Ações de Semigrupos em Fibrados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Grupos de lie de matrices reales o complejos

Como la historia lo viene diciendo, en general los resultados importantes y trascendentales en Matemática son los capaces de vincular dos estructuras, en su esencia, totalmente distintas. En el año 1973, el matemático Noruego Marius Sophus Lie (1849-1925) estudiando propiedades de soluciones de sistemas de ecuaciones diferenciales, dio origen a las ideas que conformaron la hoy denominada Teoría de Lie, la cual plantea la relación entre geometría, álgebra y la topología, este matemático creó en gran parte la teoría de la simetría continua, y la aplicó al estudio de la geometría y las ecuaciones diferenciales. Con aportes posteriores de los matemáticos Weyl, Cartan, Chevalley, Killing, Harish Chandra y otros estructuran la teoría de Lie, se presentan en este trabajo de investigación las nociones básicas que subyacen en dicha teoría. En los primeros trabajos de Sophus Lie, la idea subyacente era construir una teoría de grupos continuos, que complementara la ya existente teoría de grupos.

The 'Dirty Work' of the Lie

The panel "Duplicity/Complicity: Performing and Misperforming Lies" at PSi #15 in Croatia in July 2009 examined the half-truths, hidden assumptions and power relations embedded in every act of performance through an analysis of the way bodies, buildings, personae and communities perform and misperform lies. It was a collection of new academic voices from Australia and Croatia, intersecting and colliding and, at times, outright lying, with each other and with commentary from Alan Read. Inspired by this successful adventure in collaborative academic mis-performance, "The ‘Dirty Work’ of the Lie" takes the challenge set by the Prelude Panel at PSI #15 and subjects the ideas emerging from this panel to "friendly fire" in order to build a multi authored response to 'performance that lies', with reference to the work of A Chorus of Women, disabled artists Bill Shannon, Aaron Williamson and Kathryn Araneillo, US dance performer Ann Liv Young and US theatre and festival director Peter Sellars. In doing so, "The 'Dirty Work' of the Lie" provides a reflexive response to the duplicity inherent in the performances, and also in our own academic analyses. With Alan Read acting as interlocutor, each contributor will creatively respond to a paper presented by another, developing the key intersecting issues that emerged through the formation of the panel. These issues include impression management, self-belief and performers who are 'taken in by their own act', the dirty work of taking others in with an act, the guerrilla dimension of lying, the productivity of the lie, and questions of audience engagement and ethics. As a result, this new paper tests how the 'misperformance' of lies across different cultural sites, be it deliberate or accidental, can become a productive – and, indeed, politicised – aspect of cultural performance, betraying accepted attitudes, ideas and structures of authority and offering alternative visions. Through it’s distinctively multi vocal texture, "The 'Dirty Work' of the Lie" also interrogates the modes of analysis available to us, questioning the 'duplicity' in our reflecting, responding and listening to each other as well as the work.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Robust numeric set watermarking : numbers don’t lie

Ever since Cox et. al published their paper, “A Secure, Robust Watermark for Multimedia” in 1996 [6], there has been tremendous progress in multimedia watermarking. The same pattern re-emerged with Agrawal and Kiernan publishing their work “Watermarking Relational Databases” in 2001 [1]. However, little attention has been given to primitive data collections with only a handful works of research known to the authors [11, 10]. This is primarily due to the absence of an attribute that differentiates marked items from unmarked item during insertion and detection process. This paper presents a distribution-independent, watermarking model that is secure against secondary-watermarking in addition to conventional attacks such as data addition, deletion and distortion. The low false positives and high capacity provide additional strength to the scheme. These claims are backed by experimental results provided in the paper.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Spherical aberration and its correction using Lie algebraic methods

We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat's principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

Variants of Miyachi�s Theorem for Nilpotent lie Groups

We formulate and prove two versions of Miyachi�s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi�s theorem for the group Fourier transform.

Variants Of Miyachi’S Theorem For Nilpotent Lie Groups

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

Evaluación de dos grupos de cerdos alimentados con dos tipos de raciones, concentrado comercial y desperdicios de cocina

El presente trabajo se realizó en la granja "Santa Rosa" propiedad de la UNA, ubicada en Sabana Grande, Managua El objetivo general del estudio fue: evaluar comparativamente el concentrado comercial y los desperdicios de cocina, sobre los indicadores técnicos del cerdo en producción. Los objetivos específicos fueron: l. Evaluar el comportamiento de las variables ganancia media diaria, ganancia por periodo, peso inicial, peso final, consumo de alimento por animal y por periodo, conversión alimenticia por animal y por periodo de dos grupos de cerdos alimentados, uno con concentrado comercial y otro con desperdicios de cocina; 2. Comparar económicamente las dietas utilizadas. El experimento se analizó en tres etapas productivas (crecimiento, desarrollo y engorde) con dos grupos de cerdos alimentados con: Concentrado comercial (T1) y Desperdicios de cocina (T2). Se utilizaron 16 cerdos Híbridos divididos en dos grupos de 8 animales (4♀ y 4♂ castrados),con peso promedio de 27.5 kg., los animales se pesaron cada 30 días. Las variables evaluadas fueron: ganancia media diaria (GMD), ganancia media por periodo (GMPP), peso inicial, peso final, consumo animal (CA), consumo por periodo (CP), conversión de alimento por animal (Convan) y por periodo (convp). Las variables PI, PF, G.MD. y G.M.P.P. se analizaron como un BCA en arreglo bifactorial considerando los factores: A: Sexo y B: Dietas. Las variables CA, CP, Convan y ConvP se analizaron como un DCA. Se realizó el ANDEVA y pruebas de separaciones de medias para todas las variables. Para relacionar las variables peso inicial con el peso final, se realizó un análisis de regresión. Se realizó un análisis económico por presupuestos parciales. La variable GMD se vio afectada (0.05 %) por la interacción. sexo*dieta, no así por el tiempo, sexo y dieta La GMPP fue afectada (0.05%) dieta y no por el tiempo, sexo y la interacción. sexo*dieta. El peso inicial se vio afectado (0.05%) por el tiempo, la dieta y la interacción sexo*dieta, y no por el sexo. El peso final se vio afectado (0.05%) por el tiempo, sexo, dieta y la interacción sexo*dieta. La Convan, ConvP, CA y CP se observan diferencias significativa pan ambos tratamientos, observándose un mejor comportamiento con el T1. El peso final se ve afectado por el peso inicial en ambos tratamientos, con r2 de 0.99 y 0.97 respectivamente. El tratamiento que presentó mayor fue el T2. Se concluye que: Los desperdicios de cocina son una alternativa de alimentación no convencional viable para los productores; tanto T1 y T2 tuvieron estadísticamente igual comportamiento GMD y GMPP, no siendo así para el peso inicial y peso final que fueron mayores al el T1; El CA, CP, Convan y ConvP fueron inferiores al el T1.De igual forma en ambos tratamientos el peso final dependió del peso inicial en un 99 y 97% respectivamente. El tratamiento que mayor Utilidad Obtuvo fue el de desperdicios de cocina. Económicamente producir un kilogramo de carne de cerdo con desperdicios de cocina es más rentable que hacerlo a partir de alimentos concentrados.

Efecto de coberturas muertas de follajes de tres especies de árboles de sombra sobre la reducción de grupos de malezas en el cultivo de café (Coffea arabica L.)

El presente trabajo evaluó el efecto de coberturas muertas procedentes de hojas y ramas podadas de las especies: Simarouba glauca D.C., Clusia rosea Jacq y Giricidia sepuim (Jacq) Steud., sobre la reducción de los grupos de malezas de una plantación de café (Coffea arabica L.), manejada bajo sombra. Para ello se estableció un ensayo en la finca La Nacional, Masatepe, Nicaragua; colocando en las parcelas experimentales, material vegetal cortado de cada una de estas especies, en tres diferentes grosores de cubrimiento. Las malezas procedentes de semillas y de retoños se mantuvieron controladas a los 17, 31, 45 y 65 días después de establecido el ensayo. El testigo promedio 385 individuos por m2 y los diferentes tratamientos promediaron 22 individuos por m2 en malezas de semillas. El testigo para malezas de retoños promedio 619 brotes por m2, los diferentes tratamientos promediaron 85.5 brotes por m2. En el muestreo para determinar biomasa fresca de malezas, hubo diferencias significativas en malezas de semillas y retoños, con promedios de 21 g/m2 para el testigo, comparado con 3 g/m2 para los m2 para los tratamientos en malezas de semillas y para malezas de retoños el testigo promedio 233 g/m2 y en los tratamientos promediaron 52 g/m2. En general los grosores dobles y triples alcanzaron a reducir mayormente las malezas.