Represenation Theory

Models are of central importance in many scientific contexts. The centrality of models such as the billiard ball model of a gas, the Bohr atom model, the MIT bag model of the nucleon, the MIT Gaussian chain model of a polymer, the Lorenz atmosphere model, the Gaussian Lorenz atmosphere model, the Lotka-Volterra predatorprey interaction model, the DNA double helix model, agent and evolutionary models in the social sciences and general equilibrium models of markets are, in their respective domains, in their respective domains, examples of this. Scientists spend a great deal of time building, testing, comparing and revising models, and much space is devoted in journals to introducing, applying and interpreting these valuable tools. In short, models are one of the main tools of modern science.

Fandry (2013) is the first feature film written and directed by Nagraj Manjule. The film received a national award for the best debut director and several accolades in national and international film festivals. This paper offers introductory remarks on the representa- tion of the de-notified tribe- Kaikadi in the film Fandry (2013). It starts with the observation about the social location of de-notified tribes and stigmatization around these communities and how Fandry as a film becomes a vehicle of resistance and formation of defiant identity. I also offer a critical reading of contemporary scholarship on Fandry, which overlooks the de-notified tribe iden- tity and appropriates the struggle in the film with the larger Dalit struggle and caste issues. While the Dalit framework forms the background of the film, I argue that Manjule, through his film Fandry, is asserting personhood by bringing in lived experiences in his cinematic narrative.

In this work on GL ( 2 ) we have found that it is hard to compute the chamber homology groups from the quotient space β 1 GL ( 2 ) / GL ( 2 ) (Mobius band), so we introduced a new way to compute the chamber homology groups by restricting to the original quotient space (edge) before taking the real line R . We have not yet given a full description of what happening under base change when we work on the cuspidal representation but, we somehow, gave a way to compute the base change effect of some type of cuspidal representations which are the admissible pairs. The base change of a principal series representations is always a principal series. Similarly, the base change of a twist of Steinberg representation is again a twist of Steinberg. However, an irreducible Galois representation can certainly restrict to a reducible one. Thus it is possible for the base change of a cuspidal to be principal series. In fact, if π is any irreducible admissible representation of GL ( 2 , F ) then one c...

Computer viruses can cause significant damage to computer systems, and that damage can lead to loss of data and financial losses for computer users. To deal with computer viruses and to avoid them in the future, system can be updated and better antivirus software installed. Someone experts can remove viruses without antivirus software and fix infected computers that have serious and great damage. In this paper, we consider three types of control to deal with infected systems and preventing further spread of viruses: the installation of antivirus software on infected computers, the installation of antivirus software on susceptible computers, and the cleaning and repairing of infected computers without the use of antivirus software. We proposed a model that had three equilibrium points: two virus-free and one endemic. Pontryagin’s maximum principle was used to solve the problem of optimal control in our model. Some numerical simulations showed that an acceleration in the declining num...

El desarrollo de la tradición filosófica, ocupada en la pregunta por el conocimiento, ha demostrado los límites de un modo de pensar que, aunque limitado en su alcance, ha querido identificarse con la esencia del pensar. Frente a esto es necesario reivindicar un pensamiento que no tenga miedo de pensarse a sí mismo como labor destructiva y como reivindicación de todo lo que se ha considerado hasta ahora como nihilismo.

espanolEl desarrollo de la tradicion filosofica, ocupada en la pregunta por el conocimiento, ha demostrado los limites de un modo de pensar que, aunque limitado en su alcance, ha querido identificarse con la esencia del pensar. Frente a esto es necesario reivindicar un pensamiento que no tenga miedo de pensarse a si mismo como labor destructiva y como reivindicacion de todo lo que se ha considerado hasta ahora como nihilismo. EnglishThe development of the philosophical tradition, dominated by the question of knowledge, has demonstrated the limits of a mindset that, although still very limited, wished to be identified with the essence of thought itself. Against this, it is necessary to vindicate a thought that is not afraid to think of itself as destructive work and as a vindication of everything that is regarded as nihilism.

Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G. At the heart of these conjectures are statements about the geometric structure of Bernstein components for G, both at the level of the space of irreducible representations and at the level of the associated Hecke algebras. We relate this to two well-known conjectures: the local Langlands correspondence and the Baum-Connes conjecture for G. In particular, we present a strategy to reduce the local Langlands correspondence for irreducible G-representations to the local Langlands correspondence for supercuspidal representations of Levi subgroups.

The outlined approach allows a common philosophical viewpoint to the physical world, language and some mathematical structures therefore calling for the universe to be understood as a joint physical, linguistic and mathematical universum, in which physical motion and metaphor are one and the same rather than only similar in a sense.

Pensamiento europeo en el siglo XIX Esta etapa se caracteriza por ser de gran agitación social y política ,las cuales se expresaron en las revoluciones sociales que remecieron en Europa, del mismo modo, se llevó a replantear la manera de explicar el mundo por medio de los pensadores de la época, desarrollando teorías que se convirtieron en los nuevos paradigmas filosóficos e intelectuales de la época.

El desarrollo de la tradición filosófica, ocupada en la pregunta por el conocimiento, ha demostrado los límites de un modo de pensar que, aunque limitado en su alcance, ha querido identificarse con la esencia del pensar. Frente a esto es necesario reivindicar un pensamiento que no tenga miedo de pensarse a sí mismo como labor destructiva y como reivindicación de todo lo que se ha considerado hasta ahora como nihilismo.

We emphasized finding the explicit cycles in the chamber homology groups and the K-theory groups in term of each representation for S L(2, F ). This led to an explicit computing of chamber homology and the K-theory groups. We have identified the base change effect on each of these cycles. The base change map on the homology group level works by sending a generator of the homology group of S L(2, E) labeled by a character of E × to the generator of the homology group of S L(2, F ) labeled by a character of F × multiplied by the residue field degree. Whilst, it works by sending the K-theory group generator of the reduce C * -algebra of S L(2, E) labeled by the 1-cycle (resp. 0-cycle) to the multiplication of the residue field degree with a generator of the K-theory group of S L(2, F ) labeled by the base changed effect on 1-cycle (resp. 0-cycle). J 0 and λ − J 0 or λ − J 1 , λ + J 0 and λ − J 0 .

In this work on G L(2) we have found that it is hard to compute the chamber homology groups from the quotient space β 1 G L(2)/G L(2) (Mobius band), so we introduced a new way to compute the chamber homology groups by restricting to the original quotient space (edge) before taking the real line . We have not yet given a full description of what happening under base change when we work on the cuspidal representation but, we somehow, gave a way to compute the base change effect of some type of cuspidal representations which are the admissible pairs. The base change of a principal series representations is always a principal series. Similarly, the base change of a twist of Steinberg representation is again a twist of Steinberg. However, an irreducible Galois representation can certainly restrict to a reducible one. Thus it is possible for the base change of a cuspidal to be principal series. In fact, if π is any irreducible admissible representation of G L(2, F ) then one can find an extension E/F such that BC(π) is either unramified or Steinberg. .