Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

Fast switching ferroelectric side-chain liquid-crystalline polymer and copolymer

New ferroelectric side-chain liquid-crystalline polymers, a copolymer and a homopolymer, with siloxane backbone and a triaromatic mesogen as the side group have been synthesized. The materials exhibit a chiral smectic C phase over a large temperature range extending to room temperature. They possess high values of spontaneous polarization: 105 nC cm^-2 for the homopolymer and 180 nC cm^-2 for the copolymer. The electro-optic switching time in the chiral smectic C phase is extremely fast (150 μs). In the smectic A phase, an electroclinic effect with switching times less than 100 μs and with field induced tilt angles of 18° is observed.     

Synthesis of poly-yne polymers containing transition metals,disilane, disiloxane and phosphine groups in the main chain

The synthesis and characterization of metal poly-yne polymers containing disilane, disiloxane and phosphine groups in the main chain are described. The platinum and palladium poly-yne polymers were synthesized by polycondensation reactions between a metal chloride and an α, ω-bisethynyl complex in amines in the presence of cuprous iodide as a catalyst. The nickel poly-yne polymers were synthesized by an alkynyl ligand exchange reaction between a nickel acetylide and an α, ω-bisethynyl complex in diethylamine in the presence of cuprous iodide as a catalyst. The reaction of the platinum poly-yne polymer, containing disiloxane groups in the main chain, with copper (I) salts afforded adducts of η-²-bonded σ-acetylide polymer complexes. The reactions of the palladium poly-yne polymer, containing phosphine groups in the main chain, with transition-metal carbonyl complexes afforded polymer complexes which have phosphorus in the main chain-transition-metal bonds. A concentrated solution of the platinum poly-yne polymer containing disiloxane groups in the main chain forms a lyotropic liquid crystal in dichloromethane or 1, 2-dichloroethane.     

Measurement of the transverse Doppler shift using a stored relativistic7Li+ ion beam

We have performed for the first time precision spectroscopy on a coasting fast⁷Li⁺ ion beam in a storage ring. The ion beam moving with 6.4% speed of light was first electron cooled and then merged with two counterpropagating laser beams acting on two different hyperfine transitions sharing a common upper level (λ-system). One laser was frequency locked to thea ₃ ¹²⁷J₂ hfs frequency component established as a secondary frequency standard at 514 nm. The second laser was tuned over theλ-resonance, which was recorded relative to¹²⁷J₂ hfs components. This experiment is sensitive to the time dilation in fast moving frames and will lead to new limits for the verification of special relatively. The present status of the experiment and perspectives in accuracy are discussed.     

An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy traffic conditions. In this paper, we propose a new approximation technique, which combines the light and heavy traffic characteristics. This interpolation approximation is based on the theory of multipoint Padé approximation which is applied at two points: light and heavy traffic. We show how this can be applied for estimating the waiting time moments of the ^GI/G/1 queue. The light traffic derivatives of any order can be evaluated using the MacLaurin series analysis procedure. The heavy traffic limits of the ^GI/G/1 queue are well known in the literature. Our technique generalizes the previously developed interpolation approximations and can be used to approximate any order of the waiting time moments. Through numerical examples, we show that the moments of the steady state waiting time can be estimated with extremely high accuracy under all ranges of traffic intensities using low orders of the approximant. We also present a framework for the development of simple analytical approximation formulas. This revised version was published online in June 2006 with corrections to the Cover Date.     

Distribution of silicon over sublattices in semiconducting A3B5 compounds

The stable site of Si substitutional impurities in GaAs and AlAs at T=0 K is determined on the basis of an analysis of the energy of solution of silicon, and of the energies of formation of intrinsic defects and the reaction energies of their interaction obtained by calculating the total energy of the disordered compounds. These calculations indicate that amphotericity and vacancies have an effect on the distribution of Si. At low Si concentrations, Si in GaAs is located on the sublattice of the group III element, and in AlAs, on the sublattice of the group V element. Fiz. Tverd. Tela (St. Petersburg) 39, 264–266 (February 1997)     

Compensated Compactness, Paracommutators, and Hardy Spaces

LetB₁: ⁿ× ^N₁→ ^m₁,B₂: ⁿ× ^N₂→ ^m₂andQ: ^m₂→ ^m₁be bilinear forms which are related as follows: ifμandνsatisfyB₁(ξ, μ)=0 andB₂(ξ, ν)=0 for someξ≠0, thenμ^τQν=0. Supposep⁻¹+q⁻¹=1. Coifman, Lions, Meyer and Semmes proved that, ifuL^p( ⁿ) andvL^q( ⁿ), and the first order systemsB₁(D, u)=0,B₂(D, v)=0 hold, thenu^τQvbelongs to the Hardy spaceH¹( ⁿ), provided that both (i)p=q=2, and (ii) the ranks of the linear mapsB_j(ξ, ·) : ^N_j→ ^m₁are constant. We apply the theory of paracommutators to show that this result remains valid when only one of the hypotheses (i), (ii) is postulated. The removal of the constant-rank condition whenp=q=2 involves the use of a deep result of Lojasiewicz from singularity theory.     

Meromorphic functions in the solution of the two-dimensional problem of elasticity

We introduce meromorphic functions that follow logically from the solutions of doubly periodic problems of two-dimensional elasticity (a rectangular period lattice). We establish their properties and their connection with the known meromorphic functions. We give convenient formulas for numerical implementation. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, pp. 53–58.     

ContributionsSign-balanced covering matrices

A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]^t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C₁, C₂,…, C_t of t columns and for each choice = (₁,…,_t) Δ of signs, the linear combination ∑_j=1^t _jC_j contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (₁, …, _t) of signs in δ, the linear combination ∑_j=1^t _jC_j contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described.