The vertex-reinforced jump process (VRJP) is a form of self-interacting random walk in which the walker biased towards returning to previously visited vertices with bias depending linearly on local time at these vertices. We prove that, for any initial bias, weights sampled from magic formula two-dimensional graph decay least power-law rate. Via arguments Sabot and Zeng, result implies that VRJ...

It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class quantum models in which these plus the underlying physical Hilbert-space metric $\Theta$ are all represented terms auxiliary operator $(N+1)-$plet $Z_k$, $k=0,1,\ldots,N$. Our formalism degenerates to ${\...

Objective(s): Normoxic MAGIC-f polymer gels are established dosimeters used for three dimensional dose quantifications in radiotherapy. Nanoparticles with high atomic number such as gold are novel radiosensitizers used to enhance doses delivered to tumors. The aim of this study was to investigate the effect of gold nanoparticles (GNPs) in enhancing percentage depth doses (PDDs) within the MAGIC...

Introduction: Normoxic MAGIC-f polymer gels are established dosimeters used for three dimensional dos uantifications in radiotherapy. The high atomic number nanoparticles such as gold are nov adiosensitizers used to enhance doses delivered to tumors. The aim of this study was t vestigate the effect of gold nanoparticles (GNPs) in enhancing percentage depth doses (PDD ithin the...

This paper introduces a technique that relates the coefficients of the Magic Formula tire model to the physical properties of the tire. For this purpose, the tire model is developed by ABAQUS commercial software. The output of this model for the lateral tire force is validated by available tire information and then used to identify the tire force properties. The Magic Formula coefficients are o...

Abstract Let $\varphi _1,\ldots ,\varphi _r\in {\mathbb Z}[z_1,\ldots z_k]$ be integral linear combinations of elementary symmetric polynomials with $\text {deg}(\varphi _j)=k_j\ (1\le j\le r)$ , where $1\le k_1<k_2<\cdots <k_r=k$ . Subject to the condition $k_1+\cdots +k_r\ge \tfrac {1}{2}k(k-~1)+2$ we show that there is a paucity nondiagonal solutions Diophantine system _j({\mathbf x...

The MAGIC-I telescope is the largest single-dish Imaging Atmospheric Cherenkov telescope in the world. A second telescope, MAGIC-II, will operate in coincidence with MAGIC-I in stereoscopic mode. MAGIC-II is a clone of MAGIC-I, but with a number of significant improvements, namely a highly pixelized camera with a wider trigger area, improved optical analog signal transmission and a 2-4 GSps fas...