on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

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

general balance and treatment permutations abstract many equi replicate designs whether ordinary block designs or multi stratum designs have a structure which is left unchanged by a group g of permutations of the treatments this group g is often used in the construction of the design a survey of the properties of such designs is given and useful necessary conditions on g are found for such a design to be generally balanced if g is abelian then the necessary conditions are satisfied in this case explicit formulas for the efficiency factors are given

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

a method for constructing balanced incomplete block designs with nested rows and columns summary a general method for constructing balanced incomplete block designs with nested rows and columns is presented many designs are obtained in which none of the treatmentblock treatment row and treatment column incidence matrices is the incidence matrix of a balanced incomplete block design if the method of construction is applied to a generally balanced design then the resulting design is also generally balanced

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

nested generalized cyclic row column designs summary a nested row column design has v treatments arranged in b blocks each comprising pq units grouped into p rows and q columns a class of designs based on a cyclical method of construction is defined the canonical efficiency factors of such nested generalized cyclic row column designs are examined efficient designs are tabulated for 5 v 15 p 3 q 7 and r v where r bpq v is the number of replications of each treatment row column designs are used to eliminate heterogeneity in two directions more generally an experiment may have several blocks each containing pq plots arranged in p rows and q columns where the blocks may represent a further blocking factor or provide replications of the basic row column design these designs are called nested row column designs since rows and columns are nested within blocks the lattice square designs introduced by yates 1940 are examples of such designs a general analysis and the concept of balance have been considered by singh dey 1979 several series of balanced nested row column designs have been given by singh dey 1979 street 1981 and agrawal prasad 1982a preece 1967 provides a table of nested balanced incomplete block designs and a number of these designs can also be used as balanced nested row column designs other series based on partially balanced designs have been given by street 1981 and agrawal prasad 1982b jarrett hall 1982 gave some examples of small designs based on cyclic and generalized cyclic methods of con struction which they suggested could provide useful alternatives to nearest neighbour designs and methods as an example of a balanced nested row column design consider the following design given by singh dey 1979 for five treatments 0 1 2 3 4 arranged in five blocks of two rows and two columns

nonlinear damped partial differential equations and their uniform discretizations abstract we establish sharp energy decay rates for a large class of nonlinearly first order damped systems and we design discretization schemes that inherit of the same energy decay rates uniformly with respect to the space and or time discretization parameters by adding appropriate numerical viscosity terms our main arguments use the optimal weight convexity method and uniform observability inequalities with respect to the discretization parameters we establish our results first in the continuous setting then for space semi discrete models and then for time semi discrete models the full discretization is then inferred from the previous results by adapting the ideas to deal with linear systems our results cover for instance the schrodinger equation with nonlinear damping the nonlinear wave equation the nonlinear plate equation the nonlinear transport equation as well as certain classes of equations with nonlocal terms

asymptotic stability of the wave equation on compact surfaces and locally distributed damping a sharp result this paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping described by u tt m u x g u t 0 on m 0 where m c r 3 is a smooth oriented embedded compact surface without boundary denoting by g the riemannian metric induced on m by r 3 we prove that for each 0 there exist an open subset v c m and a smooth function f m r such that meas v meas m e hessf g on v and inf f x 0 x v in addition we prove that if x a o 0 on an open subset m c m which contains m v and if g is a monotonic increasing function such that k s g s k s for all s 1 then uniform and optimal decay rates of the energy hold

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

a unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi discretized vibrating damped systems the liapunov method is celebrated for its strength to establish strong decay of solutions of damped equations extensions to infinite dimensional settings have been studied by several authors see e g haraux 1991 11 and komornik and zuazua 1990 17 and references therein results on optimal energy decay rates under general conditions of the feedback is far from being complete the purpose of this paper is to show that general dissipative vibrating systems have structural properties due to dissipation we present a general approach based on convexity arguments to establish sharp optimal or quasi optimal upper energy decay rates for these systems and on comparison principles based on the dissipation property and interpolation inequalities in the infinite dimensional case for lower bounds of the energy we stress the fact that this method works for finite as well as infinite dimensional vibrating systems and as well as for applications to semi discretized nonlinear damped vibrating pde s a part of this approach has been introduced in alabau boussouira 2004 2005 1 2 in the present paper we identify a new simple and explicit criteria to select a class of nonlinear feedbacks for which we prove a simplified explicit energy decay formula comparatively to the more general but also more complex formula we give in alabau boussouira 2004 2005 1 2 moreover we prove optimality of the decay rates for this class in the finite dimensional case this class includes a wide range of feedbacks ranging from very weak nonlinear dissipation exponentially decaying in a neighborhood of zero to polynomial or polynomial logarithmic decaying feedbacks at the origin in the infinite dimensional case we establish a comparison principle on the energy of sufficiently smooth solutions through the dissipation relation this principle relies on suitable interpolation inequalities it allows us to give lower bounds for the energy of smooth initial data for the one dimensional wave equation with a distributed polynomial damping which improves haraux 1995 12 lower estimate of the energy for this case we also establish lower bounds in the multi dimensional case for sufficiently smooth solutions when such solutions exist we further mention applications of these various results to several classes of pde s namely the locally and boundary damped multi dimensional wave equation the locally damped plate equation and the globally damped coupled timoshenko beams system but it applies to several other examples furthermore we show that these optimal energy decay results apply to finite dimensional systems obtained from spatial discretization of infinite dimensional damped systems we illustrate these results on the one dimensional locally damped wave and plate equations discretized by finite differences and give the optimal energy decay rates for these two examples these optimal rates are not uniform with respect to the discretization parameter we also discuss and explain why optimality results have to be stated differently for feedbacks close to linear behavior at the origin

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

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

dispersive estimates for principally normal pseudodifferential operators the aim of these notes is to describe some recent re sults concerning dispersive estimates for principally normal pseu dodifferential operators the main motivation for this comes from unique continuation problems such estimates can be used to prove l q carleman inequalities which in turn yield unique continuation results for various partial differential operators with rough poten tials dispersive estimates are l q estimates for nonelliptic partial differ ential operators which are a consequence of the decay properties of their fundamental solutions these decay properties follow from spa tial spreading of the singularities of the solutions since solutions prop agate in directions conormal to the characteristic set of the operator this spreading can be related to nonzero curvatures of the characteristic set dispersive estimates for constant coefficient operators are closely related to the restriction theorem in harmonic analysis various types of dispersive estimates are known to be true for op erators such as the wave operator the schrodinger operator and the linear kdv see ginibre velo 4 keel tao 11 they have proved to be useful in the study of nonlinear problems as well as of problems with unbounded potentials more recently similar estimates have been obtained for wave op erators with variable coefficients beginning with the smooth case in kapitanskii 10 mockenhaupt seeger and sogge 14 up to operators with c 2 coefficients in smith 15 and tataru 21 23 similar results were obtained for the schrodinger equation in staffilani tataru 19 c 2 coefficients and in burq gerard tzvetkov 1 smooth coeffic ients in the variable coefficient elliptic case one should also mention sogge s l q

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

some constructions for balanced incomplete block designs with nested rows and columns summary a method of construction of balanced incomplete block designs with nested rows and columns is developed using difference techniques from which many infinite series of designs are obtained

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

on shortest paths in polyhedral spaces we consider the problem of computing the shortest path between two points in two or three dimensional space bounded by polyhedral surfaces in the 2 d case the problem is easily solved in time o n 2 log n in the general 3 d case the problem is quite hard to solve and is not even discrete we present a doubly exponential procedure for solving the discrete subproblem of determining the sequence of boundary edges through which the shortest path passes finally we consider a favorable special case of the 3 d shortest path problem namely that of finding the shortest path between two points along the surface of a convex polyhedron and solve it in time o n 3 log n

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

intrablock analysis of designs with multiple blocking criteria abstract a multidimensional block design mbd is an amalgamation of d 1 component block designs it may be represented as a d dimensional lattice with nodes where b s is the number of blocks in the sth component block design the j 1 jd node of the lattice may have h i j 1 jd 0 experimental units assigned to treatment i i 1 v js 1 b s s 1 d where v is the number of treatments if each node of the lattice is used the design is structurally complete if some of the nodes are empty the design is structurally incomplete particular mbd s may be specified through choices of the h i j 1 jd designs that may be cross classifications by blocking criteria nested classifications combinations of crossed and nested classifications or much less orderly multidimensional arrays the investigation of multidimensional block designs is accordingly very general the main results provide needed parameter estimators and the intrablock analysis of variance for a gener

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

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

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

asymptotic stability for a strongly coupled klein gordon system in an inhomogeneous medium with locally distributed damping abstract we consider a strongly coupled klein gordon system posed in an inhomogeneous medium with smooth boundary subject to a local damping distributed around a neighborhood of the boundary according to the geometric control condition we show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase space for this purpose refined microlocal analysis arguments are considered by exploiting ideas due to burq and gerard 16 by using sharp l p l q carleman estimates we prove a unique continuation property for coupled systems we also consider a strongly coupled system of wave equations with localized nonlinear damping acting only on one equation considering a compact riemannian manifold we show that the energy of the coupled system goes uniformly to zero

global nonexistence for abstract evolution equations with positive initial energy abstract in this paper we consider the problem of noncontinuation of solutions of the initial value problem for abstract evolution equations of the form pu tt q t u t a t u f t u t j 0 wherepandqare linear self adjoint operators anda t u andf t u are respectively a linear operator inu typically of differential type and a nonlinear driving force our principal concern is the noncontinuation or blow up of solutions when the initial energy is positive but appropriately bounded

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

stabilization and control for the nonlinear schrodinger equation on a compact surface in this paper we study the stabilization property and the exact controllability for the nonlinear schrodinger equation on a two dimensional compact riemannian manifold without boundary we use a pseudo differential dissipation the proofs are based on a result of propagation of singularities and on recent dispersion estimates strichartz type inequalities due to n burq p gerard and n tzvetkov

direct multiple shooting method for solving approximate shortest path problems we use the idea of the direct multiple shooting method presented by bock in proceedings of the 9th ifac world congress budapest pergamon press 1984 for solving optimal control problems to introduce an algorithm for solving some approximate shortest path problems in motion planning the algorithm is based on a direct multiple shooting discretization that includes a collinear condition a continuity condition type in the direct multiple shooting method multiple shooting structure and approximation conditions in the case of monotone polygons it is implemented by a c code and a numerical example shows that our algorithm significantly reduces the running time and memory usage of the system

multiple shooting approach for computing approximately shortest paths on convex polytopes abstract in this paper we use a multiple shooting approach in solving boundary value problems for ode to introduce a novel iterative algorithm for computing an approximate shortest path between two points on the surface of a convex polytope in 3d namely the polytope is partitioned into subpolytopes shooting points and a straightness condition are established the algorithm specifies how to combine shortest paths between shooting points in subpolytopes to become the required shortest path by the straightness condition in particular the algorithm does not rely on steiner points and graph tools on the entire polytope it is implemented in c and a comparison with agarwal har peled and karia s algorithm on the accurate construction of the shortest path is presented

some series constructions for minimal size equineighboured balanced incomplete block designs with nested rows and columns summary three infinite series for minimal size equineighboured balanced incomplete block designs with nested rows and columns are constructed for many parameter combinations the proposed equineighboured designs do not require more replicates and blocks than ordinary balanced incomplete block designs with nested rows and columns in the absence of neighbour properties available in the literature the designs can also be used as nested balanced incomplete block designs taking either the rows or the columns as subblocks with neighbour balance at all levels within the subblocks

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

uniform decay rate estimates for schrodinger and plate equations with nonlinear locally distributed damping on a compact n dimensional riemannian manifold m g we establish uniform decay rate estimates for the linear schrodinger and plate equations subject to an internal nonlinear damping locally distributed on the manifold our approach can be also employed for other equations provided that inverse inequality for the linear model occurs in the particular case of the wave equation where the well known geometric control condition gcc is equivalent to the observability inequality our method generalizes the results due to cavalcanti et al 2010 2009 9 10 regarding the optimal choice of dissipative regions

approximating shortest paths on a convex polytope in three dimensions given a convex polytope p with n faces in r3 points s t 6 p and a parameter 0 e 1 we present an algorithm that constructs a path on 6 p from s to t whose length is at most 1 e d p s t where d p s t is the length of the shortest path between s and t on 6 p the algorithm runs in o n log 1 e 1 e 3 time and is relatively simple the running time is o n 1 e 3 if we only want the approximate shortest pathdistance and not the path itself we also present an extension of thealgorithm that computes approximate shortest path distances from a givensource point on 6 p to all vertices of p

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

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

shortest paths help solve geometric optimization problems in planar regions the goal of this paper is to show that the concept of the shortest path inside a polygonal region contributes to the design of efficient algorithms for certain geometric optimization problems involving simple polygons computing optimum separators maximum area or perimeter inscribed triangles a minimum area circumscribed concave quadrilateral or a maximum area contained triangle the structure for the algorithms presented is as follows a decompose the initial problem into a low degree polynomial number of optimization problems b solve each individual subproblem in constant time using standard methods of calculus basic methods of numerical analysis or linear programming these same optimization techniques can be applied to splinegons curved polygons first a decomposition technique for curved polygons is developed this technique is substituted for triangulation in creating equally efficient curved versions of the algorithms for the shortest path tree ray shooting and two point shortest path

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

optimal blocked main effects plans with nested rows and columns and related designs optimal design is studied for factorial experiments in the nested row and column setting the approach is analogous to that of orthogonal latin squares main effects plans are found by the superimposition of one nested row and column design upon another conditions are stated for statistical orthogonality of the superimposed components resulting in orthogonal main effects plans and a number of constructions are given orthogonal collections of sets of latin squares are introduced all of the constructed designs are also optimal main effects plans for the row column and the unstructured block design settings further applications are as optimal multidimensional incomplete block designs and as optimal designs for multistage experimentation

some methods of construction of balanced incomplete block designs with nested rows and columns summary a number of methods of construction of balanced incomplete block designs with nested rows and columns are developed using the method of differences

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

the discrete geodesic problem we present an algorithm for determining the shortest path between a source and a destination on an arbitrary possibly nonconvex polyhedral surface the path is constrained to lie on the surface and distances are measured according to the euclidean metric our algorithm runs in time o n log n and requires o n2 space where n is the number ofedges ofthe surface afterwe run our algorithm the distance from the source to any other destination may be determined using standard techniques in time o log n by locating the destination in the subdivision created by the algorithm the actual shortest path from the source to a destination can be reported in time o k log n where k is the number of faces crossed by the path the algorithm generalizes to the case of multiple source points to build the voronoi diagram on the surface where n is now the maximum of the number of vertices and the number of sources

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

uniform decay rates for the wave equation with nonlinear damping locally distributed in unbounded domains with finite measure this paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation with nonlinear damping locally distributed u tt delta u a x g u t 0 hbox in omega times 0 infty subject to dirichlet boundary conditions where omega subset mathbb r n n geq 2 is an unbounded open set with finite measure and unbounded smooth boundary partial omega gamma the function a x responsible for the localized effect of the dissipative mechanism is assumed to be nonnegative and essentially bounded and in addition a x geq a 0 0 hbox a e in omega where omega omega cup x in omega x r r 0 and omega is a neighborhood in omega of the closure of partial omega cap b r where b r x in omega x r

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