power of quasi consistent integration in practice

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

construction of variable stepsize multistep formulas a systematic way of extending a general fixed stepsize multistep formula to a minimum storage variable stepsize formula has been discovered that encompasses fixed coefficient interpolatory variable coefficient variable step and fixed leading coefficient as special cases in particular it is shown that the interpolatory stepsize changing technique of nordsieck leads to a truly variable stepsize multistep formula which has implications for local error estimation and formula changing and it is shown that the variable step stepsize changing technique applicable to the adams and backward differentiation formulas has a reasonable generalization to the general multistep formula in fact it is shown how to construct a variable order family of variable coefficient formulas finally it is observed that the first dahlquist barrier does not apply to adaptable multistep methods if storage rather than stepnumber is the key consideration

sensitivity analysis for dynamic mechanical systems with finite rotations this paper presents a sensitivity analysis for dynamic systems with large rotations using a semi analytical direct differentiation technique the choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis three versions of the generalized time integration scheme are considered a residual form a linear form and a geometric form their consistency is discussed and we show that the residual form which is the most direct extension of the generalized algorithm defined in structural dynamics should not be used for problems with large rotations the sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations hence algorithms developed for the original problem can be directly reused for the sensitivities finally a numerical example is analysed in detail copyright 2007 john wiley sons ltd

optimal complete diallel crosses summary optimality of complete diallel crosses in incomplete blocks is investigated optimal complete diallel crosses are characterized and such binary plans are derived using nested balanced incomplete block designs a table of optimal complete diallel crosses for up to 15 lines is also provided

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

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

a reduction method for nonlinear structural dynamic analysis abstract a computational algorithm for predicting the nonlinear dynamic response of a structure is presented the nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a rayleigh ritz analysis the basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing only a few basis updatings are required during the whole time integration the truncation error introduced at every change of basis is pointed out as the cause for a divergence type behaviour and some means for eliminating it are discussed results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations

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

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

miscellanea optimal designs for diallel crosses with specific combining abilities summary optimal designs for diallel crosses are considered when in addition to the block effects and general combining abilities the model also includes specific combining abilities it is seen that partially balanced incomplete block designs with the triangular association scheme play a key role in this context

vibration of geometrically imperfect beam and shell structures abstract the purpose of this paper is to present a general theory for analysis of the effect of initial geometrical imperfections on vibration frequencies of undamped conservatively loaded linear elastic beam and shell structures the theory will be restricted to single mode vibrations with imperfections in the same shape as the vibration modes the mathematical tool is a perturbational procedure developed with the aid of the principle of virtual work the approach is illustrated by applications to beams plates and axisymmetric shell structures the examples show that the vibration frequency of these structures may be significantly raised or lowered due to imperfections

optimality and efficiency of two treatment repeated measurements designs for an arbitrary covariance matrix and any number of treatments and periods necessary and sufficient conditions for the optimality of a repeated measurements i e crossover or changeover design were given in the as yet unpublished report by h b kushner optimal repeated measurements designs the linear optimality equations kushner report here we specialise the results to the two treatment case we give linear equations whose solutions are the proportions of subjects allocated to each treatment sequence in the most general optimal design the treatment effects information matrix of an optimal design is also presented the results are applied to several situations for arbitrary covariance matrices we show that designs consisting of at most two treatment sequences and their duals must necessarily be dual balanced to be optimal for autoregressive covariance matrices we confirm that designs of matthews 1987 for three and four periods are optimal and we derive new optimal designs for five and six periods some optimality results of laska meisner 1985 are extended a simple formula for the efficiency of a dual balanced nonoptimal design is provided and used to compute the exact efficiencies of some of kunert s 1991 designs

adaptive time stepping and computational stability we investigate the effects of adaptive time stepping and other algorithmic strategies on the computational stability of ode codes we show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability a series of computational experiments with the standard implementation of dassl and a modified version including stepsize control based on digital filters is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense the inherent performance and stability of dassl are therefore much greater than the standard implementation seems to suggest

optimal two stage screening designs for survival comparisons summary a two stage design is presented which enables the screening at the first stage of several new experimental treatments for survival improvement over a standard regimen only promising treatments are carried forward to the second stage for definitive evaluation our procedure is to minimize the number of patients expected to be accrued to new regimens which do not offer a survival benefit over the standard regimen subject to constraints of specified alpha error power and a stopping rule wlhich allows specification of the magnitude of the hazards ratio which would warrant accrual beyond the first stage we explore the savings in patient accrual by comparing our design with a single stage design for a variety of situations our design may offer a substantial saving when the hazard rate is large relative to the patient accrual rate a situation often encountered in clinical trials in advanced cancer although computations are based on asymptotic results simulations verify that the approximations are adequate for most trials of interest in the development of treatments for advanced cancer a standard regimen with limited survival benefit may be available as well as several new promising regimens which have not been evaluated in a comparative trial to determine their possible survival benefit we offer an efficient two stage design which allows survival comparisons of the new regimens with a standard regimen but which permits early termination of accrual onto those new regimens which do not demonstrate a minimum prespecified survival advantage over the standard regimen in this way we hope to minimize the number of patients assigned to new regimens which are not promising the design also permits early accrual termination if a new treatment offers an early substantial survival advantage over the standard regimen 2 the design we propose a two stage screening design so that survival times of each of k experimental regimens will be compared to the survival of the standard treatment at possibly two time points t1 and t2 furthermore we assume proportional hazards such that

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

optimal block designs for diallel crosses summary optimal block designs for a type of diallel cross experiment are proposed these incomplete block designs are derived by using triangular partially balanced designs with two associate classes some efficient incomplete block designs for diallel crosses are also reported

a perturbation method for nonlinear vibrations of imperfect structures application to cylindrical shell vibrations abstract a perturbation method is used to analyse the nonlinear vibration behaviour of imperfect general structures under static preloading the method is based on a perturbation expansion for both the frequency parameter and the dependent variables the effects on the linearized and nonlinear vibrations caused by geometric imperfections a static fundamental state and a nontrivial static state are included in the perturbation procedure the theory is applied in the nonlinear vibration analysis of anisotropic cylindrical shells in the analysis the specified boundary conditions at the shell edges can be satisfied accurately the characteristics of the analysis capability are shown through examples of the vibration behaviour of specific shells results for single mode and coupled mode nonlinear vibrations of shells are presented parametric studies have been performed for a composite shell

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