The Ricci flow in a class of solvmanifolds

In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the omega-limit of bracket flow solutions is a single point, and that for any sequence of times there exists a subsequence in which the Ricci flow converges, in the pointed topology, to a manifold which is locally isometric to a flat manifold. We give a functional which is non-increasing along a normalized bracket flow that will allow us to prove that given a sequence of times, one can extract a subsequence converging to an algebraic soliton, and to determine which of these limits are flat. Finally, we use these results to prove that if a Lie group in this class admits a Riemannian metric of negative sectional curvature, then the curvature of any Ricci flow solution will become negative in finite time.Comment: 16 pages, 1 figur

The Services Sector in the Philippines

This paper studies the traded services in the Philippines with an emphasis on the analysis of government intervention. It examines the pattern of trade in services as well as provides the link of the former to the Philippine domestic economic structure. Details of the regulation and protection of traded services are also presented and analyzed in terms of government policies, levels of protection and economic implications. Some prospects for policy cooperation in traded services are suggested.services sector, service delivery

Homogeneous Ricci solitons in low dimensions

In this article we classify expanding homogeneous Ricci solitons up to dimension 5, according to their presentation as homogeneous spaces. We obtain that they are all isometric to solvsolitons, and this in particular implies that the generalized Alekseevskii conjecture holds in these dimensions. In addition, we prove that the conjecture holds in dimension 6 provided the transitive group is not semisimple.Comment: 20 pages, 3 tables; Appendix by Jorge Laure

The Economic and Social Impact of Tourism

This paper analyzes the economic and social impact of tourism in Pagsanjan in which tourism development project is located. Results show that the project’s various significant impacts include increases in employment and income and stimulation of political and women’s participation. While its impact on environment and on the people’s social life has been a mixture of positive and negative results, its impact on income distribution has been trifling. To maximize the tourism multiplier, the paper encourages the collaboration of the tourism project with other programs devised to boost the capacity of the local economy. Tourism manpower training agenda should include training for women skills while tourism promotions should move from sex-oriented markets to prevent several disorientations in the cultural values of the tourism industries.tourism

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page