One-Step Recurrences for Stationary Random Fields on the Sphere

Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying space. In the case of the sphere ${\mathbb S}^{d-1} \subset {\mathbb R}^d$ the (strict) positive definiteness of the zonal function $f(\cos \theta)$ is determined by the signs of the coefficients in the expansion of $f$ in terms of the Gegenbauer polynomials $\{C^\lambda_n\}$, with $\lambda=(d-2)/2$. Recent results show that classical differentiation and integration applied to $f$ have positive definiteness preserving properties in this context. However, in these results the space dimension changes in steps of two. This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials $\{C^\lambda_n\}$

Untangling CP Violation and the Mass Hierarchy in Long Baseline Experiments

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for $\nu_\mu \to \nu_e$ appearance, we derive a simple identity between the solutions in the ($\sin^2 2\theta_{13}$, $\sin \delta$) plane for the different hierarchies. The parameter $\sin^2 2\theta_{13}$ sets the scale of the $\nu_\mu \to \nu_e$ appearance probabilities at the atmospheric $\delta m^2_{atm} \approx 2.4 \times 10^{-3}$ eV$^2$ whereas $\sin \delta$ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of $\sin \delta$ for the two hierarchies equals twice the value of $\sqrt{\sin^2 2\theta_{13}}$ divided by the {\it critical} value of $\sqrt{\sin^2 2\theta_{13}}$. We apply this identity to the two proposed long baseline experiments, T2K and NO$\nu$A, and we show how it can be used to provide a simple understanding of when and why fake solutions are excluded when two or more experiments are combined. The identity demonstrates the true complimentarity of T2K and NO$\nu$A.Comment: 15 pages, Latex, 4 postscript figures. Submitted to New Journal of Physics, ``Focus on Neutrino Physics'' issu

A note about the t`Hooft`s ansatz for SU(N) real time guage theories

The t`Hooft's ansatz reduces the classical Yang--Mills theory to the $\lambda\phi^4$ one. It is shown that in the frame of this ansatz the real-time classical solutions for the arbitrary SU(N) gauge group is obtained by embedding $SU(2)\times SU(2)$ into SU(N). It is argued that this group structure is the only possibility in the frame of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown

Is there a Jordan geometry underlying quantum physics?

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of the algebra of observables, in the same way as Lie groups belong to the Lie part. Both the Lie geometry and the Jordan geometry are well-adapted to describe certain features of quantum theory. We concentrate here on the mathematical description of the Jordan geometry and raise some questions concerning possible relations with foundational issues of quantum theory.Comment: 30 page

Production of Gas Phase Zinc Oxide Nanoclusters by Pulsed Laser Ablation

We present experimental results on the photoluminescence (PL) of gas-suspended zinc oxide nanoclusters prepared during ablation of sintered ZnO targets by a pulsed ArF laser in the presence of oxygen ambient gas. The PL spectra in the UV spectral region correspond to the exciton recombination in the nanoclusters which are crystallized and cooled down to the temperature of the ambient gas in the ablation chamber. The time evolution of the spectra as well as their dependence on the ambient gas pressure are discussed.Comment: EMRS-2004, Strasbourg, France. Paper N-I.

Upscaling of solar induced chlorophyll fluorescence from leaf to canopy using the DART model and a realistic 3D forest scene

Non peer reviewe

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

Drone Measurements of Solar-Induced Chlorophyll Fluorescence Acquired with a Low-Weight DFOV Spectrometer System

Solar induced chlorophyll fluorescence (SIF) emitted from plant canopies is now retrievable from space. In addition, SIF is now also routinely measured from fixed tower platforms. However there is a scale gap between temporally continuous tower measurements and spatially coarse satellite retrievals that is now being bridged by drone technology. Drone retrievals of SIF can be used to help unravel the structural and species component dependencies that occur across space on the scale of meters in heterogeneous vegetation types. Also when flown at sufficient altitude, drones can be used to simulate, and potentially validate satellite retrievals of SIF. We flew a dual field of view spectrometer system, the Piccolo doppio, above a boreal forest with the aim of retrieving SIF. Our flights were designed to assess both spatial heterogeneity of SIF driven by changes in vegetation cover type and to simulate satellite pixels by flying at a relatively high altitude.Peer reviewe