Parameterization of quasigeostrophic eddies in primitive equation ocean models

A parameterization of mesoscale eddy fluxes in the ocean should be consistent with the fact that the ocean interior is nearly adiabatic. Gent and McWilliams have described a framework in which this can be approximated in L-coordinate primitive equation models by incorporating the effects of eddies on the buoyancy field through an eddy-induced velocity. It is also natural to base a parameterization on the simple picture of the mixing of potential vorticity in the interior and the mixing of buoyancy at the surface. The authors discuss the various constraints imposed by these two requirements and attempt to clarify the appropriate boundary conditions on the eddy-induced velocities at the surface. Quasigeostrophic theory is used as a guide to the simplest way of satisfying these constraints.

Classical Invariants for Principal Series and Isomorphisms of Root Data

We develop some new techniques to calculate the Schur indicator for self-dual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator and the real-quaternionic indicator. We make progress towards developing an algorithm to decide whether or not two root data are isomorphic. When the derived group has cyclic center, we solve the isomorphism problem completely. An immediate consequence is a clean and precise classification theorem for connected complex reductive groups whose derived groups have cyclic center.

Holomorphic functions on non-Runge domains and related problems.

Let U be a domain in CN that is not a Runge domain. We study the topological and algebraic properties of the family of holomorphic functions on U which cannot be approximated by polynomials.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Equivalent norms in polynomial spaces and applications.

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy Littlewood constants for 2-homogeneous polynomials on l(p)(2) spaces, 2 < p <= infinity. We also provide lower estimates for the Hardy-Littlewood constants for polynomials of higher degrees.

The 1998-2001 submarine lava balloon eruption at the Serreta Ridge (Azores archipelago): constraints from volcanic facies architecture, isotope geochemistry and magnetic data

The most recent submarine eruption observed offshore the Azores archipelago occurred between 1998-2001 along the submarine Serreta ridge (SSR), ~4-5 nautical miles WNW of Terceira Island. This submarine eruption delivered abundant basaltic lava balloons floating at the sea surface and significantly changed the bathymetry around the eruption area. Our work combines bathymetry, volcanic facies cartography, petrography, rock magnetism and geochemistry in order to (1) track the possible vent source at seabed, (2) better constrain the Azores magma source(s) sampled through the Serreta submarine volcanic event, and (3) interpret the data within the small-scale mantle source heterogeneity framework that has been demonstrated for the Azores archipelago. Lava balloons sampled at sea surface display a radiogenic signature, which is also correlated with relatively primitive (low) 4He/3He isotopic ratios. Conversely, SSR lavas are characterized by significantly lower radiogenic 87Sr/86Sr, 206Pb/204Pb and 208Pb/204Pb ratios than the lava balloons and the onshore lavas from the Terceira Island. SSR lavas are primitive, but incompatible trace-enriched. Apparent decoupling between the enriched incompatible trace element abundances and depleted radiogenic isotope ratios is best explained by binary mixing of a depleted MORB source and a HIMU­type component into magma batches that evolved by similar shallower processes in their travel to the surface. The collected data suggest that the freshest samples collected in the SSR may correspond to volcanic products of an unnoticed and more recent eruption than the 1998-2001 episode.