We give an overview of our philosophy of pictures in mathematics. We emphasize a bidirectional process between picture lan- guage and mathematical concepts: abstraction and simulation. This motivates a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.
We show that if X is a uniformly perfect complete metric space satisfying
the finite doubling property, then there exists a fully supported measure with lower regularity
dimension as close to the lower dimension of X as we wish. Furthermore, we show that, under
the condensation open set condition, the lower dimension of an inhomogeneous self-similar set EC
coincides with the lower dimension of the condensation set C, while the Assouad dimension of
EC is the maximum of the Assouad dimensions of the corresponding self-similar set E and the
condensation set C. If the Assouad dimension of C is strictly smaller than the Assouad dimension
of E, then the upper regularity dimension of any measure supported on EC is strictly larger than
the Assouad dimension of EC. Surprisingly, the corresponding statement for the lower regularity
Recent consumer interest in controlling and preventing chronic diseases through improved diet has promoted research on the bioactive components of agricultural products. Wheat is an important agricultural and dietary commodity worldwide with known antioxidant properties concentrated mostly in the bran fraction. The objective of this study was to determine the relative contributions of genotype (G) and growing environment (E) to hard winter wheat bran antioxidant properties, as well as correlations of these properties to growing conditions. Bran samples of 20 hard winter wheat varieties grown in two locations were examined for their free radical scavenging capacities against DPPH, ABTS cation, peroxyl (ORAC), and superoxide anion radicals and chelating properties, as well as their total phenolics and phenolic acid compositions. Results showed significant differences for all antioxidant properties tested and multiple significant correlations between these properties. A factorial designed analysis of variance for these data and pooled previously published data showed similar results for four of the six antioxidant properties, indicating that G effects were considerably larger than E effects for chelating capacity and DPPH radical scavenging properties, whereas E was much stronger than G for ABTS cation radical scavenging capacity and total phenolics, although small interaction effects (G × E) were significant for all antioxidant properties analyzed. Results also showed significant correlations between temperature stress or solar radiation and some antioxidant properties. These results indicate that each antioxidant property of hard winter wheat bran is influenced differently by genotype and growing conditions.
JEFFREY MOOREUniversity of MarylandZHIHONG CHENGUniversity of MarylandJUNJIE HAOUniversity of MarylandGANG GUOThe Mennel Milling CompanyJian-Guo LiuUniversity of MarylandCHUNJIAN LINUniversity of MarylandLIANGLI (LUCY) YUUniversity of Maryland
Journal of Agricultural and Food Chemistry, 55, (25), 10173-10182, 2007.12
The bran fraction of wheat grain is known to contain significant quantities of bioactive components. This study evaluated the potential of solid-state yeast fermentation to improve the health beneficial properties of wheat bran, including extractable antioxidant properties, protein contents, and soluble and insoluble fiber compositions. Three commercial food grade yeast preparations were evaluated in the study along with the effects of yeast dose, treatment time, and their interaction with the beneficial components. Solid-state yeast treatments were able to significantly increase releasable antioxidant properties ranging from 28 to 65, from 0 to 20, from 13 to 19, from 0 to 25, from 50 to 100, and from 3 to 333% for scavenging capacities against peroxyl (ORAC), ABTS cation, DPPH and hydroxyl radicals, total phenolic contents (TPC), and phenolic acids, respectively. Yeast treatment increased protein content 11-12% but did not significantly alter the fiber composition of wheat bran. Effects of solid-state yeast treatment on both ORAC and TPC of wheat bran were altered by yeast dose, treatment time, and their interaction. Results suggest that solid-state yeast treatment may be a commercially viable postharvest procedure for improving the health beneficial properties of wheat bran and other wheat-based food ingredients.