arXiv subjects
Publications and source records attributed to Jinshan Zhang.
These notes are dedicated to whom may be interested in algorithms, Markov chain, coupling, and graph theory etc. I present some preliminaries on coupling and explanations of the important formulas or phrases, which may be helpful for us to understand D. Weitz's paper "Combinatorial Criteria for Uniqueness of Gibbs Measures" with ease.
An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is established first in this paper, which is tighter than the famous Minc's bound and the Br$\acute{e}$gman's bound. A transformation on graphs is proposed, so that counting the number of Hamiltonian cycles of an undirected graph can be done by counting the number of Hamiltonian cycles of its corresponding symmetric directed graph. In this way, an upper bound for the number of Hamiltonian cycles of undirected graphs is also obtained.
Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to approximate the permanent, which just yields a critical ratio O($nω(n)$) for almost all the 0-1 matrices, provided it's a simple promising practical way to compute this #P-complete problem. In this paper, the performance of this method will be shown when it's applied to compute all the matchings based on that transformation. The critical ratio will be proved to be very large with a certain probability, owning an increasing factor larger than any polynomial of $n$ even in the sense for almost all the 0-1 matrices. Hence, RM fails to work well when counting all the matchings via computing the permanent of the matrix. In other words, we must carefully utilize the known methods of estimating the permanent to count all the matchings through that transformation.
This paper mainly discusses the American option's hedging strategies via binomialmodel and the basic idea of pricing and hedging American option. Although the essential scheme of hedging is almost the same as European option, small differences may arise when simulating the process for American option holder has more rights, spelling that the option can be exercised at anytime before its maturity. Our method is dynamic-hedging method.
Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to approximate the permanent, which just yields a critical ratio O($nω(n)$) for almost all the 0-1 matrices, provided it's a simple promising practical way to compute this #P-complete problem. In this paper, the performance of this method will be shown when it's applied to compute all the matchings based on that transformation. The critical ratio will be proved to be very large with a certain probability, owning an increasing factor larger than any polynomial of $n$ even in the sense for almost all the 0-1 matrices. Hence, RM fails to work well when counting all the matchings via computing the permanent of the matrix. In other words, we must carefully utilize the known methods of estimating the permanent to count all the matchings through that transformation.
We provide evidence for a finite temperature ferromagnetic transition in 2-dimensions as $H \to 0$ in thin films of $^3$He on graphite, a model system for the study of two-dimensional magnetism. We perform pulsed and CW NMR experiments at fields of 0.03 - 0.48 mT on $^3$He at areal densities of 20.5 - 24.2 atoms/nm$^2$. At these densities, the second layer of $^3$He has a strongly ferromagnetic tendency. With decreasing temperature, we find a rapid onset of magnetization that becomes independent of the applied field at temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR linewidth grow rapidly as well, which is consistent with a large (order unity) polarization of the $^3$He spins.