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).

E da fronteira veio um pioneiro : a frontier thesis de Frederick Jackson Turner (1861-1932)

O historiador Frederick Jackson Turner (1862-1931) é considerado o grande pai da historiografia moderna nos Estados Unidos. Sua frontier thesis postulava a centralidade da expansão das fronteiras ocidentais no processo de formação da nacionalidade estadunidense e na consolidação da democracia política naquela nação, abandonando uma história política factual e introduzindo uma interpretação calcada em fatores econômicos e sociais, com claras implicações presentistas. Graças a esta análise revolucionária, Turner tornou-se uma espécie de patrono da profissionalização da disciplina nos Estados Unidos, formando toda uma geração de historiadores a partir de seus seminários na Universidade Estadual do Wisconsin e em Harvard. Não só isso, mas a sua teoria encontrou apelo entre elementos da classe política e empresarial, incluindo dois Presidentes da República, Theodore Roosevelt (1901-1909) e Woodrow Wilson (1913-1921). A explicação para tal sucesso pode ser encontrada na relação entre a frontier thesis e o Mito da Fronteira, através de uma narrativa que fazia uso dos ícones e imagens do Mito enquadrados em uma retórica extremamente persuasiva. Nas páginas dos escritos de Turner, os norte-americanos marcham triunfalmente em direção a conquista de todo o continente, justificada pelo seu amor à democracia e por sua devoção ao progresso material e mental dos homens. Com isso, o historiador conseguiu unir uma valorização do agrarianismo primitivo com um elogio à evolução histórica dos Estados Unidos.

Potencial de alimentação de Chrysoperla externa (Hagen, 1861) (Neuroptera, Chrysopidae) em diferentes densidades de Uroleucon ambrosiae (Thomas, 1878) (Hemiptera, Aphididae)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Aspectos biológicos de Chrysoperla externa(Hagen, 1861)(Neuroptera: Chrysopidae) alimentada com Planococcus citri (Risso, 1813)(Hemiptera: Pseudococcidae) e Toxoptera citricida (Kirkaldy, 1907) (Hemiptera: Aphididae)

The citrus-growing ecosystem houses a great deal of species of natural enemies, among them Chrysoperla externa (Hagen, 1861), which presents a great potential for use in the biological control of pests. The aim of this work was to evaluate the effects of the preys Planococcus citri (Risso, 1813) and Toxoptera citricida (Kirkaldy, 1907) on the development of larva and pupa of C. externa. The trial was carried out in an acclimatized room at 25 +/- 1 degrees C, 70 +/- 10% RH and 12-hour photophase, the treatments consisting of the continuous and alternate supply of those two preys in each instar of the predator, in addition to eggs of Anagasta kuehniella (Zeller, 1879) utilized for comparison purposes. Both the white mealybug and the aphids were given in sufficient amounts to the C. externa larvae to be able to feed ad libitum. The lifetime and the survival rate of the phases of larva, pupa and the larval-adult period of C. externa were evaluated. It was found that T. citricida given either singly along the larval development or in two consecutive instars of the predator was not an adequate prey, 100% of mortality over the larval-adult period being found. When the larvae fed on P. citri, given in two instars of the predator, the survival rate in the larval-adult period was similar to the diet constituted of only A. kuehniella eggs, except when fed with T. citricida in the first instar.

Tempo de busca e de manuseio de larvas de Chrysoperla externa (Hagen, 1861) (Neuroptera, Chrysopidae) alimentadas com Uroleucon ambrosiae (Thomas, 1878) (Hemiptera, Aphididae)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Consumo de Uroleucon ambrosiae (Thomas, 1878) (Hemiptera: Aphididae) por larvas de Chrysoperla externa (Hagen, 1861) (Neuroptera: Chrysopidae) em casa-de-vegetação

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Desenvolvimento e capacidade de consumo de Chrysoperla externa (Hagen, 1861) alimentada com ninfas de mosca-branca criadas em hortaliças

Many arthropods are mentioned with whitefly natural enemies, including the green lacewings. The aim of this study is to analyses the development and the capacity of predation of Chrysoperla externa (Hagen, 1861) fed with Bemisia tabaci B biotype nymphs, rearing different vegetables (kale, broccoli, eggplant end tomato). The duration, viability end weight in each stage end phase of development of the insect-predator had been evaluated, as well as the predatory capacity of the larvae in the third instar. The larval phase of the predator presented minor duration when these had been fed with nymphs developed the broccoli (12.36 days) and minor duration of the tomato (14.36 days) phase when fed with nymphs developed in kale, broccoli, and eggplant (6.50, 7.20, 7.33 days, respectively). The lower indices of viability been found for the larvae fed with nymphs developed in the tomato (30%), and average weights have. The predatory capacity of the larvae during the third instar was not affected, independently on the plant host where the whitefly nymph fed itself.

Histology and histochemistry of the ventriculus of Dolichoderus (=Monacis) bispinosus (OLIVIER, 1792) (Hymenoptera : Formicidae)

In this study we histologically and histochemically describe the ventriculus of Dolichoderus bispinosus. The epithelium consists of two basic cell types, highly basophilic generative cells, and digestive cells. The latter present several cytoplasmic vesicles. rich in acidic and neutral polysaccharides, and basic proteins. Also, these. cells exhibit an apocrine secretion pattern. A mass of fibrous material is observed on the surface of the epithelium. Finally, we discuss the results obtained. (c) 2005 Elsevier Ltd. All rights reserved.

Consumo e ganho de peso de larvas de Chrysoperla Externa (Hagen, 1861) (Neuroptera: Chrysopidae) de diferentes Populaçoes e Geraçoes de Laboratório

Several studies have been made about biology, predatory capacity, and food consumption to crisopids species, trying to get informations to use in Integrated Pest Management. Raising insects in laboratory for many generations could cause blood relation problems, even annihilate the insect mass production. In this way, the objective of this work was to determine the consumption and the weight gain to Chrysoperla externa larvae from two populations and different laboratory generations, founded by 1, 5, 10, 15 and 20 couples. By the result it was possible to conclude that larvae food consumption was higher in populations founded by greater number of couples, and it is not verified variation among populations and generations.

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.