A Two-Step Smoothing Method for Varying-Coefficient Models with Repeated Measurements

Datasets involving repeated measurements over time are common in medical trials and epidemiological cohort studies. The outcomes and covariates are usually observed from randomly selected subjects, each at a set of possibly unequally spaced time design points. One useful approach for evaluating the effects of covariates is to consider linear models at a specific time, but the coefficients are smooth curves over time. We show that kernel estimators of the coefficients that are based on ordinary local least squares may be subject to large biases when the covariates are time-dependent. As a modification, we propose a two-step kernel method that first centers the covariates and then estimates the curves based on some local least squares criteria and the centered covariates. The practical superiority of the two-step kernel method over the ordinary least squares kernel method is shown through a fetal growth study and simulations. Theoretical properties of both the two-step and ordinary least squares kernel estimators are developed through their large sample mean squared risks.     

Correspondance de Jacquet–Langlands explicite II. Le cas de degréégal à la caractéristique résiduelle

Let F be a non-Archimedean locally compact field, and let p be its residual characteristic. Put G=GL _p (F) and let G ^′=D _×, where $D$ is a division algebra with centre F and of degree p ² over F. The Jacquet–Langlands correspondence is a bijection between the discrete series of G and that of G ^′. We describe this explicitly, in terms of Carayol's parametrization of these discrete series. Received: 25 November 1999     

INTEGRABILITY VIA INVARIANT ALGEBRAIC CURVES FOR PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS

1 IntroductionBy definition a complex (respectively reao planar polynomial differentialsystem or simply a polynomial system is a differential system of the formdx. da.~ = i = p(x,y), ac = i = Q(x,y), (l)dt dt ~ y = Q(x,y), (l)where the dependent variables x and y are complex (respectively real), theindependent one (the time) t is real, and P and Q are polynomials in thevariables x and y with complex (respectively real) coefficients. In all thispaper m = ma-c{deg P, deg Q} denote the degree o…     

Hydrogen-bonded sheets in the 1:1 salt of tet-b and trimesic acid

Tet-b (racemic 5,5,7,12,12,14-hexa­methyl-1,4,8,11-tetra­aza­cyclo­tetra­decane, C₁₆H₃₆N₄) and trimesic acid (1,3,5-benzene­tri­carboxylic acid, C₉H₆O₆) form a salt partially solvated by both water and methanol, i.e. 5,5,7,12,12,14-hexa­methyl-1,4,8,11-tetra­aza­cyclo­tetra­decane–1,3,5-benzene­tri­carboxyl­ic acid–methanol–water (1/1/0.78/1.12), C₁₆H₃₈N₄²⁺·C₉H₄O₆²⁻·0.78CH₄O·1.12H₂O. The anions are linked by O—H⃛O hydrogen bonds [O⃛O 2.442 (4) and 2.458 (4) Å; O—H⃛O 170 and 171°] into zigzag chains; orientationally disordered cations are linked to the anion chains by means of N—H⃛O hydrogen bonds [major orientation: N⃛O 2.695 (3)–3.071 (4) Å, N—H⃛O 148–179°; minor orientation: N⃛O 2.75 (2)–3.34 (2) Å, N—H⃛O 147–170°] and link the chains into sheets. The solvent mol­ecules are all disordered, but appear to play no significant structural role apart from space filling.     

Semisimple Types in GLn

This paper is concerned with the smooth representation theory of the general linear group G=GL(F) of a non-Archimedean local field F. The point is the (explicit) construction of a special series of irreducible representations of compact open subgroups, called semisimple types, and the computation of their Hecke algebras. A given semisimple type determines a Bernstein component of the category of smooth representations of G; that component is then the module category for a tensor product of affine Hecke algebras; every component arises this way. Moreover, all Jacquet functors and parabolic induction functors connecting G with its Levi subgroups are described in terms of standard maps between affine Hecke algebras. These properties of semisimple types depend on their special intertwining properties which in turn imply strong bounds on the support of coefficient functions.     

Isoperimetric curves on hyperbolic surfaces

Least-perimeter enclosures of prescribed area on hyperbolic surfaces are characterized.

     

Effects of block architecture and composition on the association properties of poly(oxyalkylene) copolymers in aqueous solution

A block copolymer of hydrophilic poly(ethylene oxide) and a hydrophobic poly(alkylene oxide) can associate in dilute aqueous solution to form micelles. The results of recent investigations of the micellisation behaviour and micelle properties of such copolymers are described. Copolymers of ethylene oxide with propylene oxide, 1,2‐butylene oxide or styrene oxide are considered, including aspects of their preparation. Experimental methods for determination of critical conditions for micellisation, micelle association number and spherical‐micelle radius are summarised. Effects of temperature, composition, block length and block architecture (diblock, triblock and cyclic‐diblock) are described and, where possible, related to the predictions of theory. Brief consideration is given to the dynamics of micelle formation/dissociation, to cylindrical micelles, and to effects of added salts.     

Differences Between Gas-Phase and Solid-State Molecular Structures of the Simplest Phosphonium Ylide,Me3P=CH2

Clearly different from local C ₃ symmetric is the heavy-atom core of Me₃P=CH₂, the simplest phosphonium ylide. The geometry obtained by reanalysis of gas-electron-diffraction data from 1977 is now consistent with theoretical calculations, but different from the molecular structure in the solid state. The picture shows the structure of Me₃P=CH₂ in the gas phase (a) and in the crystal (c) together with the calculated transition state (b) (viewed along the P=C bond).     

Tertiary amine catalyzed polymerizations of α‐amino acid N‐carboxyanhydrides: The role of cyclization

Sarcosine N‐carboxyanhydride, D,L ‐alanine N‐carboxyanhydride, D,L ‐phenylalanine N‐carboxyanhydride, and D,L ‐leucine N‐carboxyanhydride were polymerized with pyridine or N‐ethyldiisopropylamine as the catalyst. With pyridine, cyclic oligo‐ and polypeptides were obtained in addition to water‐initiated or water‐terminated chains. The cyclopeptides were the main products in the case of sarcosine N‐carboxyanhydride and D,L ‐phenylalanine N‐carboxyanhydride. The fraction of cycles was particularly high when N‐methylpyrrolidone was used as the reaction medium. These results suggested the existence of a pyridine‐catalyzed zwitterionic mechanism. However, cyclopeptides were also obtained with N‐ethyldiisopropylamine as the catalyst. In this case, N‐deprotonation of N‐carboxyanhydrides, followed by the formation of N‐acyl N‐carboxyanhydride chain ends, was the most likely initiation mechanism. Various chain‐growth mechanisms were examined. In the case of γ‐benzyl ester‐L ‐glutamate N‐carboxyanhydride, side reactions such as the formation of pyroglutamoyl end groups were detected. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4680–4695, 2006