A quadrilateral cylinder of length m and breadth n is the Cartesian product of a m-cycle(with m vertices) and a n-path(with n vertices). Write the vertices of the two cycles on the boundary of the quadrilateral cylinder as x1, x2, · · · , xm and y1, y2, · · · , ym, respectively, where xi corresponds to yi(i = 1, 2, . . . , m). We denote by Qm,n,r, the graph obtained from quadrilateral cylinder ...

In this note we will construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f : R → R with Cantor intermediate value property which is not almost continuous. This gives a partial answer to a question of D. Banaszewski [2]. (See also [12, Question 5.5].) We will also show that every extendable function g : R → ...

For an element $r$ of a ring $R$, Diophantine $D(r)$ $m$-tuple is $(a_1,a_2,\ldots,a_m)$ elements $R$ such that for all $i,j$ with $i\neq j$, $a_ia_j+r$ perfect square in $R$. In this article, we compute and estimate the measures sets $m$-tuples $\mathbb{Z}_p$ $p$-adic integers, as well its residue field $\mathbb{F}_p$.

Let R be a perfect Fp-algebra, equipped with the trivial norm. Let W (R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norms. We prove that via the Teichmüller map, the nonarchimedean analytic space (in the sense of Berkovich) associated to R is a (strong) deformation retract of the space associated to W (R).

Secret sharing is that a dealer distributes a piece of information (called a share) about a secret to each participant such that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. If any unauthorized subset of participants can not obtain any more information regarding the secret, then the scheme is called perfect. ...

Let P be a class of graphs. A P-set in a graph G is a vertex subset X such that G(X) ∈ P . We define the P-stability number of a graph G, αP(G), as the maximum cardinality of a P-set in G. AP-dominating set in a graph is a dominatingP-set. Accordingly, the P-domination number of a graph G, γP(G), is the minimum cardinality of a P-dominating set in G. For each r ≥ 1, we define a graph G to be an...

The aim of this study was to assess interobserver agreement of ultrasound parameters for portal hypertension in hepatosplenic mansonic schistosomiasis. Spleen size, diameter of the portal, splenic and superior mesenteric veins and presence of thrombosis and cavernous transformation were determined by three radiologists in blinded and independent fashion in 30 patients. Interobserver agreement w...

The upper chromatic number χ(H) of a hypergraph H is the maximum number of colors in a coloring avoiding a polychromatic edge. The stability number α(H) of a hypergraph H is the cardinality of the largest set of vertices of H which does not contain an edge. A hypergraph is k-uniform if the sizes of all its edges are k. A hypergraph H is co-perfect if χ(H ′) = α(H ′) for each induced subhypergra...

Certain subgraphs of a given graph G restrict the minimum number χ(G) of colors that can be assigned to the vertices of G such that the endpoints of all edges receive distinct colors. Some of such subgraphs are related to the celebrated Strong Perfect Graph Theorem, as it implies that every graph G contains a clique of size χ(G), or an odd hole or an odd anti-hole as an induced subgraph. In thi...

We present a simple and e cient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738 761, 1994). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of th...