The Quantum Galilei Group

The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are constructed.Comment: AMSTe

Quadratic integrals of motion for the systems of identical particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.Comment: 6 pages, no figure

Residual effects of fallows on selected soil hydraulic properties in a kaolinitic soil subjected to conventional tillage (CT) and no tillage (NT)

Improved fallows have been used to reduce time required for soil fertility regeneration after cropping in low input agricultural systems. In semi-arid areas of Southern Africa, Acacia angustissima and Sesbania sesban are among some of the more widely used improved fallow species. However the residual effects of improved fallows on soil hydraulic properties during the cropping phase is not known. The aim of this study was to quantify the residual effects of fallows and tillage imposed at fallow termination on soil hydraulic properties (infiltration rates, hydraulic conductivity and soil porosity) during the cropping phase. Treatments evaluated were planted fallows of Acacia angustissima, Sesbania sesban and natural fallow (NF) and continuous maize as a control. Steady state infiltration rates were measured using a double ring infiltrometer and porosity was calculated as the difference between saturated infiltration rates and tension infiltration measurements on an initially saturated soil. Unsaturated hydraulic conductivity (K-o) and mean pore sizes of water conducting pores were measured using tension infiltrometer at tensions of 5 and 10 cm of water on an initially dry soil. While there was no significant difference in steady state infiltration rates from double ring infiltrometer measurements among the fallow treatments, these were significantly higher than the control. The steady state infiltration rates were 36, 67, 59 and 68 mm h(-1) for continuous maize, A. angustissima, S. sesban and NF respectively. Tillage had no significant effect on steady state infiltration rate. Pore density at 5 cm tension was significantly higher in the three fallows than in maize and varied from 285-443 m(-2) in fallows, while in continuous maize the pore density was less than 256 m(-2). At 10 cm tension pore density remained significantly higher in fallows and ranged from 4,521-8,911 m(-2) compared to 2,689-3,938 m(-2) in continuous maize. Unsaturated hydraulic conductivities at 5 cm tension were significantly higher in fallows than in continuous maize and were 0.9, 0.7, 0.8 cm and 0.5 cm h(-1) for A. angustissima, S. sesban, NF and continuous maize, respectively. However there were no significant treatment differences at 10 cm tension. Fallows improved infiltration rates, hydraulic conductivity and soil porosity relative to continuous maize cropping. Through fallowing farmers can improve the soils hydraulic properties and porosity, this is important as it affects soil water recharge, and availability for plant growt

Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations.Comment: 38 pages, late

The high energy semiclassical asymptotics of loci of roots of fundamental solutions for polynomial potentials

In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties is given for fundamental solutions for the high complex energy limit when the energy is quantized or not. In particular due to the fact that the limit considered is semiclassical it is shown that loci of roots of fundamental solutions are collected of selected Stokes lines (called exceptional) specific for the solution considered and are distributed along these lines in a specific way. A stable asymptotic limit of loci of zeros of fundamental solutions on their exceptional Stokes lines has island forms and there are infintely many of such roots islands on exceptional Stokes lines escaping to infinity and a finite number of them on exceptional Stokes lines which connect pairs of turning points. The results obtained for asymptotic roots distributions of fundamental solutions in the semiclassical high (complex) energy limit are of a general nature for polynomial potentials.Comment: 41 pages, 14 figure

Global Symmetries of Noncommutative Space-time

The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.Comment: 7 pages, no figures; minor changes in the bibliography; final version accepted for publication in Phys. Rev.

Soil organic carbon dynamics of improved fallow-maize rotation systems under conventional and no-tillage in Central Zimbabwe

Fallowing increases soil organic carbon (SOC) during the fallowing phase. However, this benefit is lost quickly during the cropping phase. The objective of this study was to evaluate SOC dynamics of an improved fallow-maize rotation under no-tillage (NT) and conventional tillage (CT) from time of fallow termination, through the next two cropping seasons. The treatments studied were improved fallows of Acacia angustissima (A. angustissima) and Sesbania sesban (S. sesban), natural fallow and continuous maize. Our hypothesis is that fallowing maintained higher SOC and lower soil bulk densities through the cropping phase when compared with continuous maize system and that NT maintained higher SOC when compared with CT. Soil organic carbon was significantly greater under fallows than under continuous maize from fallow termination to the end of the second cropping season. Soil organic carbon for the 0¿5 cm depths was 11.0, 10.0, 9.4 and 6.6 g kg¿1 for A. angustissima, S. sesban, natural fallow and continuous maize, respectively at fallow termination. After two cropping seasons SOC for the same depth was 8.0, 7.0, 6.1, 5.9 g kg¿1 under CT and 9.1, 9.0, 8.0, 6.0 g kg¿1 under NT for A. angustissima, S. sesban, natural fallow and continuous maize, respectively. Total SOC stocks were also higher under fallows when compared with continuous maize at fallow termination and after two cropping seasons. Soil bulk densities were lower under fallows when compared with continuous maize during the period of study. We concluded that fallows maintained greater SOC and NT sequestered more SOC than CT. Acacia angustissima was the better tree legume fallow for SOC sequestration when compared with S. sesban or natural fallow because it maintained higher SOC and lower bulk densities after two seasons of maize cropping