An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mathematics Subject Classification: Primary 35R10, Secondary 44A15

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Hydrochemistry, mineralogy and sulphur isotope geochemistry of acid mine drainage at the Mt Morgan mine environment, Queensland, Australia

Mineralogical, hydrochemical and S isotope data were used to constrain hydrogeochemical processes that produce acid mine drainage from sulfidic waste at the historic Mount Morgan Au–Cu mine, and the factors controlling the concentration of SO4 and environmentally hazardous metals in the nearby Dee River in Queensland, Australia. Some highly contaminated acid waters, with metal contents up to hundreds of orders of magnitude greater than the Australia–New Zealand environmental standards, by-pass the water management system at the site and drain into the adjacent Dee River. Mine drainage precipitates at Mt. Morgan were classified into 4 major groups and were identified as hydrous sulfates and hydroxides of Fe and Al with various contents of other metals. These minerals contain adsorbed or mineralogically bound metals that are released into the water system after rainfall events. Sulfate in open pit water and collection sumps generally has a narrow range of S isotope compositions (δ34S = 1.8–3.7‰) that is comparable to the orebody sulfides and makes S isotopes useful for tracing SO4 back to its source. The higher δ34S values for No. 2 Mill Diesel sump may be attributed to a difference in the source. Dissolved SO4 in the river above the mine influence and 20 km downstream show distinctive heavier isotope compositions (δ34S = 5.4–6.8‰). The Dee River downstream of the mine is enriched in 34S (δ34S = 2.8–5.4‰) compared with mine drainage possibly as a result of bacterial SO4 reduction in the weir pools, and in the water bodies within the river channel. The SO4 and metals attenuate downstream by a combination of dilution with the receiving waters, SO4 reduction, and the precipitation of Fe and Al sulfates and hydroxides. It is suggested here that in subtropical Queensland, with distinct wet and dry seasons, temporary reducing environments in the river play an important role in S isotope systematics

On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

On a theorem of Cooper

In this paper we study some purely mathematical considerations that arise in a paper of Cooper on the foundations of thermodynamics that was published in this journal. Connections with mathematical utility theory are studied and some errors in Cooper's paper are rectified. (C) 2001 Academic Press.

Thue's theorem and the diophantine equation x2 - Dy2 = ±N

A constructive version of a theorem of Thue is used to provide representations of certain integers as x(2) - Dy-2, where D = 2, 3, 5, 6, 7.

Different mineralization styles in a volcanic-hosted ore deposit: the fluid and isotopic signatures of the Mt Morgan Au-Cu deposit, Australia

Quantitative laser ablation (LA)-ICP-MS analyses of fluid inclusions, trace element chemistry of sulfides, stable isotope (S), and Pb isotopes have been used to discriminate the formation of two contrasting mineralization styles and to evaluate the origin of the Cu and Au at Mt Morgan. The Mt Morgan Au-Cu deposit is hosted by Devonian felsic volcanic rocks that have been intruded by multiple phases of the Mt Morgan Tonalite, a low-K, low-Al2O3 tonalite-trondhjemite-dacite (TTD) complex. An early, barren massive sulfide mineralization with stringer veins is conforming to VHMS sub-seafloor replacement processes, whereas the high-grade Au-Cu. ore is associated with a later quartz-chalcopyrite-pyrite stock work mineralization that is related to intrusive phases of the Tonalite complex. LA-ICP-MS fluid inclusion analyses reveal high As (avg. 8850 ppm) and Sb (avg. 140 ppm) for the Au-Cu mineralization and 5 to 10 times higher Cu concentration than in the fluids associated with the massive pyrite mineralization. Overall, the hydrothermal system of Mt Morgan is characterized by low average fluid salinities in both mineralization styles (45-80% seawater salinity) and temperatures of 210 to 270 degreesC estimated from fluid inclusions. Laser Raman Spectroscopic analysis indicates a consistent and uniform array Of CO2-bearing fluids. Comparison with active submarine hydrothermal vents shows an enrichment of the Mt Morgan fluids in base metals. Therefore, a seawater-dominated fluid is assumed for the barren massive sulfide mineralization, whereas magmatic volatile contributions are implied for the intrusive related mineralization. Condensation of magmatic vapor into a seawater-dominated environment explains the CO2 occurrence, the low salinities, and the enriched base and precious metal fluid composition that is associated with the Au-Cu. mineralization. The sulfur isotope signature of pyrite and chalcopyrite is composed of fractionated Devonian seawater and oxidized magmatic fluids or remobilized sulfur from existing sulfides. Pb isotopes indicate that Au and Cu. originated from the Mt Morgan intrusions and a particular volcanic strata that shows elevated Cu background. (C) 2002 Elsevier Science B.V. All rights reserved.

Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.