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.

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.

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.

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.

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.