Transcendence of Certain Reciprocal Sums of Linear Recurrences

 Suppose that {R _n } _n ⩾ 0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers

The Rank of a Direct Power of a Small-Cancellation Group

We construct an example of a finitely generated group G such that rank((G )ⁿ)=2 for all n1. For each n, we construct a finitely presented group G _n such that rank((G _n )ⁿ)=2. We conjecture that if G is a word-hyperbolic group then rank(G ⁿ ) as $ n. For each m we give an example of a residually finite group K _m such that K _m has exactly two relators, but K _m has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D.     

Every closed convex set is the set of minimizers of some -smooth convex function

We show that for every closed convex set in a separable Banach space there is a -smooth convex function so that . We also deduce some interesting consequences concerning smooth approximation of closed convex sets and continuous convex functions.

     

Representation type of Hecke algebras of type

In this paper we provide a complete classification of the representation type for the blocks for the Hecke algebra of type , stated in terms of combinatorical data. The computation of the complexity of Young modules is a key component in the proof of this classification result.     

Extensions for finite Chevalley groups II

Let be a semisimple simply connected algebraic group defined and split over the field with elements, let be the finite Chevalley group consisting of the -rational points of where , and let be the th Frobenius kernel. The purpose of this paper is to relate extensions between modules in and with extensions between modules in . Among the results obtained are the following: for 2$"> and , the -extensions between two simple -modules are isomorphic to the -extensions between two simple -restricted -modules with suitably ``twisted" highest weights. For , we provide a complete characterization of where and is -restricted. Furthermore, for , necessary and sufficient bounds on the size of the highest weight of a -module are given to insure that the restriction map is an isomorphism. Finally, it is shown that the extensions between two simple -restricted -modules coincide in all three categories provided the highest weights are ``close" together.

     

An EMA study of VCV coarticulatory direction

This study addresses three issues that are relevant to coarticulation theory in speech production: whether the degree of articulatory constraint model (DAC model) accounts for patterns of the directionality of tongue dorsum coarticulatory influences; the extent to which those patterns in tongue dorsum coarticulatory direction are similar to those for the tongue tip; and whether speech motor control and phonemic planning use a fixed or a context-dependent temporal window. Tongue dorsum and tongue tip movement data on vowel-to-vowel coarticulation are reported for Catalan VCV sequences with vowels /i/, /a/, and /u/, and consonants /p/, /n/, dark /l/, /s/, /S/, alveolopalatal /n/ and /k/. Electromidsagittal articulometry recordings were carried out for three speakers using the Carstens articulograph. Trajectory data are presented for the vertical dimension for the tongue dorsum, and for the horizontal dimension for tongue dorsum and tip. In agreement with predictions of the DAC model, results show that directionality patterns of tongue dorsum coarticulation can be accounted for to a large extent based on the articulatory requirements on consonantal production. While dorsals exhibit analogous trends in coarticulatory direction for all articulators and articulatory dimensions, this is mostly so for the tongue dorsum and tip along the horizontal dimension in the case of lingual fricatives and apicolaminal consonants. This finding results from different articulatory strategies: while dorsal consonants are implemented through homogeneous tongue body activation, the tongue tip and tongue dorsum act more independently for more anterior consonantal productions. Discontinuous coarticulatory effects reported in the present investigation suggest that phonemic planning is adaptative rather than context independent.     

Gluing and Wormholes for the Einstein Constraint Equations

 We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions can be made either when the initial manifold is compact or asymptotically Euclidean or asymptotically hyperbolic, with suitable corresponding conditions on the extrinsic curvature. In the compact setting a mild nondegeneracy condition is required. In the final section of the paper, we list a number ways this construction may be used to produce new types of vacuum spacetimes. Received: 4 October 2001 / Accepted: 26 July 2002 Published online: 29 October 2002 RID="*" ID="*" Supported by the NSF under Grant PHY-0099373 RID="**" ID="**" Supported by the NSF under Grant DMS-9971975 and at MSRI by NSF grant DMS-9701755 RID="***" ID="***" Supported by the NSF under Grant DMS-9704515     

In situ analysis of solvents on breath and blood: a selected ion flow tube mass spectrometric study

We report measurements of residual vapour levels of xylenes and trimethylbenzenes, present following a floor re-surfacing procedure, using the technique of selected ion flow tube mass spectrometry (SIFT-MS). A subject exposed to controlled amounts of xylene and mesitylene was monitored by direct breath exhalation over a 4-hour period after exposure to the volatile organic compounds (VOCs) had stopped. The headspace gases above 5 mL blood samples taken over this period were also monitored. The decays of the solvent levels with time were fitted to a two-compartment model with residence times for xylene and mesitylene of 0.37 h and 0.38 h, respectively (compartment one) and 2.5 h and 2.8 h, respectively (compartment two).     

US Environmental Protection Agency Method 326.0, a new method for monitoring inorganic oxyhalides and optimization of the postcolumn derivatization for the selective determination of trace levels of bromate

The development of US Environmental Protection Agency (EPA) Method 317.0 provided a more sensitive, acceptable alternative to EPA Method 300.1 to be proposed as one of the recommended compliance monitoring methods for Stage II of the Disinfectants/Disinfection By-Products (DBP) Rule. This work was initiated to evaluate other postcolumn reagents (PCRs) that might be utilized to provide an additional, alternative method in order to augment compliance monitoring flexibility for inorganic oxyhalide DBP anions. Modifications of the method reported by Salhi and von Gunten, which included adjustment and optimization of flow-rates, reaction temperature, and delivery of the PCR, improved the method performance. Method 326.0 incorporates an acidic solution of potassium iodide containing catalytic amounts of molybdenum(VI) as the PCR and provides acceptable precision and accuracy for all analytes and a postcolumn bromate detection limit in reagent water of 0.17 microg/l.