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.
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse gamma distribution as an equilibrium in the particular case of quadratic cost functions which has been previously considered in the literature.
Jianlian CuiDepartment of Mathematics, Tsinghua UniversityChi-Kwong LiDepartment of Mathematics, College of William & Mary, WilliamsburgYiu-Tung PooncDepartment of Mathematics, Iowa State University, Ames
Linear Algebra and its Applications, 498, 160-180, 2016.6
Denote by Mnthe set of n ×ncomplex matrices. Let f:Mn→[0, ∞)be a continuous map such that f(μUAU∗) =f(A)for any complex unit μ, A ∈Mnand unitary U∈Mn, f(X) =0if and only if X=0and the induced map t →f(tX)is monotonically increasing on [0, ∞)for any rank onenilpotent X∈Mn. Characterization is given for surjective maps φon Mnsatisfying f(AB−BA) =f(φ(A)φ(B) −φ(B)φ(A)). The general theorem isthen used to deduce results on special cases when the function is the pseudo spectrum and the pseudo spectral radius.