fixed width multiple comparison procedures using common random numbers for steady state simulations abstract suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance we consider the problem of running a two stage simulation using common random numbers to construct fixed width confidence intervals for two multiple comparison problems under the assumptions that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem and that the asymptotic covariance matrix satisfies a condition known as sphericity we prove that our confidence intervals are asymptotically valid as the desired half width of the confidence intervals tend to zero we develop both absolute and relative width confidence intervals empirical results are presented indicating the procedures robustness to violations of the sphericity assumption

is the selected population the best random variables x i sim n theta i 1 i 1 2 cdots k are observed suppose x s is the largest observation if the inference theta s max i neq s theta i is made whenever x s max i neq s x i c then the probability of a false inference is maximized when two theta i are equal and the rest are infty equivalently the inference can be made whenever a two sample two sided test for difference of means based on the largest two observations would reject the hypothesis of no difference the result also holds in the case of unknown estimable common variance and in fact for location families with monotone likelihood ratio

chow groups of projective varieties of very small degree see 12 5 and the references given there these facts together with various conjectures on the cohomology and chow groups of algebraic varieties suggest that the chow groups of x might satisfy chl x q chl pk q q for l 1 compare with remark 5 6 and corollary 5 7 this is explicitly formulated by v srinivas and k paranjape in 16 conjecture 1 8 the chain of reasoning goes roughly as follows suppose x is smooth one expects a good filtration 0 f j 1 f j f 0 ch x x q whose graded pieces f f l 1 are controlled by h2j l x x see 10 according to grothendieck s generalized conjecture 8 the groups h x should be generated by the image under the gysin morphism of the homology of a codimension subset together with the classes coming from p applying this to the diagonal in x x should then force the triviality of the chow groups in the desired range for zero cycles the conjecture follows from roitman s theorem see 17 and 18

on the energy spectrum and parameter spaces of classicalcp n models it is known that a large class of smooth solutions ofcpn models can be constructed starting from holomorphic maps of an algebraic curve into complex projective spaces here we apply results from algebraic geometry to describe the energy spectrum and the parameter spaces for such models

tangent cones to discriminant loci for families of hypersurfaces a deformation of a variety with nonisolated hypersurface singularities such as a projective hypersurface or a theta divisor of an abelian variety determines a rational map of the singular locus to projective space and the resulting projective geometry of the singular locus describes how the singularities propagate in the deformation the basic principle is that the projective model of the singular locus is dual to the tangent cone to the discriminant of the deformation a detailed study of the method which emerged from interpreting andreotti mayer s work on theta divisors in terms of schlessinger s deformation theory of singularities is given along with examples applications and multiplicity formulas introduction this paper is about the geometry associated to deformations of nonisolated hypersurface singularities the basic principle is that a deformation of a hypersurface determines a projective model of the singular locus whose dual variety is the projectivized tangent cone to the discriminant this includes an infinitesimal form of bertini s theorem for a linear system of divisors and a converse to andreotti mayer s condition for double points of theta divisors now we describe the main results more precisely working in the category of complex analytic spaces let x be a space which can locally be written as a hypersurface of a nonsingular space and let x s be a deformation of x ir 1 0 then t1 the sheaf of first order deformations of x is a line bundle on sg x the singular locus of x and ir determines a kodaira spencer linear map to s k h0 t1 i e a linear system on the singular locus if x and s are nonsingular this linear system has no base locus and the corresponding morphism sg x pto s satisfies 0 p ir p tpx for p e sg x hence is called the gauss map of ir for a projective hypersurface of degree d x is the d fold veronese map restricted to the singular locus and for the theta divisor of an abelian variety 0 is the rational map assigning to a double point its quadric tangent cone assuming the restriction of ir to the critical locus c c x is proper consider the discriminant locus d ir c with its reduced analytic structure in addition to the above suppose finally that c is nonsingular of the expected codimension in x duality theorem there is a finite collection of 8ubvarietie8 zz of sg x which is intrinsic to the analytic space sg x and includes the irreducible components received by the editors march 31 1987 the contents of this paper were presented october 18 1986 by the first author in the special session on singularities and algebraic geometry at the charlotte north carolina meeting of the ams 1980 mathematics subject classification 1985 revision primary 14d15 14n05 secondary 32g11 53c57 d1988 american mathematical society 0002 9947 88 1 00 25 per page

partial regularity and amplitude the author continues the study of frobenius amplitude introduced in an earlier paper and compares this to various other positivity notions these are applied to deduce vanishing theorems a refinement of castelnuovo mumford regularity is also given

simultaneous confidence intervals for all distances from the best in practice comparisons with the best are often the ones of primary interest in this paper parametric and nonparametric simultaneous upper confidence intervals for all distances from the best are derived under the location model their improvement upon the results of bechhofer 1954 gupta 1956 1965 fabian 1962 and desu 1970 in the parametric case is discussed in the nonparametric case no comparable confidence statements were available previously

simultaneous confidence regions for multivariate bioequivalence demonstrating bioequivalence of several pharmacokinetic pk parameters such as auc and cmax that are calculated from the same biological sample measurements is in fact a multivariate problem even though this is neglected by most practitioners and regulatory bodies who typically settle for separate univariate analyses we believe however that a truly multivariate evaluation of all pk measures simultaneously is clearly more adequate in this paper we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation some of them work well for idealised scenarios but break down when faced with real data challenges such as unknown variance and correlation among the pk parameters we study the shapes of the confidence regions resulting from different methods discuss how marginal simultaneous confidence intervals for the individual pk measures can be derived and illustrate the application to data from a trial on ticlopidine hydrochloride an r package is available

on nef subvarieties abstract in this paper we first study generalizations of fujita vanishing theorems for q ample divisors we then apply them to study positivity of subvarieties with nef normal bundle in the sense of intersection theory after ottem s work on ample subschemes we introduce the notion of a nef subscheme which generalizes the notion of a subvariety with nef normal bundle we show that restriction of a pseudoeffective resp big divisor to a nef subvariety is pseudoeffective resp big we also show that ampleness and nefness are transitive properties we define the weakly movable cone as the cone generated by the pushforward of cycle classes of nef subvarieties via proper surjective maps this cone contains the movable cone and shares similar intersection theoretic properties with it thanks to the aforementioned properties of nef subvarieties on the other hand we prove that if y x is an ample subscheme of codimension r and d y is q ample then d is q r ample this is analogous to a result proved by demailly peternell schneider and kuronya

model robust test plans with applications in accelerated life testing we study a criterion based on a weighted asymptotic sample ratio asr that yields model robust test plans with relatively low asrs under different models we apply the criterion to accelerated life test planning in which interest lies in estimating life quantiles and there is uncertainty as to whether the weibull or the lognormal model best describes the lifetime distribution we use the criterion to determine optimum and best 4 2 1 allocation plans we compare the asrs of our test plans with the optimum and best 4 2 1 allocation test plans when the model is specified incorrectly test plans are evaluated in terms of asrs expected numbers of failures and extrapolation to use stress we illustrate the criterion in a practical situation

graphical procedures for multiple comparisons under general dependence abstractit has been more than half a century since tukey first introduced graphical displays that relate nonoverlap of confidence intervals to statistically significant differences between parameter estimates in this article we show how tukey s graphical overlap procedure can be modified to accommodate general forms of dependence within and across samples we also develop a procedure that can be used to more effectively resolve rankings within the tails of the distributions of parameter values thereby generalizing existing methods for multiple comparisons with the best we show that these new procedures retain the simplicity of tukey s original procedure while maintaining asymptotic control of the familywise error rate under very general conditions simple examples are used throughout to illustrate the procedures supplementary materials for this article are available online

ampleness and connectedness in complex g p this paper determines the ampleness of the tangent bundle of the complex homogeneous space g p by calculating the maximal fibre dimension of the desingularization of a nilpotent subvariety of the lie algebra of g

the regularity of tor and graded betti numbers let s k x1 xn let a b be finitely generated graded s modules and let m x1 xn s we give bounds for the regularity of the local cohomology of tork a b in terms of the graded betti numbers of a and b under the assumption that dim tor1 a b 1 we apply the results to syzygies grobner bases products and powers of ideals and to the relationship of the rees and symmetric algebras for example we show that any homogeneous linearly presented m primary ideal has some power equal to a power of m and if the first n 1 2 steps of the resolution of i are linear then i 2 is a power of m

a refined brill noether theory over hurwitz spaces let f c rightarrow mathbb p 1 be a degree k genus g cover the stratification of line bundles l in mathrm pic d c by the splitting type of f l is a refinement of the stratification by brill noether loci w r d c we prove that for general degree k covers these strata are smooth of the expected dimension in particular this determines the dimensions of all irreducible components of w r d c for a general k gonal curve there are often components of different dimensions extending results of pflueger adv math 312 46 63 2017 and jensen and ranganathan brill noether theory for curves of a fixed gonality arxiv 1701 06579 2017 the results here apply over any algebraically closed field

nonemptiness of symmetric degeneracy loci let v be a rank n vector bundle on a d dimensional complex projective scheme x assume that v is equipped with a quadratic form with values in a line bundle l and that s 2 v l is ample suppose that the maximum rank of the quadratic form at any point of x is r 0 the main result of this paper is that if d n r the locus of points where the rank of the quadratic form is at most r 1 is nonempty we give some applications to subschemes of matrices and to degeneracy loci associated to embeddings in projective space the paper concludes with an appendix on gysin maps the main result of the appendix which may be of independent interest identifies a gysin map with the natural map from ordinary to relative cohomology

retrospective optimization of mixed integer stochastic systems using dynamic simplex linear interpolation abstract we propose a family of retrospective optimization ro algorithms for optimizing stochastic systems with both integer and continuous decision variables the algorithms are continuous search procedures embedded in a ro framework using dynamic simplex interpolation rodsi by decreasing dimensions corresponding to the continuous variables of simplex the retrospective solutions become closer to an optimizer of the objective function we present convergence results of rodsi algorithms for stochastic convex systems numerical results show that a simple implementation of rodsi algorithms significantly outperforms some random search algorithms such as genetic algorithm ga and particle swarm optimization pso

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

multiple comparisons with the best treatment abstract let 1 2 k be k 2 sources of observations treatments populations and suppose the goodness of treatment i is characterized by the size of an unknown real valued parameter i let k max1 i k i if i is preferred to j when i j the parameters i k i i 1 2 k reflect in an inverse sense the goodness of each treatment relative to the best treatment a general technique for obtaining simultaneous confidence intervals on the i is demonstrated with several examples this technique can be applied in any setting where comparison with control intervals can be computed regarding any j as the control these results have special importance in ranking and selection problems in that the process of generating upper bounds on the i generates traditional confidence statements of both the indifference zone and the subset selection schools simultaneously as established by hsu 1981

estimating fatigue curves with the random fatigue limit model in a fatigue limit model units tested below the fatigue limit also known as the threshold stress theoretically will never fail this article uses a random fatigue limit model to describe a the dependence of fatigue life on the stress level b the variation in fatigue life and c the unit tounit variation in the fatigue limit we fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions small quantiles of the life distribution are often of interest to designers lower confidence bounds based on likelihood ratio methods are obtained for such quantiles to assess the fits of the model we construct diagnostic plots and perform goodness of fit tests and residual analyses

limit linear series basic theory in this paper we introduce techniques for handling the degeneration of linear series on smooth curves as the curves degenerate to a certain type of reducible curves curves of compact type the technically much simpler special case of 1 dimensional series was developed by beauville 2 knudsen 21 23 harris and mumford 17 in the guise of admissible covers it has proved very useful for studying the moduli space of curves the above papers and harris 16 and the simplest sorts of weierstrass points diaz 4 with our extended tools we are able to prove for example that in this paper we present the basic theory of limit linear series necessary for proving these results the results themselves will be taken up in our forthcoming papers 8 12 simpler applications not requiring the tools developed in this paper but perhaps clarified by them have already been given in our papers 5 7

chern schwartz macpherson classes and the euler characteristic of degeneracy loci and special divisors this concept overlaps a large family of interesting varieties for example the varieties of special divisors studied in section 3 several authors have worked out explicit formulas for the euler characteristic of dr 9 in terms of different cohomological and numerical invariants under the assumption that x is nonsingular and v is appropriately general for instance if 0 is a section of a vector bundle then the formulas for the euler characteristic x do fp were given by hirzebruch h and navarro aznar n if dr is a curve or a surface in a nonsingular x some explicit formulas for x dr v were given by harris and tu h t in terms of the chern classes of e f and x but under the extra assumption dr 1 v 0 which implies that dr q is nonsingular in loc cit the authors also posed the problem of finding a general formula for x dr o if such exists under the assumption dr 1 0 or even stronger without this assumption the first problem was solved positively by the second named author prl proposition 5 7 by the use of polynomials universally supported on degeneracy

algebraic integrability of foliations with numerically trivial canonical bundle given a reflexive sheaf on a mildly singular projective variety we prove a flatness criterion under certain stability conditions this implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second chern class does not vanish combined with the recent works of druel and greb guenancia kebekus this establishes the beauville bogomolov decomposition for minimal models with trivial canonical class

constrained simultaneous confidence intervals for multiple comparisons with the best for comparing k treatment effects 01 02 ok often the parameters of primary interest are 0i maxeioi0 i 1 k in this article we develop constrained 100p two sided simultaneous confidence intervals for 0i maxj i0j which we refer to as constrained mcb intervals it turns out that the lower bounds of the intervals imply indifference zone selection inference and the upper bounds of these intervals imply subset selection inference each given at the same confidence level 100p as mcb we also extend our

subvarieties with partially ample normal bundle we show that local complete intersection subvarieties of smooth projective varieties which have partially ample normal bundle possess the g2 property this generalizes results of hartshorne and b descu schneider

submanifolds with splitting tangent sequence a theorem of van de ven states that a projective submanifold of complex projective space whose holomorphic tangent bundle sequence splits holomorphically is necessarily a linear subspace note that the sequence always splits differentiably but in general not holomorphically we are interested in generalizations to the case when the ambient space is a homogeneous manifold different from projective space quadrics grassmannians or abelian manifolds for example split submanifolds are closely related to totally geodesic submanifolds

sequential implementation of stepwise procedures for identifying the maximum tolerated dose this article considers the problem of finding the maximum tolerated dose mtd of a drug in human trials the mtd is defined as the maximum test dose with toxicity probability less than or equal to a target toxicity rate we adopt the multiple test framework with step down tests used in an escalation stage and step up tests used in a deescalation stage to allow sequential dose assignments for ethical purposes by formulating the estimation problem as a testing problem the proposed procedures formally control the error probability of selecting an unsafe dose in addition we can control the probability of correctly selecting the mtd under a parameter subspace where no toxicity probability lies in an interval bracketed by the target toxicity rate and an unacceptably high toxicity rate the so called indifference zone this frequentist property which is currently lacking in the conduct of dose finding trials in humans is appealing from a regulatory standpoint we give the general expressions of the se

a comparison of accelerated life test plans for weibull and lognormal distributions and type i censoring previous work on planning accelerated life test plans for the weibull and lognormal distributions has concentrated on optimum test plans that minimize the variance of some specified estimator however these test plans use tests at only two levels of stress and thus have serious practical limitations this article compares optimum test plans and some compromise test plans with respect to additional criteria including a the ability to detect departures from the assumed stress life relationship and b robustness to departures from the assumptions used in determining the plans the comparisons are based on the large sample properties of maximum likelihood estimators and the test plans are compared over a range of practical testing situations the comparisons suggest some general rules for planning accelerated life tests

ulrich sheaves and higher rank brill noether theory abstract we show that the existence of an ulrich sheaf on a projective variety x p n is equivalent to the solution of a possibly higher rank brill noether problem for a curve on x that is rarely general in moduli in addition we exhibit a large family of curves for which this brill noether problem admits a solution and we show that existence of an ulrich sheaf for a finite morphism of smooth projective varieties of any dimension implies sharp numerical constraints involving the degree of the map and the ramification divisor

linked symplectic forms and limit linear series in rank 2 with special determinant abstract we generalize the prior linked symplectic grassmannian construction applying it to prove smoothing results for rank 2 limit linear series with fixed special determinant on chains of curves we apply this general machinery to prove new results on nonemptiness and dimension of rank 2 brill noether loci in a range of degrees

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

linear series with cusps and n fold points a linear series v s on a curve x has an n fold point along a divisor d of degree n if dim vr h x d dim v 1 the linear series has a cuspofordere atapoint p if dim frch0 xs e l p dim z l linear series with cusps and n fold points are shown to exist if certain inequalities are satisfied the dimensions of the families of linear series with cusps are determined for general curves introduction throughout this paper we work over the complex numbers c let x be a smooth projective curve of genus g a gd on x is a linear series of degree d and dimension r on x i e a pair v s consisting of a line bundle s of degree d on x and an r l dimensional subspace vof h x s when p g r d g r 1 g r d o then x has gd s and the family of gd s on x forms a projective scheme gd x of dimension p g r d furthermore if x is general in moduli then gd x is smooth of dimension p g r d acgh definitic n if d is an effective divisor of degree n 2 on x we say that a gd v s has an n fold point along d if dim v n h x 2 d r we say that a gd has a cusp of order e at a point p if it has an e l fold point along the divisor e 1 p the aim of this paper is to prove the following i if g n p g r d n 1 r n o and p g r 1 d n o then there exists a gd on x with an n fold point along some divisor d of degree n ii if p g r d n 1 r o p g r 1 d n 0 and d is any divisor of degree n on x then there exists a gd on x with an n fold point along d iii if p g r d er 1 0 and p g r 1 d e 1 o then there exists a gd on x with a cusp of order e at some point p iv if x is general in moduli then the family of gd s on x with a cusp of order e has dimension p g r d er 1 if it is nonempty assertion iv has been proved independently by marc coppens c it is easy to see that the hypotheses p g r 1 d n 0 in assertions i and ii and p g r 1 d e 1 0 in assertion iii are necessary if x is general in moduli received by the editors january 20 1987 1980 mclthemcltlcs subject clclsslficcltion 1985 revision primary 14h10 1987 american mathematical society 0002 9947 87 1 00 25 per page

vanishing theorems for ample vector bundles the main result of this article is a general vanishing theorem for the cohomology of tensorial representations of an ample vector bundle on a smooth complex projective variety in particular we extend classical theorems of griffiths and le potier to the whole dolbeault cohomology prove a variant of an uncorrect conjecture of sommese and answer a question of demailly as an application we prove conjectures of debarre and kim for branched coverings of grassmannians and extend a well known barth lefschetz type theorem for branched covers of projective spaces due to lazarsfeld we also obtain new restriction theorems for certain degeneracy loci

a comparison theorem if x is complete these maps are isomorphisms but in general they are not this ibllows from the following standard example due to serre 4 p 232 one takes a certain ip 1 bundle x over a non singular elliptic curve and removes a curve y the result is a non singular algebraic surface u x y on which every regular function is constant h the associated complex space ua of u is a stein naanifold biholomorphic to x where denotes tl 0 4 in particular we see that in this example the comparison map o h u gv h gv is not an isomorphism the point is that in serre s example the degree of the normal bundle nr x of y in x is zero this suggests the following problem let x be an algebraic variety over c ycx a closed subvariety defined by the ideal j find sufficient conditions on the normal sheaf nr x of y in x such that for every coherent algebraic sheaf f on x y the comparison maps h x y van

a new derivation of eigenvalue inequalities for the multinomial distribution abstract we consider the covariance matrix of the multinomial distribution we suggest a new derivation of inequalities for the eigenvalues of this matrix using a classical result on the product of two positive semi definite matrices

the surface c c on jacobi varieties and 2nd order theta functions preprint enviat per a la seva publicacio en una revista cientifica acta mathematica volume 157 1986 1 22 https projecteuclid org euclid acta 1485890436

theoremes de connexite pour les produits d espaces projectifs et les grassmanniennes we give a numerical condition on the images of two morphisms to a grassmannian or a product of projective spaces that ensures that their fibered product is connected thereby extending connectedness results of fulton and hansen this result is valid over any algebraically closed field it yields a condition on the class of an irreducible subvariety of a grassmannian that implies that it is simply connected this applies in particular to fano varieties of certain hypersurfaces in a projective space

theory for optimal test plans for the random fatigue limit model this article presents methodology for planning life tests based on the random fatigue limit model rflm the rflm describes the relationship between fatigue life and the applied load in the presence of fatigue limits a standardization of the rflm is presented and corresponding expressions for the elements of the fisher information matrix are given different test plan criteria that express various objectives that the practitioner may have in conducting experiments under the rflm are discussed these criteria include estimation of life quantiles estimation of stress strain levels that yield a specific life quantile estimation of fatigue limit quantiles and d and ds optimality equivalence theorems used to verify optimality of test plans are also presented the methods are sufficiently general so they can be applied to criteria based on any function of the model parameters they are demonstrated using a nickel base superalloy experiment

codimension and connectedness of degeneracy loci over local rings we deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules f m rightarrow n over a local noetherian ring a mathfrak m we show for instance that the expected determinantal bounds on the dimension of the t th degeneracy locus of f hold if f in mathfrak m mathrm hom m n and that this degeneracy locus is connected in the expected dimension provided hat a is a domain

using common random numbers and control variates in multiple comparison procedures this paper considers the determination of the relative merits of two or more system designs via stochastic simulation experiments by constructing simultaneous interval estimates of certain differences in expected performance tukey s all pairwise comparisons procedure hsu s multiple comparisons with the best procedure and dunnett s multiple comparisons with a control procedure are standard methods for making such comparisons we propose refinements for all three procedures through the use of two variance reduction techniques common random numbers and control variates we show that the proposed procedures are better than the standard multiple comparison procedures in the sense that they have a larger probability of containing the true difference and at the same time not containing zero when a difference exists

algebraic cycles on prym varieties this article proposes a generalization of tautological rings introduced by beauville and moonen for jacobians the main result is that under certain hypotheses the special subvarieties of prym varieties are algebraically equivalent and their classes belong to the tautological ring

a tropical proof of the brill noether theorem we produce brill noether general graphs in every genus confirming a conjecture of baker and giving a new proof of the brill noether theorem due to griffiths and harris over any algebraically closed field

algebraicity of formal varieties and positivity of vector bundles we propose a positivity condition for vector bundles on a projective variety and prove an algebraicity criterion for formal schemes then we apply the algebraicity criterion to the study of formal principle in algebraic geometry

on the existence of certain families of curves introduction 25 w 1 generalities on families of curves in ip 28 w the map 0 d 33 w 3 the number of moduli of a family 40 w 4 plane curves existence of families with the expected number of moduli 43 w 5 smoothing certain reducible curves in ip r r 3 47 w 6 curves in ip r 3 existence of families with the expected number of moduli 52 w curves in ip3 a more general existence theorem 55

using common random numbers for indifference zone selection and multiple comparisons in simulation we present a general recipe for constructing experiment design and analysis procedures that simultaneously provide indifference zone selection and multiple comparison inference for choosing the best among k simulated systems we then exhibit two such procedures that exploit the variance reduction technique of common random numbers to reduce the sample size required to attain a fixed precision one procedure is based on the bonferroni inequality and is guaranteed to be statistically conservative the other procedure is exact under a specific dependence structure but may be slightly liberal otherwise both are easy to apply requiring only simple calculations and tabled constants we illustrate the procedures with a numerical example

a path length inequality for the multivariate t distribution with applications to multiple comparisons abstract this article presents a new inequality for the multivariate t distribution which implies a new method for multiple comparisons whose foundation rests on a recent inequality due to naiman the new method is promising in view of the fact that it utilizes information estimator intercorrelations ignored by the most widely used multiple comparison methods yet is not computationally prohibitive requiring only the numerical evaluation of a single one dimensional integral in this article the validity of the new method in the normal theoretic general linear model is established and efficiency studies relative to the methods of scheffe bonferroni sidak and hunter worsley are presented the new method is shown to always improve on scheffe s method the new method is also shown to perform well that is to lead to a smaller critical point than its competitors with low degrees of freedom but the method is not as efficient as the hunter worsley method for high degrees of freedom in addition the me

on the convergence of formal equivalence between embeddings let j x w denote the morphism embedding the compact complex manifold x into the manifold w the formal principle holds for j if given any other embedding j x w together with a formal isomorphism between j and j there is an actual isomorphism between j and j for definitions see 2 1 for instance the formal principle holds for exceptional curves of the first kind on surfaces on the other hand arnold 1 recently gave the example of an embedding with a topologically trivial normal bundle of an elliptic curve into a surface for which the formal principle fails a number of articles dealing with the formal principle in algebraic as well as in analytic geometry have been published nirenberg spencer 19 grauert 7 hironaka rossi 16 griffiths 9 10 hironaka 14 hironaka matsumura 15 hartshorne 11 artin 2 gieseker 6 moreover a few weeks after the present work was written commichaugrauert 23 proved that the formal principle holds under an assumption one positivity which seems much weaker than ours we hope that the present article retains some interest because of its method which may work in the algebraic and or singular case we are interested in the complex analytic case in the situation where the normal bundle is fairly positive or non negative this means there are enough submanifolds in w around x we propose a conjecture and then give our result we let d denote the germ of the space of submanifolds near x an open subset in the douady space ud denote the universal submanifold of d x w and lid denote the projection from ud into w

divisors on general curves and cuspidal rational curves in t roduc t ion 371 0 pre l iminar ies 377 1 a pl i icker formula 378 2 d imens iona l t ransversa l i ty 380 3 d i m e n s i o n of families of r a t iona l curves with fixed degree and ass igned cusps in a project ive space 383 4 l inear series on curves with universa l s ingular i t ies 386 5 l inear series and project ive embedd ings of general curves 391 6 embedd ings of general cuspidal curves 400 7 degenera t ion of schuber t in tersect ions some special cases 403 8 degene ra t ion of schuber t in tersect ions ma in results 407 9 g c is reduced for general cuspidal r a t iona l c 414

the severi bound on sections of rank two semistable bundles on a riemann surface let c be a compact riemann surface of genus g 1 for a line bundle l on c of degree d with 0 d 2g 2 the classical theorem of clifford states that the dimension h 0 l of the space of global sections of l satisfies h 0 l d 2 1 it is also quite easy to list the cases which give equality apart from the trivial bundle and the canonical bundle these exist only on hyperelliptic curves this theorem can be extended to a semistable bundle e on c of rank n and degree d with 0 d n 2g 2 when it states that h 0 e d 2 n now let e be a semistable bundle of rank 2 in this case the authors obtain a more refined result depending on the segre invariant s e which is defined as the minimum value of dege l degl for l a line subbundle of e in particular the semistability condition becomes s e 0 the main theorem is that if dege d and s d 4g 4 s then h 0 e d s 2 where 1 or 2 note that d s is always even in a previous paper e arrondo and the second author conjectured this inequality with 1 with a small number of exceptions similar to those for rank 1 however this is not correct and 2 is sometimes necessary the authors call the bundles which attain this bound severi bundles the number is obtained as follows we define polynomials k r n n the krawtchouk polynomials by means of the generating function r k r n n z r 1 z n 1 z n n let r d s 2 1 then we can take 1 if k r g 2g s 0 and 2 otherwise the connection with krawtchouk polynomials is intriguing since these are used in coding theory and recent work of t johnsen has established links between coding theory and semistable bundles of rank 2 on riemann surfaces these links make essential use of the segre invariant s the key to the proof of the inequality is the following lemma let e be a bundle of rank 2 and degree d on a curve of genus g having at least r 1 g independent sections if k r g 2g 2r 2 d 0 then there is a nonzero section of e vanishing at r points this is proved using a computation of chern classes formal properties of k r n n and the porteous formula the authors give examples to show that for any allowable values of g s d the bound 1 can be attained in fact on a hyperelliptic curve a good deal is known about the vanishing of k r n n thus providing a restricted list of candidates for the invariants of severi bundles but these values do not all arise from actual bundles the severi bundles with d s 0 are all known and the authors compute those with d s 2 and d s 4 in particular the bundles obtained by i grzegorczyk ulam quart 3 1996 no 2 41 ff approx 3 pp electronic are severi bundles with g 5 s 4 d 8 the authors also obtain sharp bounds for the numbers of independent sections of non semistable bundles

the brill noether curve and prym tyurin varieties we prove that the jacobian of a general curve c of genus g 2a 1 with a ge 2 can be realized as a prym tyurin variety for the brill noether curve w 1 a 2 c as consequence of this result we are able to compute the class of the sum of secant divisors of the curve c embedded with a complete linear series g a 1 3a 2

limit linear series and ranks of multiplication maps we develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus 1 curves we use this approach to prove a purely elementary criterion for proving cases of the maximal rank conjecture and then apply the criterion to several ranges of cases giving a new proof of the case of quadrics and also treating several families in the case of cubics our proofs do not require restrictions on direction of approach so we recover new information on the locus in the moduli space of curves on which the maximal rank condition fails

the connectedness of symmetric and skew symmetric degeneracy loci even ranks a degeneracy locus is the set of points where a vector bundle map has rank at most a given integer such a set is symmetric or skew symmetric according as whether the vector bundle map is symmetric or skew symmetric we prove a connectedness result first conjectured by fulton and lazarsfeld for skew symmetric degeneracy loci and for symmetric degeneracy loci of even ranks

testing for the supremacy of a multinomial cell probability tests for the supremacy of a multinomial cell probability are developed the tested null hypothesis states that a particular cell of interest is not more probable than all others rejection of this null leads to the conclusion that the cell of interest has a strictly greater probability than all other cells the null hypothesis constrains the multinomial probability vector to a nonconvex region that is a union of closed convex cones the likelihood ratio test for this problem is derived and shown to be equivalent to an intersection union test the least favorable configuration of the multinomial probability vector in the null parameter space is derived and the limiting null distribution of the test statistic that is stochastically greatest is shown to be a mixture of point mass at zero and a chi square distribution with a single degree of freedom asymptotic and valid finite sample testing procedures are proposed and examined via a simulation study and the analysis of two datasets the proposed procedure