A central tenet of the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000) has been that all students can succeed in complex mathematics. This tenet is commonly referred to as the equity principle, and while it is acknowledged that students do not need to be treated in the same way, the NCTM Standards and other influential policy documents (e.g., Measuring What Counts, Nat...

Knowledge bases are useful resources for many natural language processing tasks, however, they are far from complete. In this paper, we define a novel entity representation as a mixture of its neighborhood in the knowledge base and apply this technique on TransE—a well-known embedding model for knowledge base completion. Experimental results show that the neighborhood information significantly ...

a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...

AGM-style revision operators are defined for several systems of classical modal logic. · · · draft of November 28, 2009 · · · Within AGM, consistency maintenance is done by classical logic. But the reliance on classical consistency presents a problem for exporting AGM revision to non-classical logics in general, and to modal logic in particular. A general technique for solving this problem is t...

We show that searching the k-change neighborhood is W[1]-hard for metric TSP, which means that finding the best tour in the k-change neighborhood essentially requires complete search (modulo some complexitytheoretic assumptions).

Here we present an overview of countably-normed spaces. In particular, we discuss the main topologies—weak, strong, and inductive—placed on the dual of a countably-normed space and discuss the σ-fields generated by these topologies. The purpose in mind is to provide the background material for many of the results used is White Noise Analysis. 1. Topological Vector Spaces In the introduction we ...

Here we present an overview of countably-normed spaces. We discuss the main topologies—weak, strong, and inductive—placed on the dual of a countably-normed space and discuss the σ–fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the σ–fields generated by the weak, strong, and inductive topologies are equa...

Here we present an overview of countably-normed spaces. We discuss the main topologies—weak, strong, and inductive—placed on the dual of a countably-normed space and discuss the σ–fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the σ–fields generated by the weak, strong, and inductive topologies are equa...

§0. The Gauss-Manin Connection. Let p > 2 be a prime and N ≥ 4. The p-adic modular curve X1(Np) will be denoted X. We let X = W0 ∪W∞ denote the usual decomposition of X as the union of two wide open sets. Hence Wi (i = 0 or ∞) is a wide open neighborhood of the ordinary component Zi containing the cusp i (= 0 or ∞) and the intersection W = W∞ ∩ W0 is the union the supersingular annuli. We have ...