Amenability, Tubularity, and Embeddings into R

Amenability, Tubularity, and Embeddings into R Ω

Amenability, Locally Finite Spaces, and Bi-lipschitz Embeddings

We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally finite space. Therefore, we start making a comparison between this property and other notions of amenability for locally finite metric spaces that have been...

Amenability and Weak Amenability of Triangular Banach Algebras

Labeling Subgraph Embeddings and Cordiality of Graphs

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

Anatomic Pathology / REFINED MORPHOLOGIC CRITERIA FOR TUBULAR CARCINOMA

We studied outcomes of 147 patients with stage I/II grade 1 (32 pure tubular, 115 ductal) carcinoma treated with breast-conserving therapy to evaluate the prognostic usefulness of standard and recently proposed revised criteria for tubular (tubularity percentage [proportion of neoplastic cells adjacent to open lumens], nuclear grade, and mitoses) and ductal carcinoma. Carcinomas with less than ...