odd order brauer manin obstruction on diagonal quartic surfaces abstract we determine the odd order torsion subgroup of the brauer group of diagonal quartic surfaces over the field of rational numbers we show that a non constant brauer element of odd order always obstructs weak approximation but never the hasse principle

overview and comparison of localic and fixed basis topological products this paper studies localic products traditional topological products and l topological products and gives a complete outline of the localic product comparisons of localic and l topological products are generally absent in the literature and this paper answers longstanding open questions in that area as well as provides a complete proof of the classical comparison theorem for localic and traditional topological products this paper contributes several l valued comparison theorems one of which states the localic and l topological products of l topologies are order isomorphic if and only if the localic product is l spatial providing l is itself spatial and the family of l topological spaces is prime separated these last two conditions always hold in the traditional setting capturing the traditional comparison theorem as a special case and the prime separation condition is satisfied by important lattice valued examples that include the fuzzy real line and the fuzzy unit interval for l any complete boolean algebra and the alternative fuzzy real line and fuzzy unit interval for l any semi frame separation conditions help control the sloppy behavior of the l topological product when l 2 and several separation conditions are studied in this context and it should be noted that localic products have a point free version of the product separation condition considered in this paper the traditional comparison theorem is carefully proved both to fill gaps in the extant literature and to motivate the l valued comparison theorem quoted above and reveal the special role played by cross sums of prime l open subsets en route characterizations are given of prime l open subsets of certain l products which in turn yield characterizations of prime open and irreducible closed subsets of traditional product spaces

inference for the median residual life function in sequential multiple assignment randomized trials in survival analysis median residual lifetime is often used as a summary measure to assess treatment effectiveness it is not clear however how such a quantity could be estimated for a given dynamic treatment regimen using data from sequential randomized clinical trials we propose a method to estimate a dynamic treatment regimen specific median residual life merl function from sequential multiple assignment randomized trials we present the merl estimator which is based on inverse probability weighting as well as two variance estimates for the merl estimator one variance estimate follows from lunceford davidian and tsiatis 2002 survival function based variance estimate and the other uses the sandwich estimator the merl estimator is evaluated and its two variance estimates are compared through simulation studies showing that the estimator and both variance estimates produce approximately unbiased results in large samples to demonstrate our methods the estimator has been applied to data from a sequentially randomized leukemia clinical trial

a general theory of fuzzy topological spaces abstract this paper presents a unification of different approaches to fuzzy topology originated from the early works of c l chang b hutton u hohle r lowen a sostak and l n stout

category theoretic aspects of chain valued frames part ii applications to lattice valued topology this paper is part ii of a two part series dealing with category theoretic aspects of chain valued frames using the categorical properties established for l frm in part i for l a complete chain this paper constructs upper free functor l and lower free functor r the functor l is used to create a class of non generated l frames factor the lpt spectrum functor through the s spectrum functor resolve the relationship between l sobriety and i l sobriety and give insight into the construction of universal l topological spaces and the functor r is used to create a class of non generated l frames factor the w l functor through a new spectrum functor s and give insight into the construction of co universal l topological spaces these facts universal spaces are anti stratified co universal spaces are stratified l frm produces both kinds of spaces via l and r l frm via its dual l loc is adjunctive with l top comprise a coherent argument that l top must accommodate both kinds of spaces resolving the philosophical debate over the place of the constant maps condition with respect to the axioms of l topologies

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

pointed semi quantales and lattice valued topological spaces in a way more general than variable basis approach to lattice valued topological spaces the present paper introduces an alternative approach to lattice valued topological spaces direct product representation spaces extending the notion of quantal spaces in the sense of mulvey and pelletier to semi quantales recently proposed by rodabaugh this paper aims to give an answer to the main question whether there exists a categorical connection possibly a categorical equivalence between direct product representation spaces and variable basis lattice valued topological spaces small sources in the category of semi quantales which are called pointed semi quantales can be identified with direct product representation spaces for this reason the main problem will be handled in terms of pointed semi quantales generalized quasi lattice valued topological spaces extending variable basis quasi topological spaces into the present setting are introduced to be a suitable topological counterpart of pointed semi quantales to formalize and to solve the main problem categories of pointed semi quantales and of generalized quasi lattice valued topological spaces are constructed and the relations between these categories providing a satisfactory answer to the main problem are established in this paper

sobriety and spatiality in varieties of algebras the paper considers a generalization of the classical papert papert isbell adjunction between the categories of topological spaces and locales to an arbitrary variety of algebras and illustrates the obtained results by the category of algebras over a given unital commutative quantale

examination of percentile residual life we initiate a nonparametric large sample estimation theory for the percentile residual lifetime we introduce the empirical percentile residual life process and determine its asymptotic distribution resulting in asymptotically distribution free confidence intervals and confidence bands for the percentile residual lifetime we illustrate the methods using strike duration data from the work of d c schmittlein and d g morrison

percentile residual life functions the percentile 0 1 residual life function at time t is defined as the percentile of the remaining life given survival up to time t note that percentile is used in place of 100 percentile two classes of life distributions defined by the percentile residual life function are the decreasing percentile residual life dprl class and the new better than used with respect to the percentile nbup class these two classes are respectively analogous to the well known decreasing mean residual life dmrl class and the new better than used in expectation nbue class that involve the mean residual life function we obtain properties of the percentile residual life function and of the dprl nbup and their dual classes some results differ notably from corresponding results for the mean residual life function

2 descent on elliptic curves and rational points on certain kummer surfaces abstract the first part of this paper further refines the methodology for 2 descents on elliptic curves with rational 2 division points which was introduced in j l colliot thelene a n skorobogatov peter swinnerton dyer hasse principle for pencils of curves of genus one whose jacobians have rational 2 division points invent math 134 1998 579 650 to describe the rest let e 1 and e 2 be elliptic curves d 1 and d 2 their respective 2 coverings and x be the kummer surface attached to d 1 d 2 in the appendix we study the brauer manin obstruction to the existence of rational points on x in the second part of the paper in which we further assume that the two elliptic curves have all their 2 division points rational we obtain sufficient conditions for x to contain rational points and we consider how these conditions are related to brauer manin obstructions this second part depends on the hypothesis that the relevent tate shafarevich group is finite but it does not require schinzel s hypothesis

category theoretic fuzzy topological spaces and their dualities it is shown in this paper that various approaches to fuzzy topological spaces can be extended to an abstract category c in this respect variety based generalized topological spaces variable basis fuzzy topological spaces fixed basis fuzzy topological spaces and hutton fuzzy topological spaces are defined in c we also construct their respective categories as well as establish a generalized papert papert isbell style adjunction for each of them these adjunctions are later on refined to equivalences involving appropriate definitions of spatiality and sobriety

applications of localic separation axioms compactness axioms representations and compactifications to poslat topological spaces fuzzy topology first appeared about twenty seven years ago with chang s initial paper 1968 yet the fundamental issues of compactness and low order separation axioms remain unresolved this paper resolves these issues with respect to topological compactification categorical compactification and stone representation theorems using the theory of locales and previous work of the author in fuzzy sobriety our results give the first compactification reflectors for all traditional fuzzy topology construct classes of generalized stone representations of boolean algebras and distributive lattices and show categorically that the fuzzy analogue of classical compact hausdorff spaces is the categories of chang compact localic regular sober fuzzy topological spaces

technical note when does the βth percentile residual life function determine the distribution knowledge of the th percentile residual life function does not uniquely determine the underlying distribution additional information about the tail behavior of the distribution is needed knowledge of both the 1 and 2 percentile residual life functions does uniquely determine the distribution provided that 1 and 2 are noncommensurate this corrects and extends the results of schmittlein and morrison schmittlein d c d g morrison 1981 the median residual lifetime a characterization theorem and an application opns res 29 392 399

fuzzy topologies and topological space objects in a topos abstract the purpose of this paper is to point out the link between lowen s fuzzy topologies and topological space objects in the topos l set as the main result we obtain the following theorem lowen s fuzzy topologies are the external version of the internal topologies in l set

category theoretic aspects of chain valued frames part i categorical and presheaf theoretic foundations this paper is part i of a two part series dealing with category theoretic aspects of chain valued frames a new categorical motivation for lattice valued frames is given from presheaves and then under the assumption that l be a complete chain it is established that standard category theoretic properties completeness cocompleteness factorization structures hold for l frm the category of l frames and l frame morphisms properties which are a platform for the upper free functor l and lower free functor r used in part ii to give a broad range of applications of chain valued frames to lattice valued topology

fundamental duality of abstract categories and its applications given an abstract category c c m l spaces that are categorical generalization of fixed basis fuzzy topological spaces in c and their category c m l top are introduced it is pointed out as one of the main contributions of this paper that c is dually adjoint to c m l top by defining l spatiality in c and l sobriety in c m l top this adjunction induces a dual equivalence between the full subcategory of c of all l spatial objects and the full subcategory of c m l top of all l sober objects the present adjunction and duality are fruitful categorical extensions of the classical top loc adjunction and sobtop spatloc duality to abstract categories with a great deal of applications in particular their applications to q categories quasivarieties and augmented posets are given

the median residual lifetime a characterization theorem and an application the concept of the median residual lifetime for a probability distribution is outlined and shown to have several advantages over its more common counterpart the mean residual lifetime a characterization theorem shows that a pareto distribution of the second kind or equivalently a gamma mixture of exponentials is the unique distribution with a linearly increasing median residual lifetime an empirical example from the literature on strike durations is presented

regression on quantile residual life a time specific log linear regression method on quantile residual lifetime is proposed under the proposed regression model any quantile of a time to event distribution among survivors beyond a certain time point is associated with selected covariates under right censoring consistency and asymptotic normality of the regression estimator are established an asymptotic test statistic is proposed to evaluate the covariate effects on the quantile residual lifetimes at a specific time point evaluation of the test statistic does not require estimation of the variance covariance matrix of the regression estimators which involves the probability density function of the survival distribution with censoring simulation studies are performed to assess finite sample properties of the regression parameter estimator and test statistic the new regression method is applied to a breast cancer data set with long term follow up to estimate the patients median residual lifetimes adjusting for important prognostic factors

generalized fuzzy topology versus non commutative topology the paper introduces a modification of the notions of generalized fuzzy topological space of demirci and quantal space of mulvey and pelletier suitable to explore interrelations between point set lattice theoretic topology and non commutative topology developed in the framework of c algebras or more recently of quantales as a consequence of the new approach a generalization of the concept of topological system of vickers arises moreover the currently dominating variable basis topological setting in the fuzzy community due to rodabaugh appears to be fixed basis

arithmetic of elliptic curves upon quadratic extension this paper is a study of variations in the rank of the mordell weil group of an elliptic curve e defined over a number field f as one passes to quadratic extensions k of f let s k be the selmer group for multiplication by 2 on e k in analogy with genus theory we describe s k in terms of various objects defined over f and the local norm indices dimf2 ft norm ah for each completion fv of f in particular we show that dim s k dim e k 2 has the same parity as zi we compute i when e has good or multiplicative reduction modulo v assuming that the 2 primary component of the tate shafare vitch group u1 k is finite as conjectured we obtain the parity of rank e k for semistable elliptic curves defined over q and parametrized by modular functions our parity results agree with those predicted analytically by the conjectures of birch and swinnerton dyer 1 introduction let e be an elliptic curve defined over a number field f our motivating question is this what can be said about variations in the rank of the mordell weil group e k over quadratic extensions k f dl 2 1 let e d denote the twist of e which becomes isomorphic to e over k but not over f concretely if we choose for e a model over f of the form y2 f x then a model for d is given by dy2 f x if a denotes the generator of gal k f then e f can be identified with the l eigenspace and e d f with the l eigenspace of a acting on e k it follows that rank e k rank e f rank e d f an equiv alent question therefore is to describe changes in the rank of e d f as d varies for certain specific curves defined over q this question has been discussed for

stratified categorical fixed basis fuzzy topological spaces and their duality abstract for an abstract category c a class m of c monomorphisms and a fixed c object l we introduce stratified c m l spaces to be categorical counterparts of stratified fixed basis fuzzy topological spaces in c and consider their category sc m l top as two main results of this paper it is shown that sc m l top is dually adjoint to the comma category l c and this adjunction can be restricted to a dual equivalence between the full category of l c with comma spatial objects and the full category of sc m l top with comma sober objects the present paper also describes applications and relationships of these results to stratified fixed basis fuzzy topological spaces in this respect a considerable part of this paper is devoted to stratified l quasi topological spaces and their duality