The distribution of wages and employment in rural Botswana

African Studies Center Working Paper No. 4

COMMUNITY CULTURAL DEVELOPMENT: A PUBLIC AFFAIRS EDUCATION PROGRAM IN FLORIDA

Community/Rural/Urban Development,

On the nature of the Virasoro algebra

The multiplication in the Virasoro algebra $$[e_p, e_q] = (p - q) e_{p+q} + \theta \left(p^3 - p\right) \delta_{p + q}, \qquad p, q \in {\mathbf Z},$$ $$[\theta, e_p] = 0,$$ comes from the commutator $[e_p, e_q] = e_p * e_q - e_q * e_p$ in a quasiassociative algebra with the multiplication \renewcommand{\theequation}{$*$} \be \ba{l} \ds e_p * e_q = - {q (1 + \epsilon q) \over 1 + \epsilon (p + q)} e_{p+q} + {1 \over 2} \theta \left[p^3 - p + \left(\epsilon - \epsilon^{-1} \right) p^2 \right] \delta^0_{p+q}, \vspace{3mm}\\ \ds e_p * \theta = \theta* e_p = 0. \ea \ee The multiplication in a quasiassociative algebra ${\cal R}$ satisfies the property \renewcommand{\theequation}{$**$} \be a * (b * c) - (a * b) * c = b * (a * c) - (b * a) * c, \qquad a, b, c \in {\cal R}. \ee This property is necessary and sufficient for the Lie algebra {\it Lie}$({\cal R})$ to have a phase space. The above formulae are put into a cohomological framework, with the relevant complex being different from the Hochschild one even when the relevant quasiassociative algebra ${\cal R}$ becomes associative. Formula $(*)$ above also has a differential-variational counterpart

How the projection domains of NF-L and alpha-internexin determine the conformations of NF-M and NF-H in neurofilaments

Making use of a numerical self-consistent field method and polymer brush concepts, we model the solvated corona of neurofilaments (NF) composed of projection domains (unstructured tails) of constituent proteins. Projections are modeled with amino acid resolution. We focus on the importance of the two shortest ones (alpha-internexin and NF-L) in regulating the conformations of the two longer ones (NF-M and NF-H) in an isolated NF. We take the wild-type NF with no alpha-internexin as the reference, for which the phosphorylation-induced translocation of M- and H-tails has been examined previously. We demonstrate that a subbrush of L-tails creates an electrostatic potential profile with an approximately parabolic shape. An experimentally relevant (2:1) ratio of L- to alpha-projections reduces the charge density of the L subbrush and shifts the translocation transition of the H-tails to slightly higher degrees of phosphorylation. Replacing all L-tails by alpha-projections destroys the substructure of the NF corona and this alters the NF response to the phosphorylation of long tail

On localization of pseudo-relativistic energy

We present a Kato-type inequality for bounded domain Omega \subset R^n, n>1.Comment: 17 page

Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains

On a smooth bounded domain \Omega \subset R^N we consider the Schr\"odinger operators -\Delta -V, with V being either the critical borderline potential V(x)=(N-2)^2/4 |x|^{-2} or V(x)=(1/4) dist (x,\partial\Omega)^{-2}, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Scr\"odinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a serier of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincar\'e. As a byproduct of our technique we are able to answer positively to a conjecture of E.B.Davies.Comment: 40 page

Owen coalitional value without additivity axiom

We show that the Owen value for TU games with coalition structure can be characterized without additivity axiom similarly as it was done by Young for the Shapley value for general TU games. Our axiomatization via four axioms of efficiency, marginality, symmetry across coalitions, and symmetry within coalitions is obtained from the original Owen's one by replacement of the additivity and null-player axioms via marginality. We show that the alike axiomatization for the generalization of the Owen value suggested by Winter for games with level structure is valid as well

Bathymetric surveys and lake deposits

A progress report on the bathymetric survey of Windereme undertaken in June 1937 by the Hydrographic Department of the Admiralty. The brief article outlines the background of the surveying process as well as the initial effectiveness of the survey work. There is a brief background to the geomorphological processes which were involved in shaping the Lake District topography, as well as some explanation of previous studies undertaken in the area. The report includes a figure showing the cross sections of lake beds and a figure detailing a core from the bottom deposits of Windermere

The growth of brown trout

An article discussing the factors affecting the rate of growth of brown trout, detailing the research udnertaken at Wray Castle, designed to clarify the influencing factors in different waters and investigate what would be required to increase their size. The article considers factors such as alkalinity, total hardness, the presence of coarse fish in the waterbodies and competition for food. Previous work undertaken on brown trout in Ireland by other authors is reviewed. A figure showing average growth rate of brown trout in five lakes, as determined from their scales (Lough Derg, Windermere, Loch Leven, Ullswater, Haweswater)

Hands across the border: cross-border cooperation in the making and enforcing of secure accommodation orders

No abstract available