If g is an integer ≥ 2, and M is a closed simple 3-manifold such that π1(M) has a subgroup isomorphic to a genus-g surface group and dimZ2 H1(M ;Z2) ≥ max(3g−1, 6), we show that M contains a closed, incompressible surface of genus at most g. As an application we show that if M is a closed orientable hyperbolic 3-manifold such that VolM ≤ 3.08, then dimZ2 H1(M ;Z2) ≤ 5.

The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...

We give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G = SU(2, n) has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = KA + K of G, and then carry out an approximate calculation of (KHK) ∩ A + for each closed, connected subgroup H of G. This generalizes the work of H. Oh and D. Wi...

The distributions of Cu, Zn, and Pb concentrations in the selected soft tissues (foot, cephalic tentacle, mantle, muscle, gill, digestive caecum, and remaining soft tissues) and shells of the mud-flat snail Telescopium telescopium were determined in snails from eight geographical sites in the south-western intertidal area of Peninsular Malaysia. Generally, the digestive caecum compared with oth...

conclusions closed reduction and hybrid external fixation can be used as a definitive treatment for severe comminuted fractures of the distal femur and proximal tibia, when the concomitant contusion of the skin and soft tissue damage prohibits safe open reduction and internal fixation. patients and methods in a prospective study, 44 patients with comminuted fractures of the distal femur or prox...

In this paper, we studied and introduce a new class of fuzzy sets called fuzzy strongly g *super closed sets is introduced and explore some of its characterization.

The aim of this paper is to introduce a new class of sets called (i,j) r^g closed sets and a new class of maps called D^(i,j) continuous maps and D^(i,j)irresolute maps in bitopological spaces. Also we introduce some new spaces called (i,j) – T^1/2 , (i,j) ^T 1/2 ,*T^1/2, ^T*1/2 and ^Trg and obtain their basic properties. Mathematics Subject Classification: 54A10

An epizootic of beta-hemolytic Lancefield group G streptococcal infections occurred in a specific-pathogen-free colony of laboratory cats. A total of 19 out of 68 animals in a single building were affected over a 10-day period. Clinical signs included fever, depression, lymphadenopathy, pharyngitis, and submandibular edema. The organism was recovered from the pharynx in two of five clinically n...