A new Hamiltonian for a massive relativistic particle with spin one in a generalized Heisenberg/Schr\"odinger picture

We consider a particular 4-dimensional generalization of the transition from the Heisenberg to the Schr\"odinger picture. The space-time independent expansion with respect to the unitary irreducible representations of the Lorentz group is applied, as Fourier transformation in the Heisenberg picture, to the states of a massive relativistic particle. A new Hamiltonian operator has been found for such a particle with spin one.Comment: 14 pages Latex. Submitted to Journal of Mathematical Physic

A relativistic superalgebra in a generalized Schroedinger picture

We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive relativistic particles with spin zero and spin-1/2 are expressed in terms of the principal series of the unitary representations of the Lorentz group. We also consider the massless case. New Hamilton operators are conctructed for the massless particles with spin zero and spin 1/2.Comment: 7 page

The Need for Agricultural Data in South Africa: With Specific Reference to the Western Cape Province

In order for public and private decision-makers in the agricultural sector to use agricultural information for decision-making, solving problems or increasing their knowledge, the necessary data on agriculture must be available. As a result of the deregulation of the agricultural marketing sector in South Africa, the supply of this type of data has decreased. Also, the need for data on agriculture by the various decision-makers, i.e. the policy-makers, researchers, agricultural service industries as well as the farmers and extension officers, has changed. Since information systems are always based on the needs of the decision-makers, the need for data on agriculture should be determined before either existing methodologies are improved or new methodologies are introduced, to increase the supply of data on agriculture in South Africa. The objective of this paper is to identify the agricultural data needs and supply for South Africa with specific reference to the Western Cape Province. This was done by means of postal surveys and informal methods. Recommendations for an effective information system have also be concluded.Research and Development/Tech Change/Emerging Technologies,

One particle quantum equation in a de Sitter spacetime

We consider a free particle in a de Sitter spacetime. We use a picture in which the analogs of the Schr\"odinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the de Sitter spacetime.Comment: 12 page

Morozov's principle for the augmented Lagrangian method applied to linear inverse problems

The Augmented Lagrangian Method as an approach for regularizing inverse problems received much attention recently, e.g. under the name Bregman iteration in imaging. This work shows convergence (rates) for this method when Morozov's discrepancy principle is chosen as a stopping rule. Moreover, error estimates for the involved sequence of subgradients are pointed out. The paper studies implications of these results for particular examples motivated by applications in imaging. These include the total variation regularization as well as $\ell^q$ penalties with $q\in[1,2]$. It is shown that Morozov's principle implies convergence (rates) for the iterates with respect to the metric of strict convergence and the $\ell^q$-norm, respectively

Parametric instability of the helical dynamo

We study the dynamo threshold of a helical flow made of a mean (stationary) plus a fluctuating part. Two flow geometries are studied, either (i) solid body or (ii) smooth. Two well-known resonant dynamo conditions, elaborated for stationary helical flows in the limit of large magnetic Reynolds numbers, are tested against lower magnetic Reynolds numbers and for fluctuating flows (zero mean). For a flow made of a mean plus a fluctuating part the dynamo threshold depends on the frequency and the strength of the fluctuation. The resonant dynamo conditions applied on the fluctuating (resp. mean) part seems to be a good diagnostic to predict the existence of a dynamo threshold when the fluctuation level is high (resp. low).Comment: 37 pages, 8 figure