moduli spaces of hyperelliptic curves with a and d singularities we introduce moduli spaces of quasi admissible hyperelliptic covers with at worst a and d singularities the stability conditions for these moduli spaces depend on two rational parameters describing allowable singularities for the extreme values of the parameters we obtain the stacks of stable limits of a n and d n singularities and the quotients of the miniversal deformation spaces of these singularities by natural mathbb g m actions we interpret the intermediate spaces as log canonical models of the stacks of stable limits of a n and d n singularities

modified spline collocation for linear fractional differential equations we propose and analyze a class of high order methods for the numerical solution of initial value problems for linear multi term fractional differential equations involving caputo type fractional derivatives using an integral equation reformulation of the initial value problem we first regularize the solution by a suitable smoothing transformation after that we solve the transformed equation by a piecewise polynomial collocation method on a mildly graded or uniform grid optimal global convergence estimates are derived and a superconvergence result for a special choice of collocation parameters is established theoretical results are verified by some numerical examples

on the convergence of spline collocation methods for solving fractional differential equations in the first part of this paper we study the regularity properties of solutions of initial value problems of linear multi term fractional differential equations we then use these results in the convergence analysis of a polynomial spline collocation method for solving such problems numerically using an integral equation reformulation and special non uniform grids global convergence estimates are derived from these estimates it follows that the method has a rapid convergence if we use suitable nonuniform grids and the nodes of the composite gaussian quadrature formulas as collocation points theoretical results are verified by some numerical examples

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

estimating the proportion of immunes in a censored sample summary an estimator for the proportion of immunes in a population is proposed when a sample of censored failure times is available our suggestion is to use one minus the maximum observed value of the kaplan meier empirical distribution function this estimator is shown to be consistent and asymptotically normal under modest conditions on the censoring mechanism simulations suggest that the estimator is approximately normal for quite small sample sizes provided the immune proportion is not too close to zero a simple nonparametric statistic is proposed to test whether the assumptions of the analysis are likely to be valid

positive almost periodic solutions of nonlinear discrete systems with finite delay the existence of positive almost periodic solutions of nonlinear discrete systems with finite delay is obtained by using a variant of hilbert s projective metric on a subset of the space of almost periodic sequences

numerical approximations for highly oscillatory bessel transforms and applications abstract this paper presents an efficient numerical method for approximating highly oscillatory bessel transforms based on analytic continuation we transform the integrals into the problems of integrating the forms on 0 with the integrand that does not oscillate and decays exponentially fast which can be efficiently computed by using gauss laguerre quadrature rule we then derive the error of the method depending on the frequency and the node number moreover we apply the scheme for studying the approximations of the solutions of two kinds of highly oscillatory integral equations preliminary numerical results show the efficiency and accuracy of numerical approximations

simultaneous semi stable reduction for curves with ade singularities a key tool in the study of algebraic surfaces and their moduli is brieskorn s simultaneous resolution for families of algebraic surfaces with simple du val or ade singularities in this paper we show that a similar statement holds for families of curves with at worst simple ade singularities for a family x b of ade curves we give an explicit and natural resolution of the rational map b 99k mg moreover we discuss a lifting of this map to the moduli stack mg i e a simultaneous semi stable reduction for the family x b in particular we note that in contrast to what might be expected from the case of surfaces the natural weyl cover of b is not a sufficient base change for a lifting of the map b 99k mg to mg

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

blow up collocation solutions of nonlinear homogeneous volterra integral equations in this paper collocation methods are used for detecting blow up solutions of nonlinear homogeneous volterra hammerstein integral equations to do this we introduce the concept of blow up collocation solution and analyze numerically some blow up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied finally we discuss the relationships between necessary conditions for blow up of collocation solutions and exact solutions

extending families of curves over log regular schemes in this paper we generalize to the log regular case a result of de jong and oort which states that any morphism satisfying certain conditions from the complement of a divisor with normal crossings in a regular scheme to a moduli stack of stable curves extends over the entire regular scheme the proof uses the theory of regular log schemes i e schemes with singularities like those of toric varieties due to k kato 9 we then use this extension theorem to prove that under certain natural conditions any scheme which is a successive fibration of smooth hyperbolic curves may be compactified to a successive fibration of stable curves 1991 mathematics subject classification primary subject 14h10 secondary subject 14e15

modified asymptotic orders of the direct filon method for a class of volterra integral equations the direct filon method provides efficient approximation for solutions of volterra integral equations with highly oscillatory kernels in this paper we study the rate of convergence of this method for a class of equations with trigonometric kernels the asymptotic order is developed by examining the property of the solution numerical experiments are included to verify the given order

an h p version of the continuous petrov galerkin finite element method for volterra integro differential equations with smooth and nonsmooth kernels we present an h p version of the continuous petrov galerkin cpg finite element method for linear volterra integro differential equations with smooth and nonsmooth kernels we establish a priori error estimates in the l 2 h 1 and l infty norms that are completely explicit with respect to the local discretization and regularity parameters for singular solutions caused by the weakly singular kernels we prove that algebraic convergence rates can be achieved for the h p version of the cpg method with quasi uniform meshes moreover we show that exponential rates of convergence can be achieved for solutions with start up singularities by using geometric time partitions and linearly increasing polynomial degrees numerical experiments are provided to illustrate the theoretical results

spline collocation for nonlinear fractional boundary value problems abstract we consider a class of boundary value problems for nonlinear fractional differential equations involving caputo type fractional derivatives using an integral equation reformulation of the boundary value problem some regularity properties of the exact solution are derived based on these properties and spline collocation techniques the numerical solution of boundary value problems by suitable non polynomial approximations is discussed optimal global convergence estimates are derived and a superconvergence result for a special choice of grid and collocation parameters is given theoretical results are tested by two numerical examples

integral algebraic equations theory of collocation methods i our analysis of collocation solutions for general systems of linear integral algebraic equations iaes is based on the notions of the tractability index and the nu smoothing property of a volterra integral operator these are used to decouple the given iae system into the inherent system of regular second kind volterra integral equations vies and a system of first kind vies this decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions numerical examples illustrate the theoretical results

a bivariate cure mixture approach for modeling familial association in diseases summary for modeling correlation in familial diseases with variable ages at onset we propose a bivariate model that incorporates two types of pairwise association one between the lifetime risk or the overall susceptibility of two individuals and one between the ages at onset between two susceptible individuals for estimation we consider a two stage estimation procedure similar to that of shih 1998 biometrics 54 1115 1128 we evaluate the properties of the estimators through simulations and compare the performance with that from a bivariate survival model that allows correlation between ages at onset only we apply the methodology to breast cancer using the kinship data from the washington ashkenazi study we also discuss potential applications of the proposed method in the area of cure modeling

the abelian monodromy extension property for families of curves necessary and sufficient conditions are given in terms of monodromy for extending a family of smooth curves over an open subset u subset s to a family of stable curves over s more precisely we introduce the abelian monodromy extension ame property and show that the standard deligne mumford compactification is the unique maximal ame compactification of the moduli space of curves we also show that the baily borel compactification is the unique maximal projective ame compactification of the moduli space of abelian varieties

on use of bivariate survival models with cure fraction correlated gamma frailty model in our original article we proposed the methodology in the very general setting of copula model genest and mackay 1986 marshall and olkin 1988 we illustrated the application of the methodology using three specific distribution of the general class namely clayton s 1978 frank s 1979 and stable family hougaard 1986 it is true that all of these three models correspond to an underlying shared frailty model the class of copula models however are much more general and can include correlated frailty models in fact the correlated frailty model the authors proposed to use as an extension of our methodology is a special case of the copula model with the copula function given by

preserving stability implicit euler method for nonlinear volterra and neutral functional differential equations in banach space this paper is concerned with the contractivity and asymptotic stability properties of the implicit euler method iem for nonlinear functional differential equations fdes these properties are first analyzed for volterra fdes and then the analysis is extended to the case of neutral fdes nfdes such an extension is particularly important since nfdes are more general and have received little attention in the literature the main result we establish is that the iem with linear interpolation can completely preserve these stability properties of the analytical solution to such fdes