The Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights (d(u)d(v))− 1 2 over all edges e = uv ofG. We prove that R(G) ≥ d(G)/2, where d(G) is the diameter of G. This immediately implies that R(G) ≥ r(G)/2, which is the closest result to the well-known Grafiti conjecture R(G) ≥ r(G) − 1 of Fajtlowicz [4], where r(G) is the radius of G. Asymptotically, our res...

in this paper we discuss about tenacity and its properties in stability calculation. we indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. we also give good lower and upper bounds for tenacity.

The right and left hand Motor Imagery (MI) analysis based on the electroencephalogram (EEG) signal can directly link the central nervous system to a computer or a device. This study aims to identify a set of robust and nonlinear effective brain connectivity features quantified by transfer entropy (TE) to characterize the relationship between brain regions from EEG signals and create a hierarchi...

Fracture network is a crucial element to address in any model of the thermo-hydro-mechanical behaviour reservoir rock. This study aims provide quantified datasets and further understanding critical parameters fracture pattern crystalline rocks. In Northern Upper Rhine Graben, such rock units are targeted for multiple energy applications, from deep geothermal heat extraction storage. Eleven outc...

A giant strike-slip fault-controlled Fuman Oilfield has been found in the Ordovician fractured carbonates of Tarim Basin. However, conventional seismic methods are hardly able to distinguish reservoir and its connectivity ultra-depth (>7000 m) carbonate fault zones. We propose thin-likelihood tensor-thickness process describe fracture network large cave reservoir, respectively. Together with...

this report presents a 3.5-year-old boy who was hospitalized for limping. medical history and physical exams were not suggestive for any definitive diagnosis. laboratory and radiographic exams did not support any specific diagnosis either. subsequently bone scan was performed and increased activity in the ankle due to cuboid fracture was incidentally observed.

Postmenopausal women with vertebral fractures have abnormal bone microarchitecture at the distal radius and tibia by HR-pQCT, independent of areal BMD. However, whether trabecular plate and rod microarchitecture is altered in women with vertebral fractures is unknown. This study aims to characterize the abnormalities of trabecular plate and rod microarchitecture, cortex, and bone stiffness in p...

A major issue to overcome when characterizing a deep fractured reservoir is that of data limitation due to accessibility and affordability. Moreover, the ability to map discontinuities in the rock with available geological and geophysical tools tends to decrease particularly as the scale of the discontinuity goes down. Geological characterization data include, but not limited to, measurements o...

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

conclusions the causes leading to fracture of the humerus during the act of a throw are discussed and the management strategies utilized. introduction five patients presented to the emergency department of a tertiary referral teaching hospital with atraumatic fractures of their humerus sustained during a recreational dodgeball tournament. case presentation the patients were young healthy indivi...