Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Backlund-Darboux Transformations in Sato's Grassmannian

We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.

The data type of spatial objects

A spatial object consists of data assigned to points in a space. Spatial objects, such as memory states and three dimensional graphical scenes, are diverse and ubiquitous in computing. We develop a general theory of spatial objects by modelling abstract data types of spatial objects as topological algebras of functions. One useful algebra is that of continuous functions, with operations derived from operations on space and data, and equipped with the compact-open topology. Terms are used as abstract syntax for defining spatial objects and conditional equational specifications are used for reasoning. We pose a completeness problem: Given a selection of operations on spatial objects, do the terms approximate all the spatial objects to arbitrary accuracy? We give some general methods for solving the problem and consider their application to spatial objects with real number attributes. © 2011 British Computer Society.

Powers and Logarithms

There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers of logarithmic and antilogarithmic mappings or powers of logarithms and antilogarithms (cf. for instance, the survey of Schinzel S[1].

Canonical Objects in Classes of (n, V)-Groupoids

AMS Subj. Classification: 03C05, 08B20

A Basis for Z-Graded Identities of Matrices over Infinite Fields

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

Lie Groups as Four-Dimensional Special Complex Manifolds with Norden Metric

Марта Теофилова - Конструиран е пример на четиримерно специално комплексно многообразие с норденова метрика и постоянна холоморфна секционна кривина чрез двупара-метрично семейство от разрешими алгебри на Ли. Изследвани са кривинните свойства на полученото многообразие. Дадени са необходими и достатъчни усло-вия за разглежданото многообразие да бъде изотропно келерово.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.

A Note About the Nowicki Conjecture on Weitzenböck Derivations

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

Variables affecting government debt: A comparison of certificates of participation, tax -exempt revenue bonds and tax -exempt general obligation bonds

This dissertation analyzed and compared variables affecting interest rate and yield of certificates of participation, tax-exempt revenue bonds and tax-exempt general obligation bonds. The study employed qualitative and quantitative analysis methods. ^ Qualitative research methods included surveys, interviews and focus groups. The survey solicited debt load information from 67 Florida school districts (21 responded) and addressed the question which districts used certificates of participation and why. Eight individuals with experience dealing with all three debt instruments were interviewed. A follow-up focus group of six school district financial officers gathered additional data. Results from the qualitative methods revealed school districts used certificates of participation based on millage authority amount available relative to overall tax base. Also identified was the belief of a significant difference in certificates of participation costs and the other two debt instrument types. ^ The study's quantitative methods analyzed 1998 and 1999 initial issues of Moody's AAA rated certificates of participation, tax-exempt revenue bonds and tax-exempt general obligation bonds. Through an analysis of covariance (ANCOVA), the study examined interest rates and yields while controlling for the covariates of credit enhancement, issue size, and maturity date. The analysis identified no significant difference between interest rates of certificates of participation and tax-exempt general obligation bonds (p < 0.05). There was a significant difference between interest rates of tax-exempt revenue bonds and tax-exempt general obligation bonds. This study discerned no significant difference between yield on certificates of participation and tax-exempt general obligation bonds. It identified a difference in yield between both certificates of participation and tax-exempt general obligation bonds compared with tax-exempt revenue bonds. ^ The study found COPs to have lesser overall costs than RV bonds. COPs also have a quicker entry into the market resulting in construction cost savings. The study found policy implications such as investment portfolio limitations and public choice issues about using COPs as a mechanism to grow government. ^

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Técnicas en análisis lineal (y no lineal) y aplicaciones

La presente tesis est a centrada en dos temas principales: el primero abarca el primer cap tulo y el segundo se divide entre los cap tulos dos y tres. En el primer cap tulo estudio un problema que apareci o como tal hace relativamente poco tiempo (aunque ya en la segunda mitad del pasado siglo se publicaron una serie de resultados que, con la terminolog a adecuada, estar an englobados dentro de esta teor a). Nos interesaremos en la b usqueda de estructuras algebraicas (como espacios vectoriales, algebras, espacios de Banach) contenidas en subconjuntos de funciones cuyos elementos (con la posible excepci on del elemento nulo) veri can ciertas propiedades anti-intuitivas (propiedades de dif cil visualizaci on). Ello nos puede conducir a la idea de c omo la intuci on puede enga~narnos, y sugerir que, aunque se haya dedicado una ingente cantidad de esfuerzo y tiempo para encontrar un unico ejemplo que veri que tales propiedades, y dicho trabajo pueda dar la idea de que no existen muchos m as espec menes de similares caracter sticas, de hecho existen ejemplares su cientes como para construir espacios \grandes" cuyos elementos (salvo el cero) satisfacen las mismas propiedades. M as espec camente, decimos que un subconjunto de un espacio vectorial topol ogico es -lineable (dado un numero cardinal ) si podemos garantizar la existencia de un espacio vectorial de dimensi on contenido en el conjunto (uni on el elemento cero, en caso de que cero no forme parte del conjunto de partida). Si el espacio vectorial es cerrado, nos referiremos a este conjunto como - espaciable (y la propiedad que trataremos ser a la de -espaciabilidad) y si la estructura en cuesti on es un algebra de Banach, entonces diremos que el conjunto es ( ; )-algebrable (donde aqu es la cardinalidad de un conjunto minimal de generadores del algebra)...