Zeros Distribution of the Jones Polynomial for Pretzel Links

In this paper, we deal with basic properties of some pretzel links and properties of the Jones polynomials of some pretzel links. By using these properties, the zero distribution of pretzel links is studied. We discuss the properties of the Jones polynomial of non-tame pretzel links and give that zeros of the Jones polynomial of these pretzel links are distributed on the planar curves.

Influence of replacement of wheat flour by rice flour on rheo-structural changes, in vitro starch digestibility and consumer acceptability of low-gluten pretzels

This study aimed to access the influence of rice flour incorporation on various quality attributes of low-gluten wheat-based pretzels viz., functional, rheological, starch digestibility, color, textural and sensorial properties. Significant increase in swelling power (18.33 ± 0.51) and bulk density (0.58 ± 0.04) was observed in flour blend upon incorporation of rice flour, whereas, significant decrease in oil absorption capacity (0.62 ± 0.09), solubility index (6.72 ± 0.17), foaming capacity (9.67 ± 0.34), and foaming stability (3.39 ± 0.15) was recorded. Pasting properties of samples were studied using a Rapid Visco Analyser which indicated that all the pasting properties increased with an increase in rice flour incorporation. Fourier transform infrared spectroscopic studies revealed no difference in the basic functional groups of flour blend upon the incorporation of rice flour, however, it had a pronounced effect on elastic modulus (G′) of flour blend. In vitro starch digestion characteristics revealed 7.23% surge in slowly digestible starch and 13.36% reduction in rapidly digestible starch of developed low-gluten pretzels upon the incorporation of rice flour. Apparent amylose content (27.3 ± 1.45) and resistant starch content (6.12 ± 0.97) increased and starch digestibility index (69.87 ± 1.72) decreased in developed low-gluten pretzels. In conclusion, the developed low-gluten pretzels had significantly (p < 0.05) higher mineral profile and lightness (L*) and lower breaking strength in addition to having better overall acceptability. This study indicated that substituting wheat flour with rice flour up to a level of 35% affected the quality attributes of developed low-gluten pretzels.

Incompressible Pairwise Incompressible Surfaces in Knot Exteriors

We discuss the properties of incompressible pairwise incompressible surfaces in a knot complement by using twist crossing number. Let K be a pretzel knot or rational knot that its twistindex is less than 6, and let F be an incompressible pairwise incompressible surface in S 3-K. Then F is a punctured sphere.

纽结补中曲面的分段不可压缩性(英文)

讨论了纽结补中的不可压缩、分段不可压缩曲面的性质.设K是S3中素的几乎交错纽结,F是S3-K中的不可压缩、分段不可压缩曲面,那么在F∩S2±中一定存在S2型和PS3型环路.通过研究F∩S2±中的环路性质,证明了对于固定的边界分之数,曲面类是有限(在同痕意义下),同时也证明了如果纽结K是两个排叉结的连通和,则曲面F是穿孔球面.

某些链环琼斯多项式的零点性质

主要研究某一类排叉链环的琼斯多项式零点的性质与分布.利用纽结与链环琼斯多项式的表达形式以及一些性质,结合三角函数有关知识,将前人推断的某些可能为琼斯多项式零点的单位根代入纽结或链环的琼斯多项式当中逐一进行证明,发现其并不为琼斯多项式的零点,并进行归纳总结,得到一类排叉纽结与一类排叉链环零点的性质.首先,给出本论文需要的一些理论知识.包括纽结、链环的基本概念,亚历山大多项式、琼斯多项式的定义,拧数和区域的划分等一些基本概念,给出了排叉纽结与二桥链环的性质.其次,利用某些纽结或链环琼斯多项式的表达形式,结合三角函数的相关知识证明某些单位根一定不是一类排叉纽结或一类排叉链环的琼斯多项式的零点.

Measures of Asymmetry Dual to Mean Minkowski Measures of Asymmetry for Convex Bodies

Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots P（-n,-m, m）. The computations reveal that the rank of the homology of pretzel knots is an invariant of n. The proof is based on a ＂shortcut＂ and two lemmas that recursively reduce the computational complexity of Khovanov type homology.

排叉结琼斯多项式根的分布

首先根据排叉结p(c)1,c2,c3的琼斯多项式计算给出排叉结p(k,k,l)的琼斯多项式,然后令k固定,l→∞,得到排叉结p(k,k,l)的零点分布.

基于自适应中值滤波的图像去噪技术研究

中值滤波和自适应中值滤波被广泛地应用于消除图像的椒盐噪声。传统中值滤波算法无法根据图像噪声浓度改变窗口尺寸,并且噪声浓度过高时,中值滤波算法基本失效。自适应中值滤波算法可以根据椒盐噪声浓度大小对窗口尺寸进行改变,在高浓度噪声干扰下仍然具有较好的去噪效果。针对椒盐噪声,对中值滤波算法和自适应中值滤波算法去噪结果进行比较。通过仿真实验对图像添加不同浓度的椒盐噪声,并分别使用中值滤波算法和自适应中值滤波算法进行噪声去除,实验结果表明,在去除椒盐噪声方面,自适应中值滤波克服窗口尺寸局限性后,比中值滤波具有更好地去噪效果,能很好地保留图像细节,且它的信噪比、峰值信噪比数值最大,均方误差的值最小。

排叉链环的多边形表示

本文通过整数缠绕的棒表示与排叉链环对应的整数缠绕连通和分解,给出排叉链环的一类多边形表示,对排叉链环的棍棒数进行估计.

Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity

We study properties of graded maximal Cohen-Macaulay modules over an N-graded locally finite,Auslander Gorenstein,and Cohen-Macaulay algebra of dimension two.As a consequence,we extend a part of the McKay correspondence in dimension two to a more general setting.