Multi-dimensional volumes and moduli of convexity in banach spaces

Summary Let E be a Banach space. Using the definition for the k-dimensional volume enclosed by k + 1 vectors due to Silverman [16], one can define the modulus of k-rotundity of E. In [22] it was shown that k-uniformly rotund Banach spaces are isomorphic to uniformly rotund spaces and, indeed, have some of the same isometric properties with respect to non-expansive and nearest-point maps. The present paper examines the modulus of k-rotundity more thoroughly. Included are a result on the asymptotic behavior of the moduli for l²; a generalization of Dixmier's Theorem on higher-duals of non-reflexive spaces; and an inequality relating the moduli of E^**/E and those of E. The modulus of2-rotundity is shown to be equivalent to one of the moduli defined by V. D. Milman [13] and a necessary and sufficient condition for an l^p-product of spaces to be 2-uniformly rotund is given.Some of the results of this paper are contained in the Ph. D. dissertation of the first author, written under the direction of the second author.     

Approximation of the unit step function by a linear combination of exponential functions

We approximate the unit step function, which equals 1 if t ε [0, T] and equals 0 if t > T, by functions of the form ∑_{n = 1}^N Ax_n^N e^−λ_n^t/T, where each λ_n is a given positive constant. We find the coefficients A_n^(N) by minimizing the integrated square of the difference between the unit step function and the approximating function. We first solve the specialized case where each λ_n = n. The resulting sum can be shown to converge in the mean to the unit step function as N → ∞. The general case is then solved and some interesting properties of the numbers A_n^(N) are noted.     

A comparison of the titanomagnetites produced by several volcanoes in Iceland

Samples of titanomagnetite extracted from the ejecta of volcanoes in Iceland have been separated according to the intensity of their magnetisation and analysed with Mossbauer spectroscopy and electron microprobe analysis. It is shown that the magnetic peaks in the Mossbauer spectra vary widely between different source volcanoes and magnetic fractions, and thus that the Mossbauer spectrum of the titanomagnetite could be a useful fingerprint of the tephra.     

Effect of molecular structure on mesomorphism XXI. Monodisperse tetrameric model compounds for liquid crystalline polymers

Abstract

Twinned dimeric mesogens having a rigid-flexible-rigid molecular structure have been shown to be appropriate models for some properties of regularly alternating (rigid-flexible)_n main chain liquid crystalline polymers (lcps). A family of tetrameric monodisperse liquid crystalline model compounds chemically related to known main chain liquid crystalline polymers of the 4-alkoxyphenyl 4′-alkoxy-benzoate type has been synthesized. The tetramers are nematogenic. Alternations in thermodynamic parameters (ΔH, ΔS) for the N-I transition as a function of spacer chain length indicate conformational behaviour of the internal spacers dominates mesophase properties.     

Pion interferometry in jet events at the CERN Intersecting Storage Rings

We have revised the additive quark model for inelastic hadronic cross sections with its implications to the average charged multiplicities. The correction to the additive quark model is on the level of 2 mb only if we take into account all possible quark-quark cross sections with respect to flavour. The quark-quark constitutent cross sections have been evaluated. We have attributed average charged multiplicities to the constituent quark cross sections and have found some regularities according to the flavour of the quarks.     

Enhanced VITA technique for turbulent structure identification

Enhanced Variable Interval Time Averaging (EVITA) is introduced as a method that incorporates structure information directly into the detection method. The paper tests VITA and EVITA against an ersatz turbulence signal (antisymmetric exponential time decay) inserted into a random noise distribution. It is shown that EVITA is much less dependent than VITA on the choice of both threshold level and averaging time. EVITA is then applied to particle image velocimetry turbulence data from channel flow [7] at Re = 2872, and is shown to effectively extract bursting events.This work forms part of the Ph.D. thesis of P. SullivanThe authors gratefully acknowledge Dr. R.J. Adrian for providing the channel data. The work is supported by Natural Science and Engineering Research Council of Canada, Queen's University Advisory Research Council and DANTEC, New Jersey. MD was supported through two NSERC summer undergraduate fellowships.     

Double parton scattering inpp collisions at\sqrt s = 63 GeV

In a study ofpp collisions at \(\sqrt s = 63\) GeV with more than 29 GeV total transverse energy emitted into 1.8 units of rapidity in the central region, we have extracted a sample of 4-jet events and compared it with models of the two sources of 4-jet production: double bremsstrahlung and double parton scattering. The data cannot be described by bremsstrahlung alone, and we extract the fraction of 4-jet events attributed to double parton scattering for various definitions of the 4-jet sample. We determine the double parton scattering/2-jet yield ratio, and this leads to a determination of the proton radius. We discuss the implications of our observations for the general understanding of high-ΣE _T events.