modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

baire s category and the bang bang property for evolution differential inclusions of contractive type abstract the baire category method is employed in order to establish that the bang bang property holds for a class of evolution differential inclusions of contractive type in reflexive and separable real banach spaces

necessary optimality conditions for infinite dimensional state constrained control problems abstract this paper is concerned with first order necessary optimality conditions for state constrained control problems in separable banach spaces assuming inward pointing conditions on the constraint we give a simple proof of pontryagin maximum principle relying on infinite dimensional neighboring feasible trajectories theorems proved in 20 further we provide sufficient conditions guaranteeing normality of the maximum principle we work in the abstract semigroup setting but nevertheless we apply our results to several concrete models involving controlled pdes pointwise state constraints as positivity of the solutions are allowed

the minimum time function for semilinear evolutions we study the bellman equation for the minimum time problem associated with a semilinear evolution system from the point of view of contingent solutions for this purpose new contingent derivatives are defined which involve functions instead of vectors as directions our analysis is based on flow invariance results for appropriate differential inclusions

detecting dose response with contrasts analyses of dose response studies should separate the question of the existence of a dose response relationship from questions of functional form and finding the optimal dose a well chosen contrast among the estimated effects of the studied doses can make a powerful test for detecting the existence of a dose response relationship a contrast based test attains its greatest power when the pattern of the coefficients has the same shape as the true dose response relationship however it loses power when the contrast shape and the true dose response shape are not similar thus a primary test based on a single contrast is often risky two or more appropriately chosen contrasts can assure sufficient power to justify the cost of a multiplicity adjustment an example shows the success of a two contrast procedure in detecting dose response which had frustrated several standard procedures

a viability theorem for set valued states in a hilbert space abstract applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact possibly non convex sets rather than vectors this leads to evolutions in a basic set which can be supplied with a metric like the well established pompeiu hausdorff distance but it does not have an obvious linear structure this article extends differential inclusions with state constraints to compact valued states in a separable hilbert space h the focus is on sufficient conditions such that a given constraint set of compact subsets is viable a k a weakly invariant our main result extends the tangential criterion in the well known viability theorem usually for differential inclusions in a vector space to the metric space of non empty compact subsets of h

characterization of dose response relationships inferred by statistically significant trend tests summary a method is proposed for classifying various experimental outcomes associated with statistically significant trend tests according to a set of results of sequential testing within a family of closed under intersections one sided tests the intent of the procedure is to characterize the general shape of implied dose response relationships taking care neither to inflate the false positive type i error rate by overtesting nor to sacrifice power by overadjusting for mulitple comparisons

a new product integral representation for differential equations in separable banach spaces abstract letxbe a separable banach space consider the problem formula where the continuous functionf 0 x xis locally lipschitz continuous inx uniformly inton bounded intervals and continuous intuniformly w r t x the product integral formula x t lim n i 0 n i t n f i t n x 0 0 t t max for the solutionx t of d has been shown to converge we also show that iff t is lipschitz continuous onxwith constantl then the mappingx0 x t is lipschitz continuous with constanteltfor anyt 0 this formula has been recently developed for differential inclusions inrnby wolenski but the infinite dimensional case is considerably more involved

relaxation of control systems under state constraints in this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control in particular we show that the mangasarian fromowitz constraint qualification allows us to rewrite constrained systems as differential inclusions with locally lipschitz right hand side then the filippov wazewski relaxation theorem may be applied to show that ordinary solutions are dense in the set of relaxed solutions if besides agreeing with the above constraints the state has to remain in a control independent set k then the mangasarian fromowitz condition cannot hold this case is investigated as well by means of a condition on the feasible velocities on the boundary of k

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

multiple test procedures in clinical dose finding studies abstract test procedures in clinical dose finding studies are considered when it can be assumed that increasing dose levels lead to a larger or at least equal efficacy if one is interested in various comparisons within the set of dose levels one arrives at a problem of multiple testing against ordered alternatives some multiple test procedures controlling the multiple level of significance are compared in a simulation study it follows that a simple procedure that only uses comparisons between neighboring dose levels can be recommended the degree of approximation of this bonferroni type procedure is investigated under normal assumptions

a priori estimates for operational differential inclusions we prove a set valued gronwall lemma and a relaxation theorem for the semilinear differential inclusion x ax f t x x 0 x0 where a is the infinitesimal generator of a c0 semigroup on a separable banach space x and f 0 t x x is a set valued map this allows us to investigate infinitesimal generators of reachable sets and variational inclusions the results are applied to a semilinear optimal control problem with end point constraints

relaxation theorem for the evolution differential inclusions abstract in this paper we use an improved version of baire category method to prove the existence of solutions to the evolution differential inclusion ax ext f t x under the hausdorff noncompactness measure condition we also obtain a density result for the evolution differential inclusion

lower semi continuity of the solution set for semilinear differential inclusions abstract in this paper we provide sufficient conditions for the solution set of a semilinear differential inclusion to be lower semi continuous we give an application to the propagation of continuity of the minimum time function associated with the given differential inclusion and the target zero

the maximum principle for an optimal solution to a differential inclusion with end points constraints we derive pontryagin s maximum principle for a general optimal control problem using the set valued version of variational equation we achieve this aim by exploiting an adequate differential calculus of set valued maps furthermore the calmness condition is replaced by a surjectivity condition involving reachable sets of the set valued linearization of the initial control problem duality then provides both the adjoint differential inclusion and the maximum principle

local controllability and infinitesimal generators of semigroups of set valued maps we study the semigroup properties of reachable sets of a differential inclusion x in f x using the derivative of the set valued map which associates to each initial state the set of solutions the results are applied to the local controllability problem

contingent cones to reachable sets of control systems high order necessary conditions for optimality for an optimal control problem are studied via properties of contingent cones to reachable sets along the optimal trajectory it is shown that the adjoint vector of pontryagin s maximum principle is normal to the set of variations of reachable sets results are applied to study optimal control problems for dynamical systems described by 1 closed loop control systems 2 nonlinear implicit systems 3 differential inclusions 4 control systems with jumps