a uniformization theorem for complete non compact kahler surfaces with positive bisectional curvature in this paper by combining techniques from ricci flow and algebraic geometry we prove the following generalization of the classical uniformization theorem of riemann surfaces given a complete non compact complex two dimensional kahler manifold m of positive and bounded holomorphic bisectional curvature suppose its geodesic balls have maximal volume growth then m is biholomorphic to c2 this gives a partial affirmative answer to the well known conjecture of yau 41 on uniformization theorem during the proof we also verify an interesting gap phenomenon predicted by yau in 42 which says that a kahler manifold as above automatically has quadratic curvature decay at infinity in the average sense

curvature diameter homotopy groups and cohomology rings we establish two topological results a if m is a 1 connected compact n manifold and q 2 then the minimal number of generators for the qth homotopy group q m mng q m is bounded above by a number depending only on mng h m and q where h m is the homology group c let mathscr m n y be the collection of compact orientable n manifolds whose oriented bundles admit so n invariant fibrations over y with fiber compact nilpotent manifolds such that the induced so n actions on y are equivalent then q m finitely generated m mathscr m n y contains only finite isomorphism classes depending only on n y q together with the results of cg and gr1 from a we conclude that i if m is a complete n manifold of nonnegative curvature then mng q m is bounded above by a number depending only on n and q 2 together with the results of ch and cfg from c we conclude that ii if m is a compact n manifold whose sectional curvature and diameter satisfy secm and diamm d then q m has a finite number of possible isomorphism classes depending on n d q 2 provided q m is finitely generated we also show that b if m is a compact n manifold with secm and diam m d then the cohomology ring h m may have infinitely many isomorphism classes in particular b answers some questions raised by k grove gro

a controlled plus construction for crumpled laminations given a closed n manifold m n 4 and a finitely generated perfect subgroup p of it1 m we previously developed a controlled version of quillen s plus construction namely a cobordism w m n with the inclusion j n f w a homotopy equivalence and kernel of i i1 m f it1 w equalling the smallest normal subgroup of xl1 m containing p together with a closed map p w 0 1 such that p l t is a closed n manifold for every t e 0 1 and in particular m p 1 o and n p l l we accomplished this by constructing an acyclic map of manifolds f m f n having the right fundamental groups and w arose as the mapping cylinder of f with a collar attached along n the main result here presents a condition under which the desired controlled plus construction can still be accomplished in many cases even when it1 m contains no finitely generated perfect subgroups by products of these results include a new method for constructing wild embeddings of codimension one manifolds and a better understanding of perfect subgroups of finitely presented groups

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

on a problem of yau regarding a higher dimensional generalization of the cohn vossen inequality we show that a problem asked by yau open problems in geometry chern a great geometer of the twentieth century pp 275 319 1992 cannot be true in general the counterexamples are constructed based on the recent work of wu and zheng examples of positively curved complete kahler manifolds geometry and analysis vol 17 pp 517 542 2010

tracking properties of a gradient based second order adaptive iir notch filter with constrained poles and zeros gradient type adaptive iir notch filters have many attractive merits for various real life applications since they require a small number of computations and yet demonstrate practical performance however it is generally quite difficult to assess their performance analytically their tracking properties in particular have not yet been investigated in this paper the tracking performance of a plain gradient pg algorithm is analyzed in detail for a second order adaptive iir notch filter with constrained poles and zeros which takes a linear chirp signal as its input first two sets of difference equations for the frequency tracking error and mean square error mse are established in the sense of convergence in the mean and convergence in the mean square respectively closed form expressions for the asymptotic tracking error and mse are then derived from these difference equations an optimum step size parameter for the algorithm is also evaluated based on the minimization of the asymptotic tracking error or the tracking mse it is discovered that the asymptotic tracking error may be driven to zero for a positive chirp rate by selecting a proper step size which is an interesting property for a real valued adaptive filtering algorithm extensive simulations are performed to support the analytical findings

dissolving four manifolds and positive scalar curvature we prove that many simply connected symplectic four manifolds dissolve after connected sum with only one copy of s2 s2 for any finite group g that acts freely on the three sphere we construct closed smooth four manifolds with fundamental group g which do not admit metrics of positive scalar curvature but whose universal covers do admit such metrics

the full ward takahashi identity for colored tensor models colored tensor models ctm is a random geometrical approach to quantum gravity we scrutinize the structure of the connected correlation functions of general ctm interactions and organize them by boundaries of feynman graphs for rank d interactions including but not restricted to all melonic varphi 4 vertices to wit solely those quartic vertices that can lead to dominant spherical contributions in the large n expansion the aforementioned boundary graphs are shown to be precisely all possibly disconnected vertex bipartite regularly edge d colored graphs the concept of ctm compatible boundary graph automorphism is introduced and an auxiliary graph calculus is developed with the aid of these constructs certain u invariance of the path integral measure is fully exploited in order to derive a strong ward takahashi identity for ctms with a symmetry breaking kinetic term for the rank 3 varphi 4 theory we get the exact integral like equation for the 2 point function similarly exact equations for higher multipoint functions can be readily obtained departing from this full ward takahashi identity our results hold for some group field theories as well altogether our non perturbative approach trades some graph theoretical methods for analytical ones we believe that these tools can be extended to tensorial syk models

a minimal parameter adaptive notch filter with constrained poles and zeros a new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow band or sine wave signals in an additive broad band process the algorithm is of recursive prediction error rpe form and uses a special constrained model of infinite impulse response iir with a minimal number of parameters the convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape for sufficiently large data sets the variances of the sine wave frequency estimates are of the same order of magnitude as the cramer rao bound results from simulations illustrate the performance of the algorithm under a wide range of conditions

simply connected 4 manifolds with a given boundary let m be a closed oriented connected 3 manifold for each bilinear symmetric pairing zn l our goal is to calculate the set vl m of all oriented homeomorphism types of compact 1 connected oriented 4manifolds with boundary m and intersection pairing isomorphic to zn l for each pair zn l which presents h m we construct a double coset space bl m and a function ct vl m bl m the set bt m is the quotient of the group of all link pairing preserving isomorphisms of the torsion subgroup of h1 m by two naturally occuring subgroups when zn l is an even pairing we construct another double coset space bl m a function 6l vl m b fl m and a projection p2 bl m bl m such that p2 c l ct our main result states that when zn l is even the function c l is injective as is the function c x a vl m bl m x z 2 when z l is odd here a is a kirby siebenmann obstruction to smoothing it follows that the sets vl m are finite and of an order bounded above by a constant depending only on h1 m we also show that when hi m q 0 and z l is even ct p2 c 6l is injective it seems likely that via the functions cl x a and 6l the sets bl m x z 2 and bl m calculate vl m when zn l is respectively odd and even we verify this in several cases most notably when h1 m is free abelian the results above are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between two 1connected 4 manifolds extending a given homeomorphism of their boundaries the theory developed is then applied to show that there is an m 0 depending only on h1 m such that for any self homeomorphism f of m fm extends to a self homeomorphism of any 1 connected compact 4 manifold with boundary m introduction in m freedman s fundamental paper fr he classified closed simply connected oriented 4 manifolds up to orientation preserving homeomorphism he showed that modulo the kirby siebenmann invariant these manifolds are in bijective correspondence through their intersection pairings with the set of unimodular bilinear symmetric pairings over z see theorem 1 5 of fr and corollary 2 2 3 of q in this paper we begin a classification of simply connected 4 manifolds with connected boundary our results with regard to this problem are based on a theorem which gives necessary and sufficient conditions for the existence of a homeomorphism between 1 connected 4 manifolds extending a given homeomorphism of their boundaries received by the editors september 19 1985 1980 mathematics subject classification 1985 revision primary 57n15 research supported by an nserc canada post doctoral fellowship 1986 american mathematical society 0002 9947 86 1 00 25 per page

performance analysis of the sign algorithm for a constrained adaptive iir notch filter adaptive infinite impulse response iir notch filters are very attractive in terms of their reasonable performances and low computational requirements generally it is very difficult to assess their performances analytically due to their iir nature this paper analyzes in detail the steady state performance of the sign algorithm sa for a well known adaptive iir notch filter with constrained poles and zeros slow adaptation and gaussianity of the notch filter output are assumed for the sake of analysis two difference equations are first established for the convergences in the mean and mean square in the vicinity of the steady state of the algorithm steady state estimation error or bias and mean square error mse of the sa are then derived in closed forms a coarse stability bound is also derived for the algorithm theory based comparison between the algorithm and the plain gradient pg algorithm is done in some detail extensive simulations are conducted to demonstrate the validity of the analytical results for both slow and relatively fast adaptations

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

smoothing noisy data under monotonicity constraints existence characterization and convergence rates in recent years there has been an increasing interest in the study of interpolation procedures preserving some shape defined in the form of a convex constraint such as monotonicity positivity and convexity in a recent paper the author proved that the convergence rates obtained using interpolatory monotone or positive or convex splines are the same as those obtained in the unconstrained case in this paper we aim to extend those results to the case of constrained smoothing splines we define general constrained smoothing splines and obtain theorems proving their existence uniqueness and a general result concerning their characterization we use this result to characterize the monotone smoothing spline finally we study the convergence rates of this smoothing splines when smoothing data coming from a smooth function plus noise if we calls n c to the smoothing spline and 2 to the variance of the data we prove that e left left f s n lambda c right k 2 right o lambda frac m k m sigma 2 o left frac 1 n lambda frac 2k 1 2m right this result shows that in the case of smoothing splines the attainable convergence rates are the same in the unconstrained and constrained cases

heegaard floer homology of matsumoto s manifolds abstract we consider a homology sphere m n k 1 k 2 presented by two knots k 1 k 2 with linking number 1 and framing 0 n we call the manifold matsumoto s manifold we show that m n t 2 3 k 2 never bounds any contractible 4 manifold if n 2 k 2 holds we also give a formula of ozsvath szabo s invariant as the total sum of the euler numbers of the reduced filtration we compute the invariants of the twisted whitehead doubles of torus knots and correction terms of the branched covers of the whitehead doubles by using owens and strle s obstruction we show that the 12 twisted whitehead double of the 2 7 torus knot and the 20 twisted whitehead double of the 3 7 torus knot are not slice but the double branched covers bound rational homology 4 balls these are new examples having a gap between what a knot is slice and what a double branched cover bounds a rational homology 4 ball

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

analysis and performance evaluation of an adaptive notch filter an adaptive notch filter is derived by using a general prediction error framework the proposed infinite impulse response filler has a special structure that guarantees the desired transfer characteristics the filter coefficients are updated by a version of the recursive maximum likelihood algorithm the convergence properties of the algorithm and its asymptotic behavior are discussed and its performance is evaluated by simulation results

approximation error estimates on a bounded domain in r n interpolating and smoothing discrete d m splines considerant un espace discretv h associe ah m une fonctionf h m 1 et lad m spline d interpolation discrete h d def dansv h cf 1 on etablit des estimations de l erreurf eh d en fonction de la distance de hausdorffd de et de l ensemblea d des points de donnees du type h d l o d m l en utilisant des resultats de duchon 5

an algorithm for computing constrained smoothing spline functions the problem of computing constrained spline functions both for ideal data and noisy data is considered two types of constriints are treated namely convexity and convexity together with monotonity a characterization result for constrained smoothing splines is derived based on this result a newton type algorithm is defined for computing the constrained spline function thereby it is possible to apply the constraints over a whole interval rather than at a discrete set of points results from numerical experiments are included

4 manifold topology ii dwyer s filtration and surgery kernels even when the fundamental group is intractable i e not good many interesting 4 dimensional surgery problems have topological solutions we unify and extend the known examples and show how they compare to the presumed counterexamples by reference to dwyer s filtration on second homology the development brings together many basic results on the nilpotent theory of links as a special case a class of links only slightly smaller than homotopically trivial links is shown to have free slices on their whitehead doubles

spline smoothing and optimal rates of convergence in nonparametric regression models linear estimation is considered in nonparametric regression models of the form yi f xi ei xi e a b where the zero mean errors are uncorrelated with common variance a2 and the response function f is assumed only to have a bounded square integrable qth derivative the linear estimator which minimizes the maximum mean squared error summed over the observation points is derived and the exact minimax rate of convergence is obtained for practical problems where bounds on 11 f2q 11 and a2 may be unknown generalized cross validation is shown to give an adaptive estimator which achieves the minimax optimal rate under the additional assumption of normality 1 the model consider the nonparametric regression model

monotone smoothing with application to dose response curves and the assessment of synergism a spline based procedure for monotone curve smoothing is proposed and is illustrated by application to dose response curves it is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs

surgery in dimension four and noncompact 5 manifolds this paper describes a precise relationship between the problems of completing surgery in dimension four and finding boundaries for noncompact 5 manifolds two outstanding problems of low dimensional topology are completing 4 dimensional surgery and finding boundaries for noncompact 5 dimensional manifolds although no complete theory is known for either problem some interesting results have been found see 1 4 5 10 and addendum in this paper we describe a complete relationship between these two problems consequently knowledge of 4 dimensional surgery yields information about noncompact 5 manifolds and conversely all manifolds and maps in this paper are assumed to be smooth each manifold is provided with a basepoint and when appropriate basepaths will be chosen to given 2 spheres without explicit mention i wish to thank gerald a anderson and frank quinn for helpful discussions also i wish to thank patrick gilmer for his advice and encouragement during this project 1 statement of results let f b m am y x be a degree one normal map in the sense of wall 11 where m is a compact connected 4 manifold and y x is a poincare pair not necessarily simple if x 0 then we require that f jam am x induces an isomorphism of homology groups with a z vi y coefficients also we assume that f is 2 connected k2 m is a free a module and the surgery obstruction a f b e lh 7 c is zero if h c k2 m is a subkernel we will say that h is representable in m if we can find disjoint framed embedded 2 spheres si sr c int m such that the inclusion m ui si m induces an isomorphism of fundamental groups and the classes of sl sr in h2 m a 7t2 m form a basis over a for h the subkernel h is stably representable if for some integer k 0 h ed kei ek is representable in m k s2 x s2 here ei denotes the class of s2 x 1 c ith summand s2 x s2 and e1 ek is the submodule generated by el ek we regard h ed ke ek as received by the editors august 10 1982 1980 mathematics subject classification primary 57r65 secondary 57m99 1985 american mathematical society 0002 9947 85 1 00 25 per page

monotone b spline smoothing abstract estimation of growth curves or item response curves often involves monotone data smoothing methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated built on the ideas of koenker ng and portnoy and ramsay we propose monotone b spline smoothing based on l 1 optimization this method inherits the desirable properties of spline approximations and the computational efficiency of linear programs the constrained fit is similar to the unconstrained estimate in terms of computational complexity and asymptotic rate of convergence through applications to some real and simulated data we show that the method is useful in a variety of applications the basic ideas utilized in monotone smoothing can be useful in some other constrained function estimation problems

theory of ordered spaces this is the first of a planned series of investigations on the theory of ordered spaces based upon four axioms two of these the order i 1 1 and the local structure ii 5 1 axioms provide the structure of the theory and the other two the identification i 1 11 and cone i 2 7 axioms eliminate pathologies or excessive generality in the present paper the axioms are supplemented by the nontriviality conditions i 1 9 and a regularity property ii 4 2

the global structure of simple space times according to a standard definition of penrose a space time admitting well defined future and past null infinitiesi andi is asymptotically simple if it has no closed timelike curves and all its endless null geodesics originate fromi and terminate ati the global structure of such space times has previously been successfully investigated only in the presence of additional constraints the present paper deals with the general case it is shown thati is diffeomorphic to the complement of a point in some contractible open 3 manifold the strongly causal regioni0 ofi is diffeomorphic to mathbb s 2 times mathbb r and every compact connected spacelike 2 surface ini is contained ini0 and is a strong deformation retract of bothi0 andi moreover the space time must be globally hyperbolic with cauchy surfaces which subject to the truth of the poincare conjecture are diffeomorphic to 3

fundamental groups of positively curved manifolds with symmetry we obtain a classification for the fundamental groups of closed n manifolds of positive sectional curvature which admit an isometric t k action with k ge frac n 6 1 n ne 11 15

stein structures and holomorphic mappings we prove that every continuous map from a stein manifold x to a complex manifold y can be made holomorphic by a homotopic deformation of both the map and the stein structure on x in the absence of topological obstructions the holomorphic map may be chosen to have pointwise maximal rank the analogous result holds for any compact hausdorff family of maps but it fails in general for a noncompact family our main results are actually proved for smooth almost complex source manifolds x j with the correct handlebody structure the paper contains another proof of eliashberg s int j math 1 29 46 1990 homotopy characterization of stein manifolds and a slightly different explanation of the construction of exotic stein surfaces due to gompf ann math 148 2 619 693 1998 j symplectic geom 3 565 587 2005

a decomposition theorem for h cobordant smooth simply connected compact 4 manifolds theorem let m and n be smooth h cobordant compact 1 connected 4 manifolds there exist decompositions m m0 m1 and n n0 n1 where m0 and n0 are smooth compact contractible 4 manifolds with boundary so that m1 and n1 are dieomorphic if m and n are closed then we may further arrange that m1 and n1 are 1 connected in fact if w is an h cobordism connecting m and n then w can be written w w0 i w1 where w0 m0 n0 is an often nontrivial h cobordism and w1 m1 n1 is smoothly the product h cobordism m1 i m1 f0 g m1 f1 g this theorem lies in the mainstream of combinatorial 4 manifold theory circa 1975 but oddly the result was overlooked it now ts into a rich context donaldson theory and raises new questions when compared with the known examples in 1988 akbulut a showed that a manifold x homotopy equivalent to a k3 surface could after blowing up a point be transformed into a rational surface q by cutting out and regluing a certain contractible mazur manifold by an involution of its boundary at the time a rather delicate argument of fintushel and stern relying on the observed presence of the homology sphere 2 3 7 x showed that certain donaldson invariants of x and its blow up x were nontrivial this distinguished x from the h cobordant manifold q in retrospect this was the rst nontrivial example of our theorem the result was a surprise the donaldson invariant which derives from the second homology had been localized on a contractible piece recently bizaca and gompf bg have shown that x is in fact dieomorphic to k3 allowing a more direct analysis of its donaldson invariant see e g qk or km they also nd an innite family of examples

smoothing under diffeomorphic constraints with homeomorphic splines in this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms this diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time dependent vector field this solution has a closed form expression which can be computed using classical unconstrained spline smoothing techniques this method does not require the use of quadratic or linear programming under inequality constraints and has therefore a low computational cost in a one dimensional setting incorporating diffeomorphic constraints is equivalent to imposing monotonicity thus as an illustration it is shown that such a monotone spline can be used to make monotone any unconstrained estimator of a regression function and that this monotone smoother inherits the convergence properties of the unconstrained estimator some numerical experiments are proposed to illustrate its finite sample performances and to compare them with another monotone estimator we also provide a two dimensional application on the computation of diffeomorphisms for landmark and image matching

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4

a family of freely slice good boundary links we show that every good boundary link with a pair of derivative links on a seifert surface satisfying a homotopically trivial plus assumption is freely slice this subsumes all previously known methods for freely slicing good boundary links with two or more components and provides new freely slice links

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

gromov hausdorff limits of kahler manifolds and the finite generation conjecture we study the uniformization conjecture of yau by using the gromovhausdorff convergence as a consequence we confirm yau s finite generation conjecture more precisely on a complete noncompact kahler manifold with nonnegative bisectional curvature the ring of polynomial growth holomorphic functions is finitely generated during the course of the proof we prove if m is a complete noncompact kahler manifold with nonnegative bisectional curvature and maximal volume growth then m is biholomorphic to an affine algebraic variety we also confirm a conjecture of ni on the existence of polynomial growth holomorphic functions on kahler manifolds with nonnegative bisectional curvature

group actions homeomorphisms and matching a general framework this paper constructs metrics on the space of images cal i defined as orbits under group actions cal g the groups studied include the finite dimensional matrix groups and their products as well as the infinite dimensional diffeomorphisms examined in trouve 1999 quaterly of applied math and dupuis et al 1998 quaterly of applied math left invariant metrics are defined on the product cal g times cal i thus allowing the generation of transformations of the background geometry as well as the image values examples of the application of such metrics are presented for rigid object matching with and without signature variation curves and volume matching and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another

stable mapping class groups of 4 manifolds with boundary we give a complete algebraic description of the mapping class groups of compact simply connected 4 manifolds with boundary up to connected sum with copies of s 2 s 2

rigidity theorems for right angled reflection groups let t be a right angled reflection group let m and m be coxeter manifolds then any t map f m fm is t homotopic to a homeo morphism introduction this paper contains the results given in the author s ph d the sis davis in 9 showed that in every dimension 4 there exists a cocompact reflection group on a contractible manifold not homeomorphic to an euclidean space also he gave the first example of a closed aspherical manifold not covered by euclidean space davis construction provides an infinite coxeter group acting locally smoothly effectively and properly discontinuously on a contractible manifold with compact quotient

stability bounds and steady state coefficient variance for a second order adaptive iir notch filter in this correspondence we present a stochastic convergence analysis of a second order adaptive iir notch filter the approach is based on a linearization of the gradient in the vicinity of the optimal solution expressions for stability bounds on the algorithm step size and the steady state coefficient variance are derived these closed form analytical results are verified by computer simulations for different signal and noise conditions

topologically invariant chern numbers of projective varieties abstract we prove that a rational linear combination of chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the euler and pontryagin numbers in dimension at least three we prove that only multiples of the top chern number which is the euler characteristic are invariant under diffeomorphisms that are not necessarily orientation preserving these results solve a long standing problem of hirzebruch s we also determine the linear combinations of chern numbers that can be bounded in terms of betti numbers

a diffeomorphism classification of manifolds which are like projective planes we give a complete diffeomorphism classification of 1 connected closed manifolds m with integral homology h m z z z provided that dim m 6 4

construction of group actions on four manifolds it is shown that any cyclic group of odd prime order acts on any closed simply connected topological 4 manifold inducing the identity on integral homology the action is locally linear except perhaps at one isolated fixed point in the case of primes greater than three a more careful argument is used to show that the action can be constructed to be locally linear introduction in this paper we shall show that every closed simply connected topological 4 manifold m4 admits an action of any cyclic group zp of odd prime order p the action will be homologically trivial that is induce the identity on integral homology be pseudofree that is have only isolated fixed points except in certain cases when p 3 and be locally linear except perhaps at one isolated fixed point when p 2 and the intersection form of m4 has even type then the same conclusion holds this is also due to s kwasik and p vogel 1985 by a somewhat different proof if p 2 and the intersection form of m has odd type however then an action of z2 which is homologically trivial must have a fixed point set containing two dimensional components see 7 further it is harder to control the kirby siebenmann triangulation obstruction which is then not determined by the intersection form it is interesting to ask whether these actions can be locally linear or smooth when m4 is smooth the existence of a locally linear z2 action implies the vanishing of the kirby siebenmann obstruction see kwasik and vogel 1984 we shall show however that for p 3 in general these actions can be constructed to be locally linear in a recent preprint kwasik has shown that this is the case for the fake cp2 when p is odd by a rather different proof these actions are homologically trivial and have only isolated fixed points except sometimes when p 3 the g signature theorem shows that not every simply connected 4 manifold admits pseudofree locally linear actions when p 3 we shall see for example that neither the e8 manifold the kummer surface nor a nontrivial connected sum of copies of cp2 admits such an action for p 3 in broad outline our construction goes as follows let a closed oriented simply connected 4 manifold m be given by studying equivariant framed links we construct a compact smooth 4 manifold with boundary having the intersection form of m and admitting a smooth zp action which is pseudofree and homologically trivial the action is free on the boundary homology sphere e in a paper primarily focused on equivariant plumbing diagrams for high dimensional highly connected manifolds with even intersection forms weintraub 1975 carried out most of this we give an independent development because we need to be able to better control received by the editors october 16 1985 and in revised form january 7 1986 1980 mathematics subject classification 1985 revision primary 57s17 57s25 57n15 research supported in part by a grant from the national science foundation 1987 american mathematical society 0002 9947 87 1 00 25 per page

complete riemannian manifolds with pointwise pinched curvature an analogous bonnet myers theorem is obtained for a complete and positively curved n dimensional n 3 riemannian manifold m n we prove that if n 4 and the curvature operator of m n is pointwise pinched or if n 3 and the ricci curvature of m 3 is pointwise pinched then m n is compact

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

a surgery sequence in dimension four the relations with knot concordance we present a systematic treatment of the classification problem for compact smooth 4 manifolds m it is modeled on the surgery exact sequence the central theorem in the classification of n manifolds n 5 the price for the extension to dimension 4 is a hole in m where a homotopy 1 skeleton should be there is no homotopy theoretic or surgical obstruction to complet ing m with a wedge of circles so that the completion has the topology of a compact smooth manifold this point set problem is all that stands between 4 manifolds and the tranquility that prevails in higher dimensions when m is simply connected only a point is missing from the model the applications of this are discussed in f and fq 1 the general theory has application to knot and link theory in particular knots with alexander polynomial 1 are characterized geometrically as knots admitting a certain

deforming the metric on complete riemannian manifolds soit m g ij x une variete de riemann a n dimensions complete non compacte de tenseur de complexe riemannien r ijkl satisfaisant r ijkl 2 k 0 sur m ou 0 0 dependant seulement de n et de k 0 telle que l equation d evolution g ij x t t 2r ij x t sur m g ij x o g ij x x m ait une solution lisse g ij x t 0 pour un temps court 0 t t u k 0 et satisfait l estimation suivante pour un entier m 0 il existe des constantes c m 0 dependant seulement de n m et k 0 telles que sup x m v m r ijkl x t 2 c m t m 0 t t u k 0

linking and causality in globally hyperbolic space times the classical linking number lk is defined when link components are zero homologous in 15 we constructed the affine linking invariant alk generalizing lk to the case of linked submanifolds with arbitrary homology classes here we apply alk to the study of causality in lorentzian manifolds

the uniformization theorem for compact kahler manifolds of nonnegative holomorphic bisectional curvature soit x h une variete de kahler compacte a n dimensions de courbure bisectionnelle holomorphe non negative et soit x h son espace de recouvrement universel alors il existe des entiers non negatifs k n 1 n l et des espaces symetriques hermitiens compacts ineductibles m 1 m k de rang 2 tels que x h est isometriquement bi holomorphe a c k g 0 p nu 1 1 p nu l l m 1 g 1 m p g p ou g 0 est la metrique euclidienne sur c k g 1 g p sont des metriques canoniques sur m 1 m p et i 1 i l est une metrique de kahler sur p nu i portant une courbure bisectionnelle holomorphe non negative

monotonicity preserving surface interpolation c 1 monotone quadratic splines are analyzed this motivates an algorithm for interpolating monotone data given on a rectangular grid with a c 1 monotone quadratic spline surface error estimates an operation count and numerical examples are given