Abstract:
We prove a known partitions theorem by Bell in an elementary and constructive way. Our proof yields a simple recursive method to compute the corresponding Sylvester polynomials for the partition. The previous known methods to obtain these polynomials are in general not elementary.

Abstract:
There exist in the literature various exact formulae for the primecounting function π(x) and the n-th prime pn. These formulae use thefloor function. In this note we present exact formulae for the perfectpower counting function N(x) and the n-th perfect power Pn. Theseformulae also use the floor function.

Abstract:
Let $P_n$ be the $n$-th perfect power. In this article we obtain asymptotic formulae for the sum $sum^{n}_{i=1}P_i$. We also prove the following formulae[sum^{n}_{i=1}frac{1}{sqrt{P_i}}=log n+C+o(1),qquad sum_{P_nleq x}frac{1}{sqrt{P_n}}=frac{1}{2}log x+C+o(1),]where $C$ is a constant.

Abstract:
Let $n$ be a fixed positive integer. In this article we obtain asymptotic formulae for $sum^{N}_{j=1} j^n log j$ and $prod^{N}_{i=1}j^{(j^n)}$. For example if $n=1$ we obtain the asymptotic formulae,[sum^{N}_{i=1} j log j= frac{N^2}{2}log N -frac{N^2}{4}+frac{1}{2}N log N+frac{1}{12}log N +C_1+o(1),]and[prod^{N}_{i=1}j^{j}sim e^{C_1} frac{N^{frac{N^2}{2}+frac{N}{2}+frac{1}{12}}}{e^{frac{N^2}{4}}},]where $C_1$ is a constant.

Abstract:
in the latin america region, the tobacco epidemic among women is a fact. this is related to the change in social and economic status among women and the efforts of the tobacco industry to capture their market share. the fctc has the potential to be an important treaty for women if its articles include a gender perspective. womena′s rights treaties, also represent an important tool to stop the epidemic. women's participation is key in this process.

Abstract:
Roughly 99% of the demand for electricity in Brazil is supplied by a national interconnected grid. The remaining 1% is spread in several “isolated systems” of the Amazon region—mini-grids that rely on expensive diesel gensets due to high commodity and transportation costs. The isolated systems also have remote communities disconnected altogether from the mini-grids with inadequate health, education and leisure services. These communities are precariously supplied by small inefficient diesel gensets that run for a few hours per day. In this article, we propose a sustainable and economic alternative for the electric supply of the remote communities of isolated systems through a combination of photovoltaic solar generation and storage. The objective is to improve access to electricity with savings for the communities. The present paper outlines a public policy to meet this objective.