Connections with prescribed first Pontrjagin form

Abstract

Let P be a principal O(n) bundle over a C ∞ manifold M of dimension m. If n ≥ 5m + 4 + 4 m+1 4 , then we prove that every differential 4-form representing the first Pontrjagin class of P is the Pontrjagin form of some connection on P .

Influence of Eu3+, Bi3+ co-doping content on photoluminescence of YVO4 red phosphors induced by ultraviolet excitation

“…4, the band edge shifts to longer wavelengths with increasing Bi 3+ concentration. For example, the band edge in the excitation spectrum moves from ∼254 nm (for the non-doped YVO 4 [10], not presented) to ∼328 nm for the Bi 3+ concentration of 2 mol%. This increase is due to the extra absorption involving the Bi-O component in addition to the V-O charge transfer bands.…”

“…Datta [10] has carried out detailed studies on the mechanism of absorption and energy transport in vanadate host lattices and concluded that YVO 4 is a host-sensitized phosphor and that the energy absorbed by the phosphor is transported to the activator center, mostly by non-radiative resonance energy transfer-either by electric multipole or by exchange interaction, and not by radiative cascade as has been postulated by Blasse and Bril [11]. It is generally presumed that the spectral properties reported for YVO 4 :Eu 3+ in the literature remain the same for YVO 4 :Eu 3+ , Bi 3+ as well.…”

Smooth maps into quaternionic Grassmannians inducing a prescribed 4-form

“…The above proposition is a particular case of a result that appeared in[1]. The proof requires the algebraic lemma which was overlooked previously.…”

“…While the primary characteristic forms are only topological invariant of the bundles, the secondary characteristic forms contain important geometric information. In particular, if we consider the trivial principal bundle and take ω to be the trivial connection on it, then p1 (0, α) = 1 2 trace (α ∧ Dα). We shall now show that the functor p 1 is additive.…”

A High-luminous Cold Cathode Fluorescent Lamp and Phosphors for a Wide-color-gamut LCD

“…The excitation band extended to 330 nm results from absorption of the host lattice, but the origin of the excitation is different in the long and short wavelength regions. The absorption in the long wavelength region is mostly due to the charge transfer (CT) of a V-O bond and that in the short wavelength region, including 254nm, is related to the CT of an Y-O bond [6]. If the measurement of the excitation spectra can be conducted at high excitation density, the luminescence intensity excited at around 254nm should be decreased as a result of the saturation.…”