Signature functions of knots

The signature function of a knot is an integer-valued step function on the unit circle in the complex plane. Necessary and sufficient conditions for a function to be the signature function of a knot are presented.Comment: 4 page

Comparative analysis of the <i>in-vitro</i> antioxidant activity and bioactive compounds of flaxseed in China according to variety and geographical origin

<p>The present study aimed to use a chemometric study to compare the <i>in-vitro</i> antioxidant activities and bioactive compounds of flaxseed based on the variety and geographical origins, and further explore the specific components constructed the endogenous antioxidant system of flaxseed in China. The differential contents of α-linolenic acid (35.83–58.91%), lignans (11.37–33.31 mg/g), total phenolic acids (109.93–246.88 mg/100 g) and phytosterols (56.52–125.12 mg/g) of 32 flaxseed varieties were observed. Concomitantly, the <i>in-vitro</i> antioxidant activities varied from 32.56 to 46.22 mg TE/100 g, 0.58 to 1.08 mg TE/g, and 14.22 to 36.14 mmol TE/g as determined by the 2,2’-diphenyl-1-picrylhydrazyl radical (DPPH), ferric reducing antioxidant power (FRAP) and 2,2′-azinobis-(3-ethylbenzthiazoline 6-sulfonic acid) (ABTS) assays, respectively. Significant correlations were found between the antioxidant activities and contents of free syringic acid, <i>p</i>-coumaric acid glucoside and secoisolariciresinol diglucoside (SDG) (<i>p </i>< 0.01). Principal component analysis showed a relatively dispersed distribution between samples, which was not effective enough to determine the geographical origins of the flaxseed samples. Hierarchical cluster analysis allowed flaxseed samples to be grouped based on their <i>in-vitro</i> antioxidant activities and bioactive component contents, primarily in relation to variety specificity.</p

Changes in laccase activity during liquid fermentation by <i>Trametes</i> sp.48424.

<p>Changes in laccase activity during liquid fermentation by <i>Trametes</i> sp.48424.</p

Effect of different strains on the concentration of sinapine during liquid fermentation.

<p>Effect of different strains on the concentration of sinapine during liquid fermentation.</p

Effect of different strains on the concentration of sinapine during solid-state fermentation (samples analyzed directly and transformed as dry samples).

<p>Effect of different strains on the concentration of sinapine during solid-state fermentation (samples analyzed directly and transformed as dry samples).</p

Effect of drying and moisture on the concentration of sinapine in high moisture rapeseed meals (HRM90, high moisture rapeseed meal dried at 90°C; HRM105, high moisture rapeseed meal dried at 105°C).

<p>Effect of drying and moisture on the concentration of sinapine in high moisture rapeseed meals (HRM90, high moisture rapeseed meal dried at 90°C; HRM105, high moisture rapeseed meal dried at 105°C).</p

Effect of drying on the concentration of sinapine in rapeseed meal (HRM90, high moisture rapeseed meal dried at 90°C; HRM105, high moisture rapeseed meal dried at 105°C; LRM90, original rapeseed meal dried at 90°C; LRM105, original rapeseed meal dried at 105°C).

<p>Effect of drying on the concentration of sinapine in rapeseed meal (HRM90, high moisture rapeseed meal dried at 90°C; HRM105, high moisture rapeseed meal dried at 105°C; LRM90, original rapeseed meal dried at 90°C; LRM105, original rapeseed meal dried at 105°C).</p

Cellulose-Based Composite Macrogels from Cellulose Fiber and Cellulose Nanofiber as Intestine Delivery Vehicles for Probiotics

Cellulose-based composite macrogels made by cellulose fiber/cellulose nanofiber (CCNM) were used as an intestine delivery vehicle for probiotics. Cellulose nanofiber (CNF) was prepared by a 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO)-mediated oxidation system, and the carboxyl groups in CNF acted as pore size and pH responsibility regulators in CCNMs to regulate the probiotics loading and controlled release property. The macrogel presented a porosity of 92.68% with a CNF content of 90%, and the corresponding released viable <i>Lactobacillus plantarum</i> (<i>L. plantarum</i>) was up to 2.68 × 10⁸ cfu/mL. The porous structure and high porosity benefited <i>L. plantarum</i> cells to infiltrate into the core of macrogels. In addition, the macrogels made with high contents of CNF showed sustainable release of <i>L. plantarum</i> cells and delivered enough viable cells to the desired region of intestine tracts. The porous cellulose macrogels prepared by a green and environmental friendly method show potential in the application of fabricating targeted delivery vehicles of bioactive agents

data of article and supporting information

The files of SEM-PSP, IR and TG, data of performance, XPS and XRD are the data of articles. While the files of supporting information-IR and supporting information-data of recycle performance are the data of supporting informaton