Choquet integrals in potential theory

This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean n-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions to obstacle problems, and a refined notion of pointwise differentiation of Sobolev functions

Changes in the Spatial Allocation of Cropland in the Ft. Cobb Watershed as a Result of Environmental Restrictions

Pollution runoff estimates from SWAT are used in a mathematical programming model to optimally model site-specific crop and conservation practices for pollution abatement in the Ft. Cobb watershed in Southwestern Oklahoma. Results indicate the tradeoffs between producer income, sediment and nutrient runoff and the spatial allocation of crops in the watershed.Environmental Economics and Policy,

A simplified test of universality in Lattice QCD

A simplified test of universality in Lattice QCD is performed by analytically evaluating the continuous Euclidean time limits of various lattice fermion determinants, both with and without a Wilson term to lift the fermion doubling on the Euclidean time axis, and comparing them with each other and with the zeta-regularised fermion determinant in the continuous time--lattice space setting. The determinant relations expected from universality considerations are found to be violated by a certain gauge field-dependent factor, i.e. we uncover a "universality anomaly". The physical significance, or lack thereof, of this factor is a delicate question which remains to be settled.Comment: 6 pages. v2: Revised to include a further result on the zeta-regularised fermion determinant in the continuous time--lattice space setting which impacts on the conclusions; typos corrected; acknowledgement and reference added; to appear in Phys.Rev.Let

QSO 0130-4021: A third QSO showing a low Deuterium to Hydrogen Abundance Ratio

We have discovered a third quasar absorption system which is consistent with a low deuterium to hydrogen abundance ratio, D/H = 3.4 times 10^-5. The z ~ 2.8 partial Lyman limit system towards QSO 0130-4021 provides the strongest evidence to date against large D/H ratios because the H I absorption, which consists of a single high column density component with unsaturated high order Lyman series lines, is readily modeled -- a task which is more complex in other D/H systems. We have obtained twenty-two hours of spectra from the HIRES spectrograph on the W.M. Keck telescope, which allow a detailed description of the Hydrogen. We see excess absorption on the blue wing of the H I Lyman alpha line, near the expected position of Deuterium. However, we find that Deuterium cannot explain all of the excess absorption, and hence there must be contamination by additional absorption, probably H I. This extra H I can account for most or all of the absorption at the D position, and hence D/H = 0 is allowed. We find an upper limit of D/H < 6.7 times 10^-5 in this system, consistent with the value of D/H ~ 3.4 times 10^-5 deduced towards QSO 1009+2956 and QSO 1937-1009 by Burles and Tytler (1998a, 1998b). This absorption system shows only weak metal line absorption, and we estimate [Si/H] < -2.6 -- indicating that the D/H ratio of the system is likely primordial. All four of the known high redshift absorption line systems simple enough to provide useful limits on D are consistent with D/H = 3.4 +/- 0.25 times 10^-5. Conversely, this QSO provides the third case which is inconsistent with much larger values.Comment: 18 pages, 5 figures, submitted to Ap

Sphingosine kinases : emerging structure function insights

Sphingosine kinases (SK1 and SK2) catalyse the conversion of sphingosine into sphingosine 1-phosphate and control fundamental cellular processes, including cell survival, proliferation, differentiation, migration, and immune function. In this review, we highlight recent breakthroughs in the structural and functional characterisation of SK1 and these are contextualised by analysis of crystal structures for closely related prokaryotic lipid kinases. We identify a putative dimerisation interface and propose novel regulatory mechanisms governing structural plasticity induced by phosphorylation and interaction with phospholipids and proteins. Our analysis suggests that the catalytic function and regulation of the enzymes might be dependent on conformational mobility and it provides a roadmap for future interrogation of SK1 function and its role in physiology and disease

Closed String Tachyons on C/Z_N

We analyse the condensation of closed string tachyons on the $C/Z_N$ orbifold. We construct the potential for the tachyons upto the quartic interaction term in the large $N$ limit. In this limit there are near marginal tachyons. The quartic coupling for these tachyons is calculated by subtracting from the string theory amplitude for the tachyons, the contributions from the massless exchanges, computed from the effective field theory. We argue that higher point interaction terms are are also of the same order in 1/N as the quartic term and are necessary for existence of the minimum of the tachyon potential that is consistent with earlier analysis.Comment: 19 pages, 1 figure; comments added about $N$ dependence of contact ter