Some general new Einstein Walker manifolds

In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of one-dimensional Lie subalgebras and investigate some of its group invariant solutions.Comment: 14 page

Counting and Computing by ee

In this paper we count the number of paths and cycles in complete graphs by using the number $e$. Also, we compute the number of derangements in same way. Connection by $e$ yields some nice formulas for the number of derangements, such as $D_n=\lfloor\frac{n!+1}{e}\rfloor$ and $D_n=\lfloor(e+e^{-1})n!\rfloor-\lfloor en!\rfloor$, and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; these connections are hidden in the heart of a nice polynomial that we call it derangement function and a simple ordinary differential equation concerning it.Comment: 12 pages, no figure, review of my works about the number of derangement

A universal coefficient theorem for twisted K-theory

In this paper, we recall the definition of twisted K-theory in various settings. We prove that for a twist $\tau$ corresponding to a three dimensional integral cohomology class of a space X, there exist a "universal coefficient" isomorphism K_{*}^{\tau}(X)\cong K_{*}(P_{\tau})\otimes_{K_{*}(\mathbb{C}P^{\infty})} \hat{K}_{*} where $P_\tau$ is the total space of the principal $\mathbb{C}P^{\infty}$-bundle induced over X by $\tau$ and $\hat K_*$ is obtained form the action of $\mathbb{C}P^{\infty}$ on K-theory