Authors:Pakwan Riyapan, Vichian Laohakosol, and Tuangrat Chaichana
Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered
by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method.
The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded
by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization.
Similar results are also established for continued fractions in the field of formal series over a finite base field.
Authors:Eduardo Ruiz Duarte and Octavio Páez Osuna
We present an efficient endomorphism for the Jacobian of a curve C of genus 2 for divisors having a Non disjoint support. This extends the work of Costello and Lauter in  who calculated explicit formulæ for divisor doubling and addition of divisors with disjoint support in JF(C) using only base field operations. Explicit formulæ is presented for this third case and a different approach for divisor doubling.
The paper is the first to my knowledge to explicitly examine the relationship between an invention's usefulness and the socioculturally oriented relatedness of its features. Generally speaking, a statistically significant inverse U
with a natural number k, a non-negative integer j and a complex variable θ, where Δk(x) is the error term in the divisor problem of Dirichlet and Piltz. The main purpose of this paper is to apply the “elementary
methods” and the “elementary formulas” to derive convergence properties and explicit representations of this integral with
respect to θ for k = 2.