Distance functions and statistics

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M,g) with small curvature, small curvature change and injectivity radius +∞. Here p_iM and γ_v is the maximal geodesic with initial velocity v and 0<t₁<<t_m.     

Relative production of vector and pseudoscalar states for light- and heavy-flavour mesons

The relative fractions of vector, V, and pseudoscalar, P, primary mesons produced in and decays, and primary light-flavour mesons produced in fragmentation processes are explained by the hyperfine mass splitting. The difference in corresponding fractions arises from the difference in the constituent quark masses , m_s, m_c and m_b:

The production ratios for strange, charm and beauty mesons evaluated from the ρ/(3π) ratio, measured at LEP for primary produced ρ and π, agree with the results of LEP and lower energy e⁺e⁻ experiments.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Temperature dependence of intensities and widths of N2-broadened lines in the 15 μm CO2 band from tunable laser measurements

Intensities and nitrogen-broadened widths of several low-J lines in the Q-branch of the 15 μm band of CO₂ have been determined over the temperature range 200–300 K. Measurements were made with a tunable infra-red diode laser spectrometer having a spectral resolution 10^-4 cm^-1. Measured intensities are uniformly about 7% lower than available calculations which were based on previous measurements of band intensity. Measured line widths are higher than available calculations and generally followed the relation

b_L⁰(T)=b_L⁰(T₀)(T₀|T)ⁿ

with n = 0.74 (standard deviation 0.08).     

(Q) corrections to particle multiplicity ratios in gluon and quark jets

The order (Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through (Q²) we find

, with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

Interprétation de la susceptibilité magnétique de l'oxysulfure de samarium par un modèle de champ cristallin

The paramagnetic susceptibility of polycrystalline samarium oxysulfide has been measured between 3° and 300°K. The data are interpreted with an approximation to the crystal potential of the form

V_c = _JV₂⁰O₂⁰ + β_JV₄⁰O₄⁰ + β_JV₄³O₄³

and correction taking into account exchange is made. The energy levels and crystal fields parameters have been calculated. Fluorescence studies of Gd₂O₂S: Sm³⁺ and Y₂O₂S: Sm³⁺ have confirmed these results.     

How unitarity imposes a steep small-x rise of spin structure function gLT=g1+g2 and breaking of DIS sum rules

We derive a unitarity relationship between the spin structure function g_LT(x,Q²)=g₁(x,Q²)+g₂(x,Q²), the LT interference diffractive structure function and the spin-flip coupling of the pomeron to nucleons. Our diffractive mechanism gives rise to a dramatic small-x rise

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, where δ_g is an exponent of small-x rise of the unpolarized gluon density in the proton at a moderate hard scale for light flavour contribution and large hard scale for heavy flavour contribution. It invalidates the Burkhardt–Cottingham sum rule. The found small-x rise of diffraction driven g_LT(x,Q²) is steeper than given by the Wandzura–Wilczek relation under conventional assumptions on small-x behaviour of g₁(x,Q²).     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Integral geometry on families of surfaces in the space

A complex {B_ξ} of submanifolds is called admissible in the sense of integral geometry if there are such densities μ_ξ on B_ξ, that the integral transformation

has a local inversion formula. We prove that compact smooth surfaces of an admissible complex in P³ has degree 3 and obtain complete classification of admissible complexes of quadrics. Several general theorems and conjectures about admissible complex of k-dimensional submanifolds are stated.     

The first eigenvalue of the Dirac operator on Kähler manifolds

If M^2m is a closed Kähler spin manifold of positive scalar curvature R, then each eigenvalue λ of type r (r {1, …, [(m + 1)/2]}) of the Dirac operator D satisfies the inequality λ² ≥ rR₀/4r − 2, where R₀ is the minimum of R on M^2m. Hence, if the complex dimension m is odd (even) we have the estimation

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for the first eigenvalue of D. In the paper is also considered the limiting case of the given inequalities. In the limiting case with m = 2r − 1 the manifold M^2m must be Einstein. The manifolds S², S² × S², S² × T², P³( ), F( ), P³( ) × T² and F( ³) × T², where F( ³) denotes the flag manifold and T² the 2-dimensional flat torus, are examples for which the first eigenvalue of the Dirac operator realizes the limiting case of the corresponding inequality. In general, if M^2m is an example of odd complex dimension m, then M^2m × T² is an example of even complex dimension m + 1. The limiting case is characterized by the fact that here appear eigenspinors of D² which are Kählerian twistor-spinors.     

Differential operators on a Riemann surface with projective structure

Let X be a Riemann surface equipped with a projective structure and a theta characteristic on X, or in other words, is a holomorphic line bundle equipped with a holomorphic isomorphism with the holomorphic cotangent bundle Ω_X. The complement of the zero section in the total space of the line bundle has a natural holomorphic symplectic structure, and using , this symplectic structure has a canonical quantization. Using this quantization, holomorphic differential operators on X are constructed. The main result is the construction of a canonical isomorphism

, n≥0, provided i[−2(k−1),0].     

Measurement of the slope parameter for the neutral pion spectrum in KL → πππ decay

The π⁰ spectrum in the K_L⁰ → 3π decay was measured using a wire chambers magnetic spectrometer. In the usual approximation, the matrix element can be expressed as: M² ≈ 1 + 2a₀(M_K/M_π²)(2T_π⁰−T_π⁰max) + a₁(M_K²/M_π⁴)(2T_π⁰−T_π⁰max)². We obtained a₀ = −0.282 ± 0.011 and a₁ consistent with zero.     

Escape of charged particles at stopping annihilation of antiprotons in the heavy nuclei of nuclear photoemulsion

“Rare” annihilation channels for antiprotons stopping on heavy (Ag, Br) nuclei of photoemulsion, have been sought; 4872 stops of antiprotons on photoemulsion nuclei are analysed. Events of formation and decay of the hyperfragment _Λ⁴H, escape of ⁸He and ⁸Li nuclei, one-prong stars with the mean range 79.5±5.1 μm of secondary slow “b” particles are found among the annihilation stars at capture on nuclei (Ag, Br). The lower limits for the production probability of _Λ⁴H and ⁸He, ⁸Li nuclei per antiproton stopping in the nuclei (Ag, Br) are

W_Λ⁴H2×10⁻⁴ and W_⁸He,⁸Li=(1.3±0.6)×10⁻³.

The branching ratio for the production of one-prong stars with the secondary “b” particles is at least (1.3±0.6)×10⁻³. Possible mechanisms for a production of these events in annihilation processes are considered.     

On the Curie temperature of a spin one XY ferromagnet with uniaxial anisotropy

A spin one XY ferromagnet with uniaxial anisotropy has been investigated, using Green's function technique in random phase approximation (RPA). The Green functions associated with the anisotropy energy are treated without decoupling. A set of coupled equations have been obtained to find the critical temperature T_c and (S^Z)² at T_c as function of the uniaxial anisotropy parameter D. T_c and (S^Z)² at T_c are found to increase with D. The results are compared with the earlier results obtained in the Narath type of RPA.     

Nonlinear and nonlocal dynamics of spatially extended systems: Stationary states, bifurcations and stability

Spatially extended systems with nonlocal dynamics (e.g. ferromagnetic resonance or current instability) of the type

with uε ⁿ will be studied near the soft-mode instability (wave number k_c ≠ 0) of a stationary and uniform state. An amplitude equation is derived within the framework of a multiple-scale perturbation theory. A particular example of this class of nonlocal dynamics is also treated numerically. As the main result we find that in contrast to the well-known supercritical bifurcation into a stable periodic state, the uniform state can bifurcate supercritically into a stationary state of an amplitude-modulated fast oscillation in space.     

Spectral intensities in the ν1 band of NH3

Intensities have been measured for individual transitions in the Q and R branches of the ν₁ band of NH₃ using a difference-frequency laser spectrometer. The data yield an integrated band strength of S⁰_v=219.36±1.03 cm^-2/MPa at 297 K, corresponding to a transition moment of μ_v = 8.535(20) × 10^-32 C·m, and a Herman-Wallis correction factor, (1 + _jm)², where _j = 0.0209(20). The intensities of a few lines for K 7 were noticeably perturbed by a perpendicular Coriolis interaction with 2ν₄ (E, L = 2), so were excluded from the fit. A small sample of ν₃ band lines occurring in the ν₁ band scans also yields a rough estimate of the ν₃ band intensity with evident irregular perturbations.     

A limit on the lepton-family number violating process π → μe

A FNAL E799 Collaboration has carried out a search for the lepton-family number violating decay π⁰ → μ^±e using π⁰'s produced from K_L → π⁰π⁰π⁰ decays in flight. No events were observed. Assuming that lepton-family number violation is charge independent, the 90% confidence level upper limit on

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was determined to be 8.6 × 10⁻⁹.     

Granularity, microstructure, and flux creep in TlBa2Ca2Cu3O9+δ superconducting powder and silver-sheated tapes

Silver-sheathed TlBa₂Ca₂Cu₃O_9+δ (Tl-1223) tapes, with a transport critical current density, J_ct, of 6200 A/cm² at 75 K under zero magnetic field, were fabricated by the oxide-powder-in-tube (OPIT) method and characterized using an X-ray diffractometer (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), and superconducting quantum interference device (SQUID) magnetometer. The results of the magnetization and SEM study indicate that, in these tapes, individual grains are distributed randomly in orientation and weak links exist. However, strongly linked percolative current paths within the tape persisting in increasing fields, accompanied by strong intrinsic interplanar coupling, sustain a significant J_ct at high fields and lead to the plateau in the J_ct-H curve. Dislocation networks, which may act as effective pinning centers, are the common features observed in the tapes. To investigate the effects on flux pinning due to thermomechanical processing, magnetic relaxation at 1 and 2 T over 5–50 K was measured. The tape shows slightly lower normalized relaxation rates (S=-(1/M_o)dM/ dln t) than the cauliflower-like precursor powder. Analyses of the relaxation data obtained from the tape, after incorporating temperature dependence and field scaling, yield an expression for the effective pinning energy U_eff(J,T,H) = (U₁/H^0.54)[1-(T/ 72.5)²]⁴(J/J_i)^μ. This result was compared with the prediction of the collective flux-creep model, which suggests that Tl-1223 has a three-dimension-like (3D-like) vortex lattice. Presumably, a more plate-like powder morphology may result in improved texturing by the OPIT process. Tl_0.5Bi_0.5Sr₂CaCu₂O_7+δ ((Tl,Bi)-1212) powder with this morphology was therefore synthesized for comparison.