Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

Symplectic bosons, Fermi fields and super Jordan algebras

A construction relating the structures of super Lie and super Jordan algebras is proposed. This may clarify the role played by field theoretical realizations of super Jordan algebras in constructing representations of super Kač-Moody algebras. The case of OSP(m, n) and super Clifford algebras involving independent Fermi fields and symplectic bosons is discussed in detail.

Food categories reconstruction and feeding consumption estimates for the Sciaenid Macrodon ancylodon (Bloch & Schneider), and the congeneric fishes Stellifer rastrifer (Jordan) and Stellifer naso (Jordan) (Pisces, Perciformes) in the Caeté Estuary, Northern Coast of Brazil

Um método quantitativo para se estimar o consumo alimentar e o aporte energético das diferentes categorias alimentares é apresentado através da reconstrução das presas ingeridas com base em estruturas corporais não digeríveis. Para tal, o presente estudo estabelece, através do exame dos conteúdos estomacais de 1.086 exemplares dissecados de Macrodon ancylodon (Bloch & Schneider, 1801), Stellifer rastrifer (Jordan, 1889) e Stellifer naso (Jordan, 1889), as equações das relações funcionais entre o peso das presas e estruturas corporais. Com as categorias reconstruídas foi possível quantificar o alimento ingerido pelos espécimes. Os resultados indicaram que existe uma marcada diferença, tanto na composição das categorias alimentares, bem como no aporte energético acompanhando o desenvolvimento ontogênico do predador.

THE INFLUENCE OF THE 1992-1993 EL NINO ON THE REPRODUCTIVE BIOLOGY OF Scomber japonicus peruanus (JORDAN & HUBB, 1925)

The influence of the 1992-1993 El Nino events on the reproductive behavior of the Scomber japonicus peruanus (Chub mackerel) was studied from samples collected monthly, along the Peruvian coast (3 degrees 23`S-14 degrees 00`S), from January 1990 to December 1993. The monthly variation of the gonadosomatic index and the frequency of the periods of gonad maturation evidenced that the spawning of the species occurred all year long, being more intense in summer. The values of the gonadosomatic index were higher during the occurrence of the 1992-1993 El Nino, while the body weight and gonad weight decreased. Regarding the condition factor, its values decreased in females over 35 cm in fork length.

Growth parameters and mortality rate of the Scomber japonicus peruanus (Jordan & Hubb, 1925) along the Peruvian coast, South Pacific

The growth parameters and the mortality rates of the Scomber japonicus peruanus (Chub mackerel) were studied based on monthly data of frequency of fork length classes obtained from commercial landings off the Peruvian coast from 1996 to 1998. The asymptotic body length and growth rate values obtained by the ELEFAN I (Electronic Length Frequency Analysis) ranged from 40.20 cm to 42.20 cm and from 0.38 to 0.39, respectively. The oscillation amplitude was 0.60; the Winter point values varied from 0.50 to 0.60 and the performance index from 2.79 to 2.84. The total mortality rate of the Chub mackerel obtained by the linearized catch curve oscillated between 1.68 and 3.35. The rate of fishing mortality varied from 1.16 to 2.78 and the exploitation rate from 0.68 to 0.84. The annual rate of natural mortality estimated by the Pauly`s method ranged from 0.52 to 0.53. The results obtained allow us to conclude that the longevity of the Chub mackerel was slightly over seven years.

Il teorema dei quattro vertici e il teorema di Jordan-Schönflies

Una curva di Jordan è una curva continua nel piano, semplice e chiusa. Lo scopo della tesi è presentare tre teoremi riguardanti le curve di Jordan. Il teorema dei quattro vertici afferma che ogni curva di Jordan regolare di classe C^2 ha almeno quattro punti in cui la curvatura orientata ha un massimo o un minimo locali. Il teorema della curva di Jordan asserisce che una curva di Jordan divide il piano esattamente in due parti, l'interno e l'esterno della curva. Secondo il teorema di Schönflies, la chiusura dell'interno di una curva di Jordan è omeomorfa a un disco chiuso.