The Number of Nonisomorphic Two-dimensional Algebras over a Finite Field

In this paper, we derive explicit formulas for the number of nonisomorphic two-dimensional nonassociative algebras, possibly without a unit, over a finite field. The proof combines the first author’s general classification theory of two-dimensional nonassociative algebras over arbitrary base fields with elementary counting arguments which are primarily addressed to the problem of determining the number of orbits of a finite set acted upon by the group of integers mod 2. The number of nonisomorphic two-dimensional division algebras will also be determined.     

A truncated Kv1.1 protein in the brain of the <Emphasis Type="Italic">megencephaly</Emphasis>mouse: expression and interaction

Background  

The megencephaly mouse, mceph/mceph, is epileptic and displays a dramatically increased brain volume and neuronal count. The responsible mutation was recently revealed to be an eleven base pair deletion, leading to a frame shift, in the gene encoding the potassium channel Kv1.1. The predicted MCEPH protein is truncated at amino acid 230 out of 495. Truncated proteins are usually not expressed since nonsense mRNAs are most often degraded. However, high Kv1.1 mRNA levels in mceph/mceph brain indicated that it escaped this control mechanism. Therefore, we hypothesized that the truncated Kv1.1 would be expressed and dysregulate other Kv1 subunits in the mceph/mceph mice.     

Birefringence-induced splitting of the zero-dispersion wavelength in nonlinear photonic crystal fibers

We investigate how the strongly wavelength-dependent birefringence in nonlinear photonic crystal fibers leads to a splitting in the zero-dispersion wavelength for the two polarizations. We translate the requirements for the maximum splitting of the zero-dispersion wavelength to requirements for transverse structural uniformity by adopting a simple effective-index approach in which the birefringence is calculated in a step-index fiber with an elliptical core. We find that to reduce the splitting to less than 1 nm the birefringence should be less than 2 x 10(-5), resulting in a transverse uniformity requirement of 1-3%, depending on the index step from the core to the cladding.     

Approximations for modal coupling in scattered fields from orifices

Previous investigations have used Hankel transforms to establish the velocity potentials of the wave fields resulting from arbitrary angle plane wave impingement on a circular orifice in a rigid, thick wall. The scattered field from the orifice is examined, in particular the modal contributions to the amplitude of its velocity potential. For each m,n mode the amplitude is dependent upon the amplitude of the in-orifice waves and a driving term unique to each m,n mode. In establishing the amplitudes of the in-orifice waves, the effects of modal coupling are also considered. In this work these two components of the scattered wave amplitude are investigated on a modal basis and approximations given for coupling effects. These approximations are then used to calculate the scattered field and the results compared with conventional solutions that use full modal coupling.     

Spontaneous chiral symmetry breaking for a U(N) gauge theory on a lattice

We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.     

Domain configuration and dynamic processes in orthorhombic NaCN studied by 23Na NMR satellite lines and relaxation times

The orientational dependences of the ²³Na NMR spectra which were measured in a NaCN single crystal below T_c1 are related to the EFG tensor at the Na sites in different domains. The results are consistent with the assumption that 12 different domains may arise in the orthorhombic phase. Below T_c1 also the temperature dependences of the spin relaxation times T₁ and T_1ρ of the ²³Na nucleus were measured and related to dynamic processes. Particularly the activation energy and the frequency of the flip motions of the CN^--dipoles are determined.     

Total cross section for inclusive electron scattering in the lowQ 2 region

Absolute cross sections for inclusive electron scattering on H, D, Be, Al, and Si have been measured in the kinematical region 0.08 (GeV/c)²<Q ²<1.0 (GeV/c)² and 0.3 GeV<v<6.5 GeV. The measurements have been performed at incident energies of 3, 5, 6, and 7 GeV and at the fixed scattering angle of 10°. A careful treatment of radiative corrections due to elastic electron nucleus scattering, quasielastic and inelastic scattering on the bound nucleons has been applied to the measured cross sections. The comparison of the nuclear cross sections with the elementary ones leads to a value ofA _eff<A with a rapid onset of this effect at small values of the scaling variablex′.