On the mean value of some new sequences

The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of the Smarandache repetitional sequence, and give two asymptotic formulas for it

Zero bias transformation and asymptotic expansions II : the Poisson case

We apply a discrete version of the methodology in \cite{gauss} to obtain a recursive asymptotic expansion for \esp[h(W)] in terms of Poisson expectations, where $W$ is a sum of independent integer-valued random variables and $h$ is a polynomially growing function. We also discuss the remainder estimations

Association Mining in Database Machine

Association rule is wildly used in most of the data mining technologies. Apriori algorithm is the fundamental association rule mining algorithm. FP-growth tree algorithm improves the performance by reduce the generation of the frequent item sets. Simplex algorithm is a advanced FP-growth algorithm by using bitmap structure with the simplex concept in geometry. The bitmap structure implementation is particular designed for storing the data in database machines to support parallel computing the association rule mining

Multiple defaults and contagion risks

We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference default-free filtration in the random measure framework. On each default scenario, the formula can be interpreted as a Radon-Nikodym derivative of random measures. The contagion risks are studied in the multi-defaults setting where we consider the optimal investment problem in a contagion risk model and show that the optimization can be effectuated in a recursive manner with respect to the default-free filtration

Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions

We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also make some relevant conjectures for the admissible constant curvatures in G(m, n) and give some explicit expressions, in particular, for G(2, 4) and G(2, 5).Comment: 14 page