We prove that, if M is a weakly 4-connected matroid with |E(M)| 7 and neither M nor M∗ is isomorphic to the cycle matroid of a ladder, then M has a proper minor M ′ such that M ′ is weakly 4-connected and |E(M ′)| |E(M)| − 2 unless M is some 12-element matroid with a special structure. © 2007 Elsevier Inc. All rights reserved.

Let G be a simple connected graph and t be a given real number. The zero-order general Randić index αt(G) of G is defined as ∑ v∈V (G) d(v) t , where d(v) denotes the degree of v. In this paper, for any t , we characterize the graphs with the greatest and the smallest αt within two subclasses of connected unicyclic graphs on n vertices, namely, unicyclic graphs with k pendant vertices and unicy...

The Randić index R(G) of a graph G is defined as the sum of 1 √dudv over all edges uv of G, where du and dv are the degrees of vertices u and v, respectively. Let D(G) be the diameter of Gwhen G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path Pn achieves the minimum values for both R(G)/D(G) and R(G) − D(G). We prove this conjecture...

A graph G is weakly 4-connected if it is 3-connected, has at least five vertices, and for every pair (A,B) such that A ∪ B = V (G), |A ∩ B| = 3 and no edge has one end in A − B and the other in B − A, one of the induced subgraphs G[A], G[B] has at most four edges. We describe a set of constructions that starting from a weakly 4-connected planar graph G produce a finite list of non-planar weakly...

Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G \ v. Denote the algebraic connectivities of G and G \ v by α(G) and α(G \ v), respectively. In this paper, we consider the functions φ(v) = α(G) − α(G \ v) and κ(v) = α(G\v) α(G) , provide attainable upper and lower bounds on both functions, and characterise the equality ...

Background: Osteoporosis is a common condition among the elderly population, and is associated with an increased risk of fracture. One of the most common fragility fractures involve the distal radius, and are associated with risk of subsequent fragility fracture. Early treatment with bisphosphonates has been suggested to decrease the population hip fracture burden. However, there have been no p...

Natural fractures are regarded as important reservoir spaces and effective seepage channels at metamorphic buried hills. Continuous networks associated with multi-scale good connectivity is critical for high-quality reservoirs well high stable production in the tight rocks. The Bozhong 19–6 hills were characterized through integrating image logs, cores, thin-sections, scanning electron microsco...

Introduction: Mental arithmetic analysis based on Electroencephalogram (EEG) signal for monitoring the state of the user’s brain functioning can be helpful for understanding some psychological disorders such as attention deficit hyperactivity disorder, autism spectrum disorder, or dyscalculia where the difficulty in learning or understanding the arithmetic exists. Most mental arithmetic recogni...

Introduction: Medial temporal sclerosis (MTS) is a form of mesial temporal lobe epilepsy (mTLE). It is typically characterized by structural alterations in hippocampus (HC) and related mesial temporal lobe (MTL) network. Resting state functional connectivity (RSFC) is considered an ideal technique in quantifying the dysfunction and maladaptation in MTL network. It is well- dem...

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...