Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.     

The sextet construction for cubic graphs

We show how to construct cubic graphs which have automorphism groups acting regularly on thes-arcs,s=4 or 5.     

Wide-band intracavity microwave cells for laser-microwave double resonance spectroscopy

The design and use of two wide-band microwave cells suitable for double resonance experiments within the resonator of a cw CO₂-laser are described. The high sensitivity of the intracavity arrangement allowed very strong double-resonance and two-photon transition signals to be observed with high microwave-frequency scan-rates (1 GHz/min), and low microwave pumping powers (≦10mW/cm²). Both cells were used over a range 15 to 63 GHz, with transmission and VSWR measurements made over the range 18 to 26.5 GHz.     

Explicit constructions of graphs without short cycles and low density codes

We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to low density codes is given.     

The vibrational force field of halogenated aromatic molecules: II. Out-of-plane vibrations of fluoroaromatics

A general quadratic force field is determined for the out-of-plane vibrations of florobenzenes. The force constants for the out-of-plane wagging of both CH and CF bonds decrease by about 10 % for each ortho fluorine substituent. No significant meta dependence could be detected. It is shown that the present field is in excellent accord with the chlorobenzene field of Scherer and with the benzene fields of Whiffen and of Kydd when due allowance is made for differences in coordinate definitions.     

On 3-skein isomorphisms of graphs

It is shown that a 3-skein isomorphism between 3-connected graphs with at least 5 vertices is induced by an isomorphism. These graphs have no loops but may be infinite and have multiple edges.     

On kaonic hydrogen. Phenomenological quantum field theoretic model revisited

We argue that due to isospin and U-spin invariance of strong low-energy interactions the S-wave scattering lengths a ⁰ ₀ and a ¹ ₀ of ˉN scattering with isospin I = 0 and I = 1 satisfy the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0 valid to leading order in chiral expansion. In the model of strong low-energy ˉN interactions at threshold (Eur. Phys. J. A 21, 11 (2004)) we revisit the contribution of the Σ(1750) resonance, which does not saturate the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0, and replace it by the baryon background with properties of an SU(3) octet. We calculate the S-wave scattering amplitudes of K^-N and K^-d scattering at threshold. We calculate the energy level displacements of the ground states of kaonic hydrogen and deuterium. The result obtained for kaonic hydrogen agrees well with recent experimental data by the DEAR Collaboration. We analyse the cross-sections for elastic and inelastic K^-p scattering for laboratory momenta 70MeV/c < p _K < 150MeV/c of the incident K^--meson. The theoretical results agree with the available experimental data within two standard deviations.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

Invariant of the hypergeometric group associated to the quantum cohomology of the projective space

We present a simple method to calculate the Stokes matrix for the quantum cohomology of the projective spaces CP^k−1 in terms of certain hypergeometric group. We present also an algebraic variety whose fibre integrals are solutions to the given hypergeometric equation.