On the spring and mass of the Dirac oscillator

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented

The Impact of Agricultural Technology in Sub-Saharan Africa: A Synthesis of Symposium Findings

The Symposium on the Impact of Technology on Agricultural Transformation in Sub-Saharan Africa funded by AID/AFR/ARTS and AID/RD/EID under the Michigan State University Food Security Cooperative Agreements, was held in Washington, D.C., Oct. 14-16, 1992. A primary purpose of the symposium was to present evidence which would either confirm or contradict the perception that the accomplishments of TDT were insufficient to justify continued funding. A secondary objective was to consider the adequacy of available analytical tools for impact assessment. The rate of return (ROR) is the most commonly used valuative measure of investments in technology development and transfer. Examined as a group, the estimated RORs support the proposition that African agricultural research has had people-level impacts, and that these impacts are large enough to justify the level of investment that led to the impacts. An important part of the impact assessment story is the analysis of factors that had a positive or negative effect on the impact of TDT. Five major factors emerged from the studies presented and comments by symposium participants: agroclimatic conditions, civil unrest, research system performance, policy, and markets. Progress has been made in moving forward with the process of TDT, in spite of adverse conditions. This progress includes enhancing the capabilities of national, regional and international institutions to generate new techniques, pushing forward the technology frontier, transferring technology, and increasing productivity both in farm production and post-harvest activities. Activities such as structural adjustment, improvements in agricultural and macroeconomic policy, greater reliance on democracy and capitalism, investments in infrastructure, and a greater willingness to work with the private sector have increased the potential for TDT to have significant impact. Given the importance of raising productivity in agriculture as a step towards agricultural transformation, continued investment in agricultural TDT is merited. The evidence of impact achieved from previous investments shows that those investments have paid off. Coupled with the evidence of beneficial changes in the macroeconomic policy environment in many countries, this provides the basis for expecting that future investments will pay off. What is perhaps unique about the symposium is the movement towards a commodity sector perspective as the next logical step toward including more demand-side considerations in the TDT agenda.International Development, Research and Development/Tech Change/Emerging Technologies, Downloads July 2008 - June 2009: 18,

ANALYSIS OF PROJECTS WITH PRICE EFFECTS, AND APPLICATION TO INNOVATION AND TECHNICAL CHANGE

Replaced with revised version of paper 04/21/06.Research and Development/Tech Change/Emerging Technologies,

Payoffs to Investments in Agricultural Technology in Sub-Saharan Africa

Research and Development/Tech Change/Emerging Technologies, Downloads July 2008-June 2009: 7,

In-Danger Animals

An Army Ranger reflects on his experiences with wild animals during his military career, especially an encounter with a tiger in the DMZ. Articles, stories, and other compositions in this archive were written by participants in the Mighty Pen Project. The program, developed by author David L. Robbins, and in partnership with Virginia Commonwealth University and the Virginia War Memorial in Richmond, Virginia, offers veterans and their family members a customized twelve-week writing class, free of charge. The program encourages, supports, and assists participants in sharing their stories and experiences of military experience so both writer and audience may benefit

Effect of polar and non-polar solvents on the rotatory power and dispersion of L. benzoin, L. benzoin methyl ether, and methyl L-mandelate

The optical behaviour of L.-benzoin, L-benzoin methyl ether and methyl L-mandelate, with change of solvent, concentrat ion, and temperature has been examined for a range of wavelengths over the visible region of the spectrum. The results may be summarised as follows.(a) On the whole the negative rotation of L-benzoin varies with the polarity of the solvent in such a manner that solvents of high polarity depress the negative rotatory power. This depression is attributed to the greater degree of association existing between the active, solute and solvents of higher polarity.(b) In agreement with (a), an increase in the concentration of L-benzoin in a non-polar solvent also lowers the negative rotation, owing to a rise in the degree of association of the solute molecules with one another.(c) Among non-polar solvents the solutions with cyclohexane, mesitylene, toluene and benzene gave abnormally low negative rotations as compared with their non-polar character. These displacements were assumed to be due to the association of L-benzoin in such media, and this view is supported by molecular weight measurements .(d) On rise of temperature the T-R curves for L-benzoin in bromobenzene and. nitrobenzene respectively (typical of weakly and strongly polar solvents) tend to converge. This is in agreement with the dipole theory.(e) For L-benzoin methyl ether, molecular weight determinations now show that very little association at low concentrations occurs even in non-polar solvents. In agreement with this difference, the rotatory powers of the ether are in much closer agreement with the polarity of the solvents than was found for L-benzoin. Cyclohexane, mesitylene, and other non-polar solvents fall into position at one end of the series to give dextro-rotatory solutions. Strongly polar solvents On the other hand yield laevo-rotatory solutions.The typical effect of polar and non-polar solvents corresponds to the remarkable variation in rotatory power of L-benzoin methyl ether with change of concentration in benzene solution. With increase in concentration, the dextro-rotation changes into a laevo-rotation.With rise of temperature the T-R curves for mesitylene, bromobenzene and nitrobenzene converge strongly. These solvents were selected as being typical of non-polar, weakly polar and strongly polar media respectively.(f) Methyl L-mandelate, as was expected, resembles L-benzoin in many of its optical properties. The laevo-rotation tends to fall with increase in the dipole moment of the solvent, although certain non- polar media yield abnormally low values. The latter may be explained by the fact that the ester exists in these solvents in the associated state. The changes with rise of concentration and temperature are also in agreement with the predictions of the theory of dipoles.(g) The dispersions of L-benzoin and methyl L-mandelate are in every case normal and complex. When is plotted against λ² , the deviation of the graph from the line joining the extreme points is in the same direction.This statement also holds for L-benzoin methyl ether in non-polar and strongly polar solvents respectively. In solvents of medium polarity, or in the homogeneous state the deviation of the graph may be in the opposite direction to the above, or anomalous dispersion may be exhibited