On the nullstellensätze for stein spaces and C-analytic sets.

In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).

Pitfalls on computing liquid-liquid phase equilibria using the k-value method

Poster presented in the 11th Mediterranean Congress of Chemical Engineering, Barcelona, October 21-24, 2008.

A childhood in Brittany eighty years ago /

"This little sheaf of childish memories has been put together from many talks, in her own tongue, with an old French friend."

The works of Donald G. Mitchell ...

[v. 12] English lands, letters and kings, from Elizabeth to Anne.--[v. 13] English lands, letters and kings; Queen Anne and the Georges.--[v. 14] English lands, letters and kings; the later Georges to Victoria.--[v. 15] American lands and letters; the Mayflower to Rip Van Winkle.--[v. 16] American lands and letters; Leather-Stocking to Poe's Raven.

On Selmer groups and factoring p-adic L-functions

Thesis (Ph.D.)--University of Washington, 2016-06

Toward Clemens' Conjecture in Degrees between 10 and 24

1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.

On Local Uniform Topological Algebras

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.

On realizability of p-groups as Galois groups

2000 Mathematics Subject Classification: 12F12, 15A66.

On the microstructure, growth pattern and original porosity of belemnite rostra: insights from calcitic Jurassic belemnites

Calcitic belemnite rostra are usually employed to perform paleoenvironmental studies based on geochemical data. However, several questions, such as their original porosity and microstructure, remain open, despite they are essential to make accurate interpretations based on geochemical analyses.This paper revisits and enlightens some of these questions. Petrographic data demonstrate that calcite crystals of the rostrum solidum of belemnites grow from spherulites that successively develop along the apical line, resulting in a “regular spherulithic prismatic” microstructure. Radially arranged calcite crystals emerge and diverge from the spherulites: towards the apex, crystals grow until a new spherulite is formed; towards the external walls of the rostrum, the crystals become progressively bigger and prismatic. Adjacent crystals slightly vary in their c-axis orientation, resulting in undulose extinction. Concentric growth layering develops at different scales and is superimposed and traversed by a radial pattern, which results in the micro-fibrous texture that is observed in the calcite crystals in the rostra.Petrographic data demonstrate that single calcite crystals in the rostra have a composite nature, which strongly suggests that the belemnite rostra were originally porous. Single crystals consistently comprise two distinct zones or sectors in optical continuity: 1) the inner zone is fluorescent, has relatively low optical relief under transmitted light (TL) microscopy, a dark-grey color under backscatter electron microscopy (BSEM), a commonly triangular shape, a “patchy” appearance and relatively high Mg and Na contents; 2) the outer sector is non-fluorescent, has relatively high optical relief under TL, a light-grey color under BSEM and low Mg and Na contents. The inner and fluorescent sectors are interpreted to have formed first as a product of biologically controlled mineralization during belemnite skeletal growth and the non-fluorescent outer sectors as overgrowths of the former, filling the intra- and inter-crystalline porosity. This question has important implications for making paleoenvironmental and/or paleoclimatic interpretations based on geochemical analyses of belemnite rostra.Finally, the petrographic features of composite calcite crystals in the rostra also suggest the non-classical crystallization of belemnite rostra, as previously suggested by other authors.

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.

Rational O(2)–Equivariant Spectra

The category of rational O(2)-equivariant cohomology theories has an algebraic model A(O(2)), as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational O(2)-equivariant spectra and the derived category of the abelian model DA(O(2)). In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.

Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules

MSC 19L41; 55S10.