Pakikipagkapwa: A Filipino Value in Attempt to Counter Biodiversity and Cultural Diversity Loss

Many would think of biodiversity merely in the context of environment, ecology, or nature. Species thrive because of diversity, and that includes human beings. However, this article treks an unusual terrain of biodiversity. The damage we made towards nature bespeaks the harm we likewise do against the vulnerable ‘other’in society, in particular the Deaf people. The people who are Deaf discussed in this article are the ones who identify themselves as entho-linguistic cultural minority. In addition, they do not consider deafness to be a deficit; rather, some of them view their condition as different, or to some is diversity. Contextually, this writer presents an alternate way to afford respect with humility by employing a moral Filipino value of pakikipagkapwa (shared inner-self). In a society that seems to remain numb to the groaning of our kapwa (the Other or fellow-being), this article challenges us to reconsider if we truly care for the non-human and the Deaf, who remains the vulnerable ‘other’ today

On vector-valued Poincar\'e series of weight 2

Given a pair $(\Gamma,\rho)$ of a Fuchsian group of the first kind, and a unitary representation $\rho$ of $\Gamma$ of arbitrary rank, the problem of construction of vector-valued Poincar\'e series of weight 2 is considered. Implications in the theory of parabolic bundles are discussed. When the genus of the group is zero, it is shown how an explicit basis for the space of these functions can be constructed.Comment: Final version, 21 pages. To appear in the Journal of Geometry and Physics (2017

On reduction curves and Garside properties of braids

In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. Then we study how a cyclic sliding (which is a particular kind of conjugation) affects the normal form of a braid with respect to the normal forms of its components. Finally, using the above methods, we provide the example of a family of braids whose sets of sliding circuits (hence ultra summit sets) have exponential size with respect to the number of strands and also with respect to the canonical length.Comment: 20 pages, 3 figure