$\mathscr \{R\}$-compact spaces with $\{\text \{\rm weight\}\}X < \{\text \{\rm Exp\}\{\}\textunderscore \{\mathscr \{R\}\} X\}$

THE PRODUCT OF r−k AND ∇δ ON Rm

In the theory of distributions, there is a general lack of definitions for products and powers of distributions. In physics (Gasiorowicz (1967), page 141), one finds the need to evaluate δ2 when calculating the transition rates of certain particle interactions and using some products such as (1/x)·δ. In 1990, Li and Fisher introduced a “computable” delta sequence in an m-dimensional space to ob...

Topological superconductor in quasi-one-dimensional ${\rm Tl}_{2-x}{\rm Mo}_6{\rm Se}_6$

Functional identities of degree 2 in CSL algebras

‎Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$‎, ‎${rm Alg}mathscr{L}$‎ ‎the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$‎. ‎This article is aimed at describing the form of‎ ‎additive mapppi...

Multiplication operators on Banach modules over spectrally separable algebras

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

Text Clustering with String Kernels in R

We present a package which provides a general framework, including tools and algorithms, for text mining in R using the S4 class system. Using this package and the kernlab R package we explore the use of kernel methods for clustering (e.g., kernel k-means and spectral clustering) on a set of text documents, using string kernels. We compare these methods to a more traditional clustering techniqu...