We consider a four-vertex model introduced by Bálint Tóth: a dependent bond percolation model on Z 2 , in which every edge is present with probability 1/2, and each vertex has exactly two incident edges, perpendicular to each other. We prove that all components are finite cycles almost surely, but the expected diameter of the cycle containing the origin is infinite. Moreover, we derive the foll...

For a point T and a circle δ, if two congruent circles of radius r touching at T also touch δ at points different from T , we say T generates circles of radius r with δ, and the two circles are said to be generated by T with δ. If the generated circles are Archimedean, we say T generates Archimedean circles with δ. Frank Power seems to be the earliest discoverer of this kind Archimedean circles...

Mapping axon diameter is of interest for the potential diagnosis and monitoring of various neuronal pathologies. Advanced diffusion-weighted MRI methods have been developed to measure mean axon diameters non-invasively, but suffer major drawbacks that prevent their direct translation into clinical practice, such as complex non-linear data fitting and, more importantly, long scanning times that ...

To determine the skeletal muscle stimulation parameters that are most important in establishing vasodilation in the microvasculature, I tested whether arteriolar diameter during 2 min of repetitive, short-duration, tetanic skeletal muscle contractions increased with changes in stimulus frequency, stimulation train duration, and contraction frequency. To test this, the diameter of transverse art...

BACKGROUND Tumor dimension is an established prognostic factor for metastasis-related death after radiotherapy for uveal melanoma. OBJECTIVE To compare various methods of modeling the relationship between tumor dimension and metastatic death. PATIENTS AND METHODS The analyses were based on a consecutive series of 1204 patients with primary choroidal melanoma treated with proton beam irradia...

The Density Functional Theory (DFT) and the Natural Bond Orbital (NBO) calculations basedmethod B3LYP/6-31G* were carried out to study the interaction of carbon nanotube (8,0) withnitrobenzene in two situations perpendicular and parallel. Formation energies of compounds,charges, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular'orbital (LUMO) and the HOMO-LUMO ba...

The purpose of this study was to investigate the effect of dose perturbations for two metallic spinal screw implants in proton beam therapy in the perpendicular and parallel beam geometry. A 5.5 mm (diameter) by 45 mm (length) stainless steel (SS) screw and a 5.5 mm by 35 mm titanium (Ti) screw commonly used for spinal fixation were CT-scanned in a hybrid phantom of water and solid water. The C...

The manufacturing of single wall carbon nanotubes (SWNTs) results in mixtures that are polydisperse with respect to both size and chirality, the latter of which strongly affects the tube electronic properties. For nanotubes to achieve their full potential in applications, it is desirable to be able to separate them according to both of these physical characteristics. Field-flow fractionation (F...

A self-built laser projection system for optical transverse strain measurements in tensile testing is presented. The setup based on diode modules, charge-coupled device array detectors, and standard optomechanical components proposed to be a low-cost polymer samples. mobile can easily mounted test machine. Circular cross-sectional changes diameter were detected with 10-μm resolution stress-stra...