An edge of a k-connected graph is said to be k-contractible if its contraction yields a k-connected graph. A non-complete k-connected graph possessing no k-contractible edges is called contraction-critical k-connected. Let G be a contraction-critical 7-connected graph with n vertices, and V7 the set of vertices of degree 7 in G. In this paper, we prove that |V7| ≥ n 22 , which improves the resu...

Abstract. The energy of a simple graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of eigenvalues of G. We consider the asymptotic energy per vertex (say asymptotic energy) for lattice systems. In general for a type of lattice in statistical physics , to compute the asymptotic energy with toroidal, cylindrical, Mobius-band, Klein-bottle, and free...

We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all root-key distances or over all root-node distances) in random m-ary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when 3 6 m 6 13 but becomes of higher order when m > 14. Surprisingly, the corresponding asymptotic correl...

It has been known that endothelin-1 (ET-1) exerts important actions in gastrointestinal smooth muscle motility, but its precise mechanism remains unsolved. We investigated the intracellular mechanism of ET-1-induced circular smooth muscle cell contraction in cat esophagus. ET-1 produced contraction of smooth muscle cells isolated by enzymatic digestion. The contraction in response to ET-1 was c...

This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract , syntax-free contraction-weakening proofs; (3) distribution ; (4) axioms p ∨ p. Abstract propositions correspond to objects of the category G(Rel L) where G is the Hyland-Tan double glue-ing construction, Rel is the standar...

This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract , syntax-free contraction-weakening proofs; (3) distribution ; (4) axioms p ∨ p. Abstract propositions correspond to objects of the category G(Rel L) where G is the Hyland-Tan double glue-ing construction, Rel is the standar...

It is well-known that the number of spanning trees, denoted by $\tau(G)$, in a connected multi-graph $G$ can be calculated Matrix-Tree theorem and Tutte's deletion-contraction theorem. In this short note, we find an alternate method to compute $\tau(G)$ degrees vertices.

Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite the Riemannian metric. In infinite-dimensional setting, however, such analysis generally restricted to norm-contracting systems. We develop a generalization of geodesic rates Banach spaces using smoothly-weighted semi-inner product structure on tangent s...