The spectral radius of a graph is the largest eigenvalue of the adjacency matrix of the graph. Let T (n,∆, l) be the tree which minimizes the spectral radius of all trees of order n with exactly l vertices of maximum degree ∆. In this paper, T (n,∆, l) is determined for ∆ = 3, and for l ≤ 3 and n large enough. It is proven that for sufficiently large n, T (n, 3, l) is a caterpillar with (almost...

Dumbbell-shaped spinal extradural cavernous hemangioma is rare. The differential diagnosis of dumbbell-shaped spinal tumors based on magnetic resonance imaging includes schwannoma and lymphoma. Here, we report a dumbbell-shaped spinal extradural cavernous hemangioma with intrathoracic growth on T2-3 in a 64-year-old man complaining of right side infrascapular area back pain with no neurologic d...

We report on the efficient biochemical synthesis of a large DNA dumbbell starting from a pair of short DNA hairpins with long single-stranded tails of arbitrary sequence. The DNA dumbbell is obtained by enzymatic ligation yielding a 94-bp duplex stem closed at both termini by single-stranded loops of 5 nt. Following ligation, all unligated precursors and monoligated by-products were multiply bi...

Monodispersed dumbbell-like Au-Fe3O4 nanoparticles (NPs) were synthesized and studied for use in supercapacitors. These dumbbell NPs show Au/Fe3O4-size dependent capacitive behaviors and the 7-14 nm Au-Fe3O4 NPs have the best specific capacitance of 464 F g(-1) at 1 A g(-1) and capacity retention of 86.4% after 1000 cycles, much larger than pure Fe3O4 NPs (160 F g(-1) and 72.8% retention). This...

Primary spinal non-Hodgkin's lymphoma is extremely rare, and the occurrence of spinal dumbbell-shaped lymphoma is exceptional. We present a case of primary spinal dumbbell-shaped lymphoma to clarify the diagnosis and the management of these lesions. A 45-year-old man presented with sensory symptoms for 8 months. Magnetic resonance imaging of the thoracic spine demonstrated a dumbbell-shaped les...

Uniform dumbbell-like ZnO microcrystals had been successfully fabricated on a large scale via a facile solution technique under mild conditions. Obtained ZnO, with length of 1.2 to 1.6 μm and diameters of 350 to 600 nm, exhibited well-defined dumbbell-like morphology and hexagonal wurtzite structure and grew along the [001] direction. Effects of the reactant concentration on the sizes and morph...

We studied the behavior of a dumbbell bouncing upon a sinusoidally vibrating plate. By introducing chiral asymmetry to the geometry of the dumbbell, we observed a cascade of bifurcations with an increase in the vibration amplitude: spinning, orbital, and rolling. In contrast, for an achiral dumbbell, bifurcation is generated by a change from random motion to vectorial inchworm motion. A simple ...

We present theoretical results on the deterministic and stochastic motion of a dumbbell carried by a uniform flow through a three-dimensional spatially periodic potential. Depending on parameters like the flow velocity, there are two different kinds of movement: transport along a potential valley and a stair-like motion oblique to the potential trenches. The crossover between these two regimes,...

We present a numerical investigation of the Brownian motion and diffusion of a dumbbell in a two-dimensional periodic potential. Its dynamics is described by a Langevin model including the hydrodynamic interaction. With increasing values of the amplitude of the potential we find along the modulated spatial directions a reduction of the diffusion constant and of the impact of the hydrodynamic in...

In this note we consider an example to test three lower bounds presented in Diaconis– Stroock [4] (one by Diaconis and Stroock (DS), another by Sinclair (S) [9], and the third by Jerrum–Sinclair (JS) [8]) of the first positive eigenvalue of a finite graph. The lower bounds are quite sharp in many of the examples studied in [4], and seem to measure the bottlenecks or complexity of the graphs stu...