analytic torsion and holomorphic determinant bundles in this paper we prove that in the case of holomorphic locally kahler fibrations the analytic and algebraic geometry constructions of determinant bundles for direct images coincide we calculate the curvature of the holomorphic hermitian connection for the quillen metric on the determinant bundle we study the behavior of the quillen metric under change of metrics in the fibers and also on the twisting vector bundles we thus generalize the conformal anomaly formula to kahler manifolds of arbitrary dimension we also study the quillen metrics on determinants associated with exact sequences of vector bundles we prove that the quillen metric is smooth on the grothendieck knudsen mumford determinant for arbitrary holomorphic fibrations

a fast combined field volume integral equation solution to em scattering by 3 d dielectric objects of arbitrary permittivity and permeability a fast solution to the combined field volume integral equation cfvie for electromagnetic scattering by large three dimensional dielectric bodies of arbitrary permittivity and permeability is presented the cfvie is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents the resultant integral equation is solved using the method of moments mom then the precorrected fast fourier transform p fft method is applied to reduce the memory requirement and accelerate the matrix vector multiplication in the mom solution in the implementation of the p fft method two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources in addition two sets of interpolation operators are also applied respectively for the computation of the vector scalar potentials and the curl of the vector potentials in the support of the testing functions the resultant method has a memory requirement of o n and a computational complexity of o nlogn respectively where n denotes the number of unknowns

analytic torsion and holomorphic determinant bundles i bott chern forms and analytic torsion we attach secondary invariants to any acyclic complex of holomorphic hermitian vector bundles on a complex manifold these were first introduced by bott and chern bot c our new definition uses quillen s superconnections we also give an axiomatic characterization of these classes these results will be used in bgs2 and bgs3 to study the determinant of the cohomology of a holomorphic vector bundle

on a spectral flow formula for the homological index abstract consider a selfadjoint unbounded operator d on a hilbert space h and a one parameter norm continuous family of selfadjoint bounded operators a t t r that converges in norm to asymptotes a at then under certain conditions 22 that include the assumption that the operators d t d a t t r all have discrete spectrum the spectral flow along the path d t can be shown to be equal to the index of t d t when the latter is an unbounded fredholm operator on l 2 r h in 16 an investigation of the index spectral flow question when the operators in the path may have some essential spectrum was started but under restrictive assumptions that rule out differential operators in general in 11 the question of what happens when the fredholm condition is dropped altogether was investigated in these circumstances the fredholm index is replaced by the witten index in this paper we take the investigation begun in 11 much further we show how to generalize a formula known from the setting of the l 2 index theorem to the non fredholm setting restricting back to the case of selfadjoint fredholm operators our formula extends the result of 22 in the sense of relaxing the discrete spectrum condition it also generalizes some other fredholm operator results of 21 16 11 that permit essential spectrum for the operators in the path our result may also apply however when the operators d t have essential spectrum equal to the whole real line our main theorem gives a trace formula relating the homological index of 7 to an integral formula that is known for a path of selfadjoint fredholms with compact resolvent and with unitarily equivalent endpoints to compute spectral flow our formula however applies to paths of selfadjoint non fredholm operators we interpret this as indicating there is a generalization of spectral flow to the non fredholm setting

interval censored survival data a generalized linear modelling approach a method is described for weak parametric modelling of arbitrarily interval censored survival data using generalized linear models the method makes use of an associated bernoulli model with standard errors based on the observed information matrix three types of models are discussed additive and multiplicative hazard models with piecewise constant baseline hazard and a proportional hazards model with discrete baseline survivor function these models may be fitted in the statistical package glim

determinant bundles manifolds with boundary and surgery we define determinant bundles associated to the following data i a family of generalized dirac operators on even dimensional manifolds with boundary ii the choice of a spectral section for the family of dirac operators induced on the boundary under the assumption that the operators of the boundary family have null spaces of constant dimension we define through the notion ofb zeta function a quillen metric we also introduce the analogue of the bismut freed connection we prove that the curvature of a natural perturbation of the bismut freed connection equals the 2 form piece in the right hand side of the family index formula thus extending to manifolds with boundary results of quillen bismut and freed given a closed fibration we investigate the behaviour of the quillen metric and of the bismut freed connection under the operation of surgery along a fibering hypersurface we prove in particular additivity formulae for the curvature and for the logarithm of the holonomy

a highly accurate fgg fg fft for the combined field integral equation in this paper a novel realization of the integral equation in combination with the fast fourier transform for the cfie is established by fitting both the green s function and its gradient onto the nodes of a uniform cartesian grid the new method has been compared with several existing popular fft based methods including the aim the ie fft and the p fft the accuracy of the proposed method is significantly higher than other fft based methods and the method is not sensitive to both the grid spacing and the expansion order the outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions therefore when the higher order basis functions would be adopted in the method of moments only one fitting procedure for the green s function and its gradient on a basis function support is needed to meet all of basis functions defined on this support some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method

eta invariant and holonomy the even dimensional case abstract in previous work we introduced eta invariants for even dimensional manifolds it plays the same role as the eta invariant of atiyah patodi singer which is for odd dimensional manifolds it is associated to k 1 representatives on even dimensional manifolds and is closely related to the so called wzw theory in physics in fact it is an intrinsic interpretation of the wess zumino term without passing to the bounding 3 manifold spectrally the eta invariant is defined on a finite cylinder rather than on the manifold itself thus it is an interesting question to find an intrinsic spectral interpretation of this new invariant we address this issue here using adiabatic limit technique the general formulation relates the mod z reduction of eta invariant for even dimensional manifolds with the holonomy of the determinant line bundle of a natural family of dirac type operators in this sense our result might be thought of as an even dimensional analogue of witten s holonomy theorem proved by bismut freed and cheeger independently

a proportional hazards model for arbitrarily censored and truncated data turnbull 1976 journal of royal statistical society series b 38 290 295 proposed a method for nonparametric estimation of the distribution function when the data are incomplete because of censoring and truncation however as noted by frydman 1994 journal of royal statistical society series b 56 71 74 turnbull s method has to be modified to accommodate both truncation and censoring this paper presents a detailed correction of turnbull s method and an extension to the regression analysis a method of fitting the proportional hazards model for arbitrarily censored and truncated data is developed the method allows partial testing for zero regression coefficients the test can be performed using the likelihood ratio test or the wald test the methodology is applied to estimate the distribution of the induction time of patients diagnosed with transfusion associated aids and to estimate the distribution of time from diabetes onset to development of diabetic nephropathy for insulin dependent diabetics

spinq twistor and spinc spinq structures induce spinq style twistor spaces which possess canonical spinc structures such structures produce dirac operators their indices for the even dimensional case and the adiabatic limit of their reduced invariants for the odd dimensional case are discussed

the ζ determinant and the additivity of the η invariant on the smooth self adjoint grassmannian in this paper we discuss the existence of the determinant of a dirac operator on a compact manifold with boundary we show that the determinant is well defined in the case of the operator with a domain determined by a boundary condition from the smooth self adjoint grassmannian discussed in the papers 5 13 29 we prove a generalization of a pasting formula for the invariant see 34 the results of the paper are used in the recent proof of the projective equality of the determinant and quillen determinant on see 30 31

families index for manifolds with boundary superconnections and cones ii the chern character abstract this is part ii of a work in which we establish a formula for the chern character of a family of dirac operators of atiyah patodi and singer here we establish the existence of associated superconnection heat kernels and we prove the final index formula

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

a modification of peto s nonparametric estimation of survival curves for interval censored data summary peto 1973 applied statistics 22 86 91 gave a nonparametric generalized maximum likelihood estimate of the survival function for interval censored data his method has a tendency to concentrate probability masses at the endpoints of the intervals even for the ordinary grouped data instead of spreading them through the intervals as one might expect them to be in the underlying distribution we describe a modification that overcomes this the new estimate reduces to the standard binomial estimate when applied to grouped data it also reduces to the kaplan meier estimate when applied to survival data that consist of only exact or right censored observations both estimates are maximum likelihood estimates but are based on different interpretations of the endpoints of the intervals

the use of parametric elements in the moment method solution of static and dynamic volume integral equations the use of two and three dimensional parametric curved subdomains elements in the numerical solution of electromagnetic problems formulated in terms of volume integro differential equations is considered and a technique to evaluate the static and dynamic moment integrals on these domains is presented in the source region the evaluation of the moment integrals is performed by separating the integrands into a singular and a regular part the regular integrals are numerically evaluated in a parameter space where the integration domain assumes a very simple form the singular integrals are shown to be always reducible to nonsingular boundary integrals by use of a nonlinear transformation for the integration variables and an analytic integration on one variable the reduced singular integrals are then evaluated numerically in a second parameter space where the boundary of the original curved element is expressed in a simple form two simple two dimensional scattering problems in the frequency domains are considered to compare the results obtained using quadratic isoparametric curved elements against the results given by linear expansion functions on triangular elements the use of curved parametric elements permit a better geometrical description of the problem a reduced number of unknowns shorter computation times and more accurate results with respect to the usually employed linear elements

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

the additivity of the η invariant the case of a singular tangential operator we prove the decomposition formula for the invariant of the compatible dirac operator on a closed manifoldm which is a sum of two submanifolds with common boundary

essential spectrum and heat kernel abstract upper bounds are derived for the large time behavior of the heat kernel on riemannian manifolds whose essential spectrum has a positive lower bound applications include a relative signature theorem and the construction of bounded harmonic functions

on the formulation of hybrid finite element and boundary integral methods for 3 d scattering this paper studies in detail a variety of formulations for the hybrid finite element and boundary integral fe bi method for three dimensional 3 d electromagnetic scattering by inhomogeneous objects it is shown that the efficiency and accuracy of the fe bi method depends highly on the formulation and discretization of the boundary integral equation bie used a simple analysis of the matrix condition number identifies the efficiency of the different fe bi formulations and an analysis of weighting functions shows that the traditional fe bi formulations cannot produce accurate solutions a new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance finally the multilevel fast multipole algorithm mlfma is employed to significantly reduce the memory requirement and computational complexity of the proposed fe bi method

inversion of electromagnetic scattering for 3d dielectric objects through integral equation method with nystrom discretization reconstruction of unknown objects requires efficient inversion for measured electromagnetic scattering data in frequency domain integral equation method for reconstructing dielectric objects the volume integral equations vies are involved because the imaging domain with both true unknown objects and part of background is inhomogeneous when solving the forward scattering integral equation fsie the nystrom method is used since the traditional method of moments mom with the schaubert wilton glisson swg basis function may not be convenient due to the inhomogeneity of the imaging domain the benefits of the nystrom method include the simple implementation without using any basis and testing functions and lower requirement on geometrical discretization so it is very suitable for inhomogeneous problems when solving the inverse scattering integral equation isie the gauss newton minimization approach gnma with a multiplicative regularization method mrm is employed numerical examples for reconstructing three dimensional dielectric objects are presented to illustrate the inversion approach

z k manifolds and families of dirac operators the index of a family of a family of dirac operators is ak theory element in the parameter space sullivan s k manifolds are used to detect this index completely for the first chern class this gives a topological interpretation of witten s global anomaly the relationship with the geometry of the index bundle is considered

hitchin thorpe inequality for noncompact einstein 4 manifolds we prove a hitchin thorpe inequality for noncompact einstein 4 manifolds with specified asymptotic geometry at infinity the asymptotic geometry at infinity is either a cusp bundle over a compact space the fibered cusps or a fiber bundle over a cone with a compact fiber the fibered boundary many noncompact einstein manifolds come with such a geometry at infinity

heat kernel on smooth metric measure spaces with nonnegative curvature we derive a local gaussian upper bound for the f heat kernel on complete smooth metric measure space m g e f dv with nonnegative bakry emery ricci curvature as applications we obtain a sharp l f 1 liouville theorem for f subharmonic functions and an l f 1 uniqueness property for nonnegative solutions of the f heat equation assuming f is of at most quadratic growth in particular any l f 1 integrable f subharmonic function on gradient shrinking and steady ricci solitons must be constant we also provide explicit f heat kernel for gaussian solitons

corners in m theory m theory can be defined on closed manifolds as well as on manifolds with boundary as an extension we show that manifolds with corners appear naturally in m theory we illustrate this with four situations the lift to bounding 12 dimensions of m theory on anti de sitter spaces ten dimensional heterotic string theory in relation to 12 dimensions and the two m branes within m theory in the presence of a boundary the m2 brane is taken with or as a boundary and the worldvolume of the m5 brane is viewed as a tubular neighborhood we then concentrate on the variant of the heterotic theory as a corner and explore analytical and geometric consequences in particular we formulate and study the phase of the partition function in this setting and identify the corrections due to the corner s the analysis involves considering m theory on disconnected manifolds and makes use of the extension of the atiyah patodi singer index theorem to manifolds with corners and the b calculus of melrose

spectral sequences and adiabatic limits a taylor series analysis of the laplacian as the underlying manifold is demormed leads to a hodge theoretic derivation of the leray spectral sequence

η invariants and determinant lines the invariant of an odd dimensional manifold with boundary is investigated the natural boundary condition for this problem requires a trivialization of the kernel of the dirac operator on the boundary the dependence of the invariant on this trivialization is best encoded by the statement that the exponential of the invariant lives in the determinant line of the boundary our main results are a variational formula and a gluing law for this invariant these results are applied to reprove the formula for the holonomy of the natural connection on the determinant line bundle of a family of dirac operators also known as the global anomaly formula the ideas developed here fit naturally with recent work in topological quantum field theory in which gluing which is a characteristic formal property of the path integral and the classical action is used to compute global invariants on closed manifolds from local invariants on manifolds with boundary

aps boundary conditions eta invariants and adiabatic limits we prove an adiabatic limit formula for the eta invariant of a manifold with boundary the eta invariant is defined using the atiyah patodisinger boundary condition and the underlying manifold is fibered over a manifold with boundary our result extends the work of bismut cheeger to manifolds with boundary

twistor spaces and the general adiabatic expansions abstract we investigate the behavior of derivatives of the fundamental solution of a parabolic equation for the square of dirac operator on a twistor space when the metric is blown up in the base space direction such a blowing up operation is expected to be an effective method for extracting some intrinsic values from various geometric invariants most of whose cores consist of some derivatives of the fundamental solution

bar partial torsion for complex manifolds and the adiabatic limit torsion for complex manifolds and the adiabatic limit we consider a complex fibration f m l b and pull back bundles e 1 and e 2 over m using the adiabatic limit idea we compute the metric invariant tp e1 tp e2 where tp e denotes the complex ray singer torsion

scattering from 3 d inhomogeneous chiral bodies of arbitrary shape by the method of moments a method of moments mom solution is presented for the problem of electromagnetic scattering by a three dimensional 3d inhomogeneous chiral scatterer illuminated by an arbitrary incident field the volume equivalence principle was used to obtain coupled integral equations for equivalent volume currents these integral equations were then solved numerically using mom the volume of the scatterer was modeled by tetrahedral cells and face based expansion functions were used to approximate the equivalent currents computed results are in very good agreement with exact data or other published data

fast analysis of rcs over a frequency band using pre corrected fft aim and asymptotic waveform evaluation technique the pre corrected fast fourier transform pfft adaptive integral method aim is combined with the asymptotic waveform evaluation awe technique to present fast rcs calculation for arbitrarily shaped three dimensional pec objects over a frequency band the electric field integral equation efie is used to formulate the problem and the method of moments mom is employed to solve the integral equation by using the awe method the unknown equivalent current is expanded into a taylor series around a frequency in the desired frequency band then instead of solving the equivalent current at each frequency point it is only necessary to solve for the coefficients of the taylor series called ldquomomentsrdquo at each expansion point since the number of the expansion points is usually much smaller than that of the frequency points the awe can achieve fast frequency sweeping to facilitate the analysis of large problems in this paper all the full matrices are stored in a sparse form and the pfft aim method is employed to accelerate all the matrix vector products on both sides of the matrix equation for the moments further the incomplete lu preconditioner is used at each expansion point to improve the convergence behaviour of the matrix equation for the moments the present method can deal with much larger problems than the conventional mom awe method since the pfft aim achieves considerable reduction in memory requirement and computation time numerical results will be presented to show the efficiency and capability of the method

precorrected fft solution of the volume integral equation for 3 d inhomogeneous dielectric objects this work presents a fast solution to the volume integral equation for electromagnetic scattering from three dimensional inhomogeneous dielectric bodies by using the precorrected fast fourier transform fft method the object is modeled using tetrahedral volume elements and the basis functions proposed by schaubert et al are employed to expand the unknown electric flux density the basis functions are then projected onto a fictitious uniform grid surrounding the nonuniform mesh enabling the fft to be used to speed up the matrix vector multiplies in the iterative solution of the matrix equation the resultant method greatly reduces the memory requirement to o n and the computational complexity to o nlogn where n is the number of unknowns as a result this method is capable of computing electromagnetic scattering from large complex dielectric objects

adiabatic limit bismut freed connection and the real analytic torsion form for a complex flat vector bundle over a fibered manifold we consider the 1 parameter family of certain deformed sub signature operators introduced by ma zhang in mz we compute the adiabatic limit of the bismut freed connection associated to this family and show that the bismut lott analytic torsion form shows up naturally under this procedure

a note on nonparametric estimation of the distribution function from interval censored and truncated observations this paper is concerned with the nonparametric estimation of the distribution function f from interval censored and truncated data as discussed by turnbull it is observed that turnbun s characterization of f the maximum likelihood estimator of f is not applicable in general when the data are interval censored and truncated it is shown however that turnbull s characterization can be easily modified to obtain the appropriate characterization of f

plancherel type estimates and sharp spectral multipliers abstract we study general spectral multiplier theorems for self adjoint positive definite operators on l2 x where x is any open subset of a space of homogeneous type we show that the sharp hormander type spectral multiplier theorems follow from the appropriate estimates of the l2 norm of the kernel of spectral multipliers and the gaussian bounds for the corresponding heat kernel the sharp hormander type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the riesz means summability which we also study here we discuss several examples which include sharp spectral multiplier theorems for a class of scattering operators on r3 and new spectral multiplier theorems for the laguerre and hermite expansions

nystrom method solution of volume integral equations for electromagnetic scattering by 3d penetrable objects the volume integral equations vies for electromagnetic em scattering by three dimensional 3d penetrable objects are solved by nystrom method the vies are essential and cannot be replaced by surface integral equations sies for inhomogeneous problems but they are usually solved by the method of moments mom the nystrom method as an alternative for the mom has shown much promise and has been widely used to solve the sies but it is less frequently applied to the vies especially for 3d em problems in this work we implement the nystrom method for 3d vies by developing an efficient local correction scheme for singular and near singular integrals over tetrahedral elements the scheme first interpolates the unknown functions within the tetrahedral elements and then derives analytical solutions for the resultant singular or near singular integrals after singularity subtraction the scheme is simpler and more efficient in implementation compared with those based on the redesign of quadrature rules for the singular or near singular integrands numerical examples are presented to demonstrate the effectiveness of the proposed scheme and its convergence feature is also studied

pseudo differential projections and the topology of certain spaces of elliptic boundary value problems we calculate the homotopy groups of the space of elliptic boundary value problems for an elliptic differential operatora of a first order and of the space of elliptic self adjoint boundary value problems whena is a formally self adjoint in particular we show that the spectral flow of ans1 family of self adjoint elliptic boundary value problems is well defined this provides some information on spectral properties along the lines of the vafa witten approach to spectral inequalities

analysis of volume integral equation formulations for scattering by high contrast penetrable objects the volume integral equation method is applied in electromagnetic scattering from arbitrarily shaped three dimensional inhomogeneous objects the properties of the volume electric and magnetic field integral equations vefie and vmfie are investigated numerical experiments show that if the galerkin s method with the lowest mixed order basis functions is used to discretize the equations the accuracy of the vmfie can be significantly poorer than the accuracy of the vefie in particular for high contrast objects at high frequencies the accuracy of the vmfie can be essentially improved with full first order linear basis functions the linear basis functions are found to be useful also when a single volume integral equation is used to model a general scatterer where both permittivity and permeability differ from the background

boundedness of spectral multipliers of generalized laplacians on compact manifolds with boundary consider a second order strongly elliptic negative semidefinite differential operator l may be a system on a compact riemannian manifold overline m with smooth boundary where the domain of l is defined by a coercive boundary condition classically known results and also recent work in duong et al j funct anal 196 443 485 2002 and duong and mcintosh rev math iberoam 15 233 265 1999 establish sufficient conditions for l infty text bmo l continuity of varphi sqrt l where varphi in s 0 1 mathbb r and l is a suitable elliptic operator using a variant of the cheeger gromov taylor functional calculus due to mauceri et al math res lett 16 861 879 2009 and short time upper bounds on the integral kernel of e tl due to greiner arch ration mech anal 41 168 218 1971 we prove that a variant of such sufficient conditions holds for our operator l

self adjoint elliptic operators and manifold decompositions part i low eigenmodes and stretching this paper is the first of a three part investigation into the behavior of analytical invariants of manifolds that can be split into the union of two submanifolds in this article we will show how the low eigensolutions of a self adjoint elliptic operator over such a manifold can be studied by a splicing construction this construction yields an approximated solution of the operator whenever we have two l2 solutions on both sides and a common limiting value of two extended l2 solutions in part 11 the present analytic mayer vietoris results on low eigensolutions and further analytic work will be used to obtain a decomposition theorem for spectral flows in terms of maslov indices of lagrangians in part i11 after comparing infinite and finite dimensional lagrangians and determinant line bundles and then introducing canonical perturbations of lagrangian subvarieties of symplectic varieties we will study invariants of 3 manifolds including casson s invariant 0 1996 john wiley sons inc

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

eta invariants and their adiabatic limits 0 introduction 1 algebraic preliminaries 2 the finite dimensional case superconnections a odd dimensional base spaces b even dimensional base spaces appendix 1 coupling to general superconnections 3 auxiliary grassman variables and auxiliary adiabatic limits 4 the infinite dimensional case fibrations a elementary geometry of fibrations b odd dimensional base spaces c even dimensional base spaces d the case in which the dirac operator on the fiber is not invertible appendix 2 multifibrations

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

on the gluing problem for the eta invariant we solve the gluing problem for the invariant consider a generalized dirac operator d over a compact riemannian manifold m that is partitioned by a compact hypersurface n such that m m un m2 we assume that the riemannian metric of m and d have a product structure near n i e d i d d dn with some dirac operator dn on n using boundary conditions of atiyah patodi singer type parametrized by lagrangian subspaces l of kerd we define selfadjoint extensions d i 1 2 over m we express the invariant of d in terms of the invariants of di an invariant m l l2 of the pair of the lagrangian subspaces l l2 which is related to the maslov index and an integer valued term j in the adiabatic limit i e if a tubular neighborhood of n is long enough the vanishing of j is shown under certain regularity conditions we apply this result in order to prove cutting and pasting formulas for the invariant a wall nonadditivity result for the index of atiyah patodi singer boundary value problems and a splitting formula for the spectral flow 1 the gluing problem and applications 1 1 introduction we solve the gluing problem for the invariant of generalized dirac operators consider a closed compact riemannian manifold carrying a dirac bundle with a generalized dirac operator assume that this manifold is separated into two pieces by a compact hypersurface the gluing problem for the invariant consists in expressing the invariant of the original dirac operator in terms of the invariants of the dirac operators living on the pieces the selfadjoint operators on the two components with boundary depend on a boundary condition given by lagrangian subspaces lx l2 of a certain symplectic vector space the gluing formula also contains an additional real valued term m l l2 which is nicely related to the symplectic geometry and the maslov index