Simple piecewise geodesic interpolation of simple and Jordan curves with applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.

Diet and herding strategies in a changing environment: stable isotope analysis of Bronze Age and Late Antique skeletal remains from Ya'amūn, Jordan

Carbon and nitrogen stable isotope ratios of 45 human and 23 faunal bone collagen samples were measured to study human diet and the management of domestic herbivores in past Jordan, contrasting skeletal remains from the Middle and Late Bronze Age and the Late Roman and Byzantine periods from the site of Ya'amūn near Irbid. The isotope data demonstrate that the management of the sheep and goats changed over time, with the earlier animals consuming more plants from semi-arid habitats, possibly because of transhumant herding strategies. The isotope data for fish presented here are the first from archaeological contexts from the Southern Levant. Although fish of diverse provenance was available at the site, human diet was predominately based on terrestrial resources and there was little dietary variability within each time-period. Isotopic variation between humans from different time-periods can mostly be explained by ‘baseline shifts’ in the available food sources; however, it is suggested that legumes may have played a more significant role in Middle and Late Bronze Age diet than later on.

Jordan Gradings on Associative Algebras

In this paper we apply the method of functional identities to the study of group gradings by an abelian group G on simple Jordan algebras, under very mild restrictions on the grading group or the base field of coefficients.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Noncommutative Jordan superalgebras of degree n > 2

We prove a coordinatization theorem for noncommutative Jordan superalgebras of degree n > 2, describing such algebras. It is shown that the symmetrized Jordan superalgebra for a simple finite-dimensional noncommutative Jordan superalgebra of characteristic 0 and degree n > 1 is simple. Modulo a ""nodal"" case, we classify central simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0.

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.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

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.