(Pontificia Universidad Católica del Perú, 2013) Rabanal, Roland
We describe some classical results on global injectivity of local dieomorphism on Euclidian spaces. This is not exhaustive, and it does not purport to be a complete history, it simply describes some useful results in injectivity. The first part describes some results related to the Qualitative Theory of Diferential Equations, and presents a characterization of global injectivity on planar applications by using the existence of an isochronous global center. The Global Asymptotic Stability Problem is also described. The second part describes the so called Palais-Smale condition.
(Pontificia Universidad Católica del Perú, 2013) Beltrán, Johel
In this monograph we continue with the inspection initiated in [1] on the fundamental tools introduced in the approach proposed in [2,3] for the study of metastability. We give the definition of the Poisson random measures and prove the main properties that we will subsequently use to construct Markov processes with finite state space. Such construction will allow us to provide a probabilistic proof of the fact that the law of a Markov process solves the martingal problem.
(Pontificia Universidad Católica del Perú, 2013) Ahmad Khan, Mumtaz; Hakim Khan, Abdul; Ahmad, Naeem
The present paper is a study of modied Hermite polynomials of two variables Hn(x; y; a) which for a = e reduces to Hermite polynomials of two variables Hn(x; y) due to M.A. Khan and G.S. Abukhammash.
(Pontificia Universidad Católica del Perú, 2013) Fernandez Sánchez, Percy; Mozo Fernández, Jorge; Neciosup Puican, Hernán
The main aim of this paper is proof that the reduction of the singularities of a generalized hypersurfaces agrees with a reduction of singularities of its separatrix; which is a generalization of the result presented in [8] by the first two authors.
(Pontificia Universidad Católica del Perú, 2013) Cuadros Valle, Jaime
We define hypersato structures: these structures admit three inequivalent Sasakian structures such that each of these structures shares a common Reeb vector field and a common contact form with the others two. It is interestingto notice that hypersato manifolds can be viewed as U(1) principal orbibundles with base space a 4n-dimensional hyperkahler orbifold. We also discuss some results on the moduli problem of these structures.
(Pontificia Universidad Católica del Perú, 2013) Valqui Haase, Christian Holger; Guccione, Jorge A.; Guccione, Juan J.
We analyze a possible minimal counterexample to theJacobian Conjecture P;Q with gcd(deg(P); deg(Q)) = 16 and show that its existence depends only on the existence of solutions for a certain Abel dierential equation of the second kind.
(Pontificia Universidad Católica del Perú, 2013) Oré, Casio R.
On sunday october 14, 2012, the Austrian Felix Baumgartner did a spectacular jump in Roswell, New Mexico. He ascended 39 km high in a helium contained globe and jumped. In this work I try to applay physical laws to understand the details of the trajectory.
