Finite determinacy of matrices and ideals

The main aim of this paper is to characterize ideals I in the power series ring R=K[[x1,...,xs]] that are finitely determined up to contact equivalence by proving that this is the case if and only if I is an isolated complete intersection singularity, provided dim(R/I) > 0 and K is an infinite field (of arbitrary characteristic). Here two ideals I and J are contact equivalent if the local K-algebras R/I and R/J are isomorphic. If I is minimally generated by a1,...,am, we call I finitely contact determined if it is contact equivalent to any ideal J that can be generated by b1,...,bm with ai - bi in ^k for some integer k. We give also computable and semicontinuous determinacy bounds. The above result is proved by considering left-right equivalence on the ring M of m x n matrices A with entries in R and we show that the Fitting ideals of a finitely determined matrix in M have maximal height, a result of independent interest. The case of ideals is treated by considering 1-column matrices. Fitting ideals together with a special construction are used to prove the characterization of finite determinacy for ideals in R. Some results of this paper are known in characteristic 0, but they need new (and more sophisticated) arguments in positive characteristic partly because the tangent space to the orbit of the left-right group cannot be described in the classical way. In addition we point out several other oddities, including the concept of specialization for power series, where the classical approach (due to Krull) does not work anymore. We include some open problems and a conjecture.Comment: References updated, clearer formulation of some statements. To appear in Journal of Algebr

Effects of GATT/WTO on Asia's Trade Performance

Our review of the literature suggests that the effects of GATT/WTO are insignificant or relatively small for participants in general, but potentially very large for groups that make heavy use of it. Our empirical analysis suggests that these gains are disproportionately large for the Asia-Pacific countries—perhaps by reducing resistance to the rapid growth and change in trade patterns in the region. We also highlight a potentially important source of future gains through helping to restrain the costly growth of agricultural protection in rapidly-developing countries in the region.Asian trade growth, GATT commitments, WTO accession

Arithmetic results on orbits of linear groups

Let $p$ be a prime and $G$ a subgroup of $GL_d(p)$. We define $G$ to be $p$-exceptional if it has order divisible by $p$, but all its orbits on vectors have size coprime to $p$. We obtain a classification of $p$-exceptional linear groups. This has consequences for a well known conjecture in representation theory, and also for a longstanding question concerning 1/2-transitive linear groups (i.e. those having all orbits on nonzero vectors of equal length), classifying those of order divisible by $p$.Comment: slight revisions after referee's comment

Directional and singular surface plasmon generation in chiral and achiral nanostructures demonstrated by Leakage Radiation Microscopy

In this paper, we describe the implementation of leakage radiation microscopy (LRM) to probe the chirality of plasmonic nanostructures. We demonstrate experimentally spin-driven directional coupling as well as vortex generation of surface plasmon polaritons (SPPs) by nanostructures built with T-shaped and $\Lambda$- shaped apertures. Using this far-field method, quantitative inspections, including directivity and extinction ratio measurements, are achieved via polarization analysis in both image and Fourier planes. To support our experimental findings, we develop an analytical model based on a multidipolar representation of $\Lambda$- and T-shaped aperture plasmonic coupler allowing a theoretical explanation of both directionality and singular SPP formation. Furthermore, the roles of symmetry breaking and phases are emphasized in this work. This quantitative characterization of spin-orbit interactions paves the way for developing new directional couplers for subwavelength routing

Char quality and tar formation interdependence: First experiments in a new two-stage gasifier

For small scale gasification for CHP purposes, it is of great importance that tar content in the gas remains below 10-50 mg/Nm3. Such low tar concentrations have been reported with staged gasification processes operated for long periods by TK Energi A/S (TKE) and the Danish Technical University (DTU). But for production of syngas, tar concentration must be 1-2 orders of magnitude lower. Such a two-stage gasifier (75 kWth) has been recently installed at CIRAD facilities. The present paper deals with the description of this new equipment and the first pyrolysis tests results obtained. The general objectives of the work are to investigate the influence of the char quality on the gas quality (tar content) and to support the design of two-stage gasifiers and char beds for thermal gas cleaning. (Résumé d'auteur

Intracranial fusarium fungal abscess in an immunocompetent patient: case report and review of the literature.

Introduction Fusarium spp is an omnipresent fungal species that may lead to fatal infections in immunocompromised populations. Spontaneous intracranial infection by Fusarium spp in immunocompetent individuals is exceedingly rare. Case Report An immunocompetent 33-year-old Hispanic woman presented with persistent headaches and was found to have a contrast-enhancing mass in the left petrous apex and prepontine cistern. She underwent a subsequent craniotomy for biopsy and partial resection that revealed a Fusarium abscess. She had a left transient partial oculomotor palsy following the operation that resolved over the next few weeks. She was treated with long-term intravenous antifungal therapy and remained at her neurologic baseline 18 months following the intervention. Discussion To our knowledge, this is the first reported case of Fusarium spp brain abscess in an immunocompetent patient. Treatment options include surgical intervention and various antifungal medications. Conclusion This case demonstrates the rare potential of intracranial Fusarium infection in the immunocompetent host, as well as its successful treatment with surgical aspiration and antifungal therapy