Geometric models for the spectra of certain Gelfand pairs associated with Heisenberg groups

Let K be a compact Lie group acting on a finite dimensional Hermitian vector space V via some unitary representation. Now K acts by automorphisms on the associated Heisenberg group ${H_V=V \times \mathbb{R}}$ , and we say that (K, H _V ) is a Gelfand pair when the algebra ${L^1_K(H_V)}$ of integrable K-invariant functions on H _V commutes under convolution. In this situation an application of the Orbit Method yields a injective mapping ${\Psi}$ from the space Δ(K, H _V ) of bounded K-spherical functions on H _V to the space ${\mathfrak{h}_V^{*}/K}$ of K-orbits in the dual of the Lie algebra for H _V . We prove that ${\Psi}$ is a homeomorphism onto its image provided that the action of K on V is “well-behaved” in a sense made precise in this work. Our result encompasses a widely studied class of examples arising in connection with Hermitian symmetric spaces.     

Optical characterization of InGaN/AlGaN/GaN diode grown on silicon carbide

Electroluminescence (EL) properties of In_xGa_1−xN/Al_yGa_1−yN/GaN/SiC diode were studied. The spectral range for which EL spectra were recorded is 1–3.5 eV. Room temperature EL was obtained for forward bias (3.18 V, 220 μA) at 446.067 nm (blue luminescence band), 606.98 nm (yellow luminescence band) and 893.84 nm (Infrared luminescence band). The EL temperature dependence shows that, BL band is mostly given by e–h recombination corresponding to indium composition equal to 0.17 ± 0.01 and 0.14 ± 0.02 obtained theoretically and experimentally, respectively. The yellow band is generally weak and absent at low temperature. The IRL band is more consistent with the DAP recombination and could be explained by the thermal activation of Mg states. The luminescence bands shift to lower energies is due probably to the larger potential fluctuations effect.     

Sub region-specific modulation of synchronous neuronal burst firing after a kainic acid insult in organotypic hippocampal cultures

Background  

Excitotoxicity occurs in a number of pathogenic states including stroke and epilepsy. The adaptations of neuronal circuits in response to such insults may be expected to play an underlying role in pathogenesis. Synchronous neuronal firing can be induced in isolated hippocampal slices and involves all regions of this structure, thereby providing a measure of circuit activity. The effect of an excitotoxic insult (kainic acid, KA) on Mg²⁺-free-induced synchronized neuronal firing was tested in organotypic hippocampal culture by measuring extracellular field activity in CA1 and CA3.     

Iterative Methods for Systems of First-order Differential Equations

In this paper, we study the applicability of the iterative asynchronousalgorithms to systems of first order differential equations.These algorithms can be implemented on monoprocessors as wellas on multiprocessors, therefore this study extends Picard'smethod and opens a future perspective for treating differentialsystems in a parallel and asynchronous manner using multiprocessors     

SU3 comparison of line reversed charge exchange and hyperchange exchange reactions

The recent data at 10.1 GeV/c on the hypercharge reactions π⁺p → K⁺Σ⁺ (1385) and the line reversed processes are compared with the SU₃ related charge exchange processes K⁺n → K^op and K⁺p →K^oΔ⁺⁺ and their line reversed partners in order to study the systematics of line reversal breaking. Allowing for a t- independent SU₃ breaking between charge and hypercharge exchange the data follow the SU₃ relations. We conclude that the line reversal breaking in the hypercharge exchange reactions is in agreement with the breaking in exchange degeneracy (in both flip and non-flip amplitudes) which is observed for the charge exchange processes.     

Electronic transition dipole moment functions for NaK

Phase-consistent electronic transition dipole moment functions were calculated (as a function of internuclear separation) for the 80 dipole selection rule allowed transitions in the manifold of states of NaK treated previously [W. J. Stevens, D. D. Konowalow, and L. B. Ratcliff, (1984) J. Chem. Phys. 80, 1215–1224]. Agreement was found with experimental determinations of the 2¹Π-1¹Σ⁺ transition. Agreement of the asymptotic values with experimental and previous theoretical determinations of corresponding atomic transition moments suggests that the present computations may be relatively reliable. The positions of a number of satellite bands are predicted from the potential energy difference curves.     

A study of the reaction pp → π− π+ at 10 GeV/c

The reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ has been studied at 10.1 GeV/c in the ?t interval from 0.15 to 1.5 (GeV/c)². A line-reversal comparison with backward elastic scattering π⁺p → pπ⁺ shows good agreement for ?t > 0.3 (GeV/c)².     

Projections of Veronese surface and morphisms from projective plane to Grassmannian

In this note, we describe the image of ?² in Gr(2, ?⁴) under a morphism given by a rank two vector bundle on ?² with Chern classes (2, 2).