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Rota-Baxter Categories  [PDF]
Edmundo Castillo,Rafael Diaz
Mathematics , 2007,
Abstract: We introduce Rota-Baxter categories and construct examples of such structures.
Rota-Baxter Coalgebras  [PDF]
Run-Qiang Jian,Jiao Zhang
Mathematics , 2014,
Abstract: We introduce the notion of Rota-Baxter coalgebra which can be viewed as the dual notion of Rota-Baxter algebra. We provide various concrete examples and establish some basic properties of this new object.
O CIRCLO EM ROTA O CIRCLE IN ROTATION  [cached]
Orlando Antunes Batista
Signótica , 1987, DOI: 10.5216/sig.v1i1.7187
Abstract: O CIRCLO EM ROTA O CIRCLE IN ROTATION
Characteristics of Rota-Baxter Algebras  [PDF]
Li Guo,Houyi Yu
Mathematics , 2015,
Abstract: The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota-Baxter algebra, called the Rota-Baxter characteristic. We introduce an invariant, called the ascent set, of a Rota-Baxter characteristic. By studying its properties, we classify Rota-Baxter characteristics in the homogenous case and relate Rota-Baxter characteristics in general to the homogeneous case through initial ideals. We show that the Rota-Baxter quotients of Rota-Baxter characteristics have the same underlying sets as those in the homogeneous case. We also give a more detailed study of Rota-Baxter characteristics with special base rings. In particular, we determine the prime characteristics of Rota-Baxter rings.
Localization of Rota-Baxter algebras  [PDF]
Chenghao Chu,Li Guo
Mathematics , 2012,
Abstract: A commutative Rota-Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota-Baxter algebra, we extend the central concept of localization for commutative algebras to commutative Rota-Baxter algebras. The existence of such a localization is proved and, under mild conditions, its explicit constructions are obtained. The existence of tensor products of commutative Rota-Baxter algebras is also proved and the compatibility of localization and tensor product of Rota-Baxter algebras is established. We further study Rota-Baxter coverings and show that they form a Gr\"othendieck topology.
An identity in Rota-Baxter algebras  [PDF]
Rafael Diaz,Marcelo Paez
Mathematics , 2006,
Abstract: We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.
Equa es de volume para galhos de espécies em diferentes grupos de valor econ mico em uma Floresta Ombrófila Mista / Selection of mathematical equations to estimate the volume of branches for diferent groups of economic value in an Araucaria Forest  [cached]
Geedre Adriano Borsoi,Bruna Verediana Müller,Doádi Ant?nio Brena
Ambiência , 2012,
Abstract: ResumoO objetivo deste estudo foi testar equa es matemáticas e estimar o volume de galhos para espécies de três grupos de valor econ mico em uma área de Floresta Ombrófila Mista, situada na regi o nordeste do estado do Rio Grande do Sul. Foi realizada a cubagem rigorosa dos galhos de 287 árvores-amostra. Além dos galhos de cada árvore selecionada, o restante do fuste comercial (resíduo) foi considerado na determina o do volume total de galhos. As árvores-amostra selecionadas foram separadas e classificadas em grupos de valor econ mico. Dez modelos volumétricos foram testados, sendo que para a sele o do melhor modelo foram analisados o coeficiente de determina o ajustado, o coeficiente de varia o; os desvios médios relativos, desvio absoluto relativo, o valor ponderado e a distribui o gráfica dos valores residuais. A divis o da floresta em grupos de valor comercial mostrou-se eficiente no ajuste de equa es matemáticas. As equa es selecionadas para estimar o volume de galhos foram: “1 de Meyer”, para o grupo de baixo valor; a “5 de Spurr”, para o grupo de médio valor, a “2 de Meyer – modificada”, para o grupo de alto valor comercial; e a “equa o 3, de Naslund – modificada”, para a floresta.AbstractThe objective of this study was to test mathematical equations, and estimate the volume of branches for groups of three species of economic value in an area of Araucaria Forest, located in the northeast region of Rio Grande do Sul. Rigorous scaling of branches of 287 sample trees were performed. Besides considering the branches of each tree selected, the rest of the commercial tree trunks (residue) were taken into account for the determination of the total amount of branches. The selected sample trees were separated and classified into groups of economic value. Ten volumetric models were tested. For selecting the best model, the analysis focused on the determination coefficient, the coefficient of variation, the average relative and absolute deviations, the weighted elative value and the graphic distribution of residual values. The division of the forest in groups of commercial value was efficient to adjust the mathematical equations. The equations selected to estimate the volume of branches were the “1 of Meyer”, for the group of low value; the “5 of Spurr”, for the group of medium value; the “2 of changed Meyer”, for the group of high commercial value; and the “equation 3 of changed Naslund” for the forest.
O Banco de sementes de um trecho de uma floresta Atlantica montana (S o Paulo - Brasil)  [cached]
BAIDER C.,TABARELLI M.,MANTOVANI W.
Revista Brasileira de Biologia , 1999,
Abstract: Durante a regenera o da floresta tropical, após perturba es naturais ou antrópicas, o banco de sementes do solo está envolvido no estabelecimento de grupos ecológicos e na restaura o da riqueza de espécies lenhosas. Para a análise da composi o de espécies do banco de sementes de um trecho de floresta Atlantica madura, no Sudeste do Brasil, foram coletadas 57 amostras de solo, distribuídas aleatoriamente em 2 ha, totalizando 28.500 cm3 de solo coletado. Durante um período de 17 meses germinaram 497 sementes, 65% distribuídas entre 0 e 2,5 cm de profundidade, totalizando 872 sementes/m2. O banco de sementes dessa floresta caracterizou-se pela presen a de dois componentes: o herbáceo, composto por 66 morfotipos, pertencentes a famílias ricas em espécies pioneiras; e o arbustivo-arbóreo, formado por 19 espécies, em sua maioria, pioneiras com diásporos menores que 1 mm de comprimento. Os resultados obtidos sugerem que, na floresta Atlantica montana, o banco de sementes pode ter importancia no estabelecimento de espécies de árvores e arbustos pioneiros, componentes de grupos ecológicos envolvidos na regenera o da floresta após corte e queima. Após a abertura de clareiras naturais, o banco de sementes pode ser o responsável pelo estabelecimento de espécies de Melastomataceae, principal grupo de árvores e arbustos pioneiros observados nas clareiras.
Enumeration of Rota-Baxter Words  [PDF]
Li Guo,William Y. Sit
Mathematics , 2006,
Abstract: In this paper, we prove results on enumerations of sets of Rota-Baxter words in a finite number of generators and a finite number of unary operators. Rota-Baxter words are words formed by concatenating generators and images of words under Rota-Baxter operators. Under suitable conditions, they form canonical bases of free Rota-Baxter algebras and are studied recently in relation to combinatorics, number theory, renormalization in quantum field theory, and operads. Enumeration of a basis is often a first step to choosing a data representation in implementation. Our method applies some simple ideas from formal languages and compositions (ordered partitions) of an integer. We first settle the case of one generator and one operator where both have exponent 1 (the idempotent case). Some integer sequences related to these sets of Rota-Baxter words are known and connected to other combinatorial sequences, such as the Catalan numbers, and others are new. The recurrences satisfied by the generating series of these sequences prompt us to discover an efficient algorithm to enumerate the canonical basis of certain free Rota-Baxter algebras. More general sets of Rota-Baxter words are enumerated with summation techniques related to compositions of integers.
Rota-Baxter 3-Lie algebras  [PDF]
Ruipu Bai,Li Guo,Jianqian Li,Yong Wu
Mathematics , 2013, DOI: 10.1063/1.4808053.
Abstract: In this paper we introduce the concepts of a Rota-Baxter operator and a differential operator with weights on an $n$-algebra. We then focus on Rota-Baxter 3-Lie algebras and show that they can be derived from Rota-Baxter Lie algebras and pre-Lie algebras and from Rota-Baxter commutative associative algebras with derivations. We also establish the inheritance property of Rota-Baxter 3-Lie algebras.
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