Characterizing slopes for torus knots

A slope $\frac pq$ is called a characterizing slope for a given knot $K_0$ in $S^3$ if whenever the $\frac pq$-surgery on a knot $K$ in $S^3$ is homeomorphic to the $\frac pq$-surgery on $K_0$ via an orientation preserving homeomorphism, then $K=K_0$. In this paper we try to find characterizing slopes for torus knots $T_{r,s}$. We show that any slope $\frac pq$ which is larger than the number $\frac{30(r^2-1)(s^2-1)}{67}$ is a characterizing slope for $T_{r,s}$. The proof uses Heegaard Floer homology and Agol--Lackenby's 6--Theorem. In the case of $T_{5,2}$, we obtain more specific information about its set of characterizing slopes by applying more Heegaard Floer homology techniques.Comment: Version 2: 19 pages. This is a major revision. The title of the first version was "Towards a Dehn surgery characterization of $T_{5,2}$". We extended the result in the first version to general torus knots. We also fixed a gap in the first version, so our result for $T_{5,2}$ is slightly weaker than the originally claimed on

Dehn surgery on knots in S3S^3 producing Nil Seifert fibred spaces

We prove that there are exactly $6$ Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in $S^3$, with $\{60, 144, 156, 288, 300\}$ as the exact set of all such surgery slopes up to taking the mirror images of the knots. We conjecture that there are exactly $4$ specific hyperbolic knots in $S^3$ which admit Nil Seifert fibred surgery. We also give some more general results and a more general conjecture concerning Seifert fibred surgeries on hyperbolic knots in $S^3$.Comment: 11 page

Sustainable Energy Crop Production: A Case Study for Sugarcane and Cassava Production in Yunnan, China

The possibility of using biomass as a source of energy in reducing the greenhouse-effect imposed by carbon dioxide emission and relieving energy crisis is a matter of great interest, such as bioethanol production. Nevertheless, the cultivation of dedicated energy crops dose meet with some criticisms (conflict with food security and environmental degradation, for example). Nowadays sugarcane and cassava are regarded as the potential energy crops for bioethanol production. Endowed with natural resources and favorable weather condition, Yunnan province, China, is the major sugarcane and cassava production area in China. This paper presents production structures of these two crops in Yunnan and compares the sustainable production between the usages of sugarcane and cassava as bioethanol feedstock. Firstly, we estimated the technical efficiency for sugarcane and cassava production by adopting the production function and stochastic frontier production function. Field surveys from 61 sugarcane farmers and 50 cassava farmers were collected in June and September, 2008. Secondly, the sustainability of each crop production was evaluated. Since there is no generally accepted definition of sustainable production, a set of criteria was defined including 2 concerns (employment and food supply) from socio-economic area and 3 concerns (conversion rate to ethanol, water requirement, and fertilizer pollution) from environmental area. Empirical results demonstrated that the average production function was located below the frontier production function, 5% for sugarcane production and 7% for cassava production. These findings reflect the existence of technical inefficiency not only in the sugarcane production but also in the cassava production as well. But after considering sustainable production, cassava, which requires low agro-chemical, should be recommended as a prior energy crop in Yunnan with higher rates in ethanol conversion and dry matter.International Development, Production Economics, Energy crop, stochastic frontier production, Sustainable production, Yunnan province, Bioethanol,

An intelligent genetic algorithm for PAPR reduction in a multi-carrier CDMA wireless system

Abstract— A novel intelligent genetic algorithm (GA), called Minimum Distance guided GA (MDGA) is proposed for peak-average-power ratio (PAPR) reduction based on partial transmit sequence (PTS) scheme in a synchronous Multi-Carrier Code Division Multiple Access (MC-CDMA) system. In contrast to traditional GA, our MDGA starts with a balanced ratio of exploration and exploitation which is maintained throughout the process. It introduces a novel replacement strategy which increases significantly the convergence rate and reduce dramatically computational complexity as compared to the conventional GA. The simulation results demonstrate that, if compared to the PAPR reduction schemes using exhaustive search and traditional GA, our scheme achieves 99.52% and 50+% reduction in computational complexity respectively