Let F denote a totally real number field of degree d > 1 over Q, let p be a prime number and let χ be a totally odd Hecke character of finite order of F . Klingen and Siegel have shown that the values of the Hecke L-series L(χ, s) at integers n ≤ 0 lie in the algebraic closure Q ⊆ C of Q. In [14] Shintani gave another proof by constructing a nice fundamental domain (i.e. a finite disjoint union...

A new study clarifies a relationship between growth, gene expression, and cell size in cyanobacteria. Quite unexpectedly, cyanobacteria and Escherichia coli appear to share an invariance principle to coordinate growth and chromosome replication. This principle allows quantitative predictions of cell size across a range of growth conditions in both organisms.

It is our purpose to study curvature structures of compact hypersurfaces in the unit sphere S(1). We proved that the Riemannian product S( √ 1 − c2) ×Sn−1(c) is the only compact hypersurfaces in S(1) with infinite fundamental group, which satisfy r ≥ n−2 n−1 and S ≤ (n − 1)n(r−1)+2 n−2 + n−2 n(r−1)+2 , where n(n − 1)r is the scalar curvature of hypersurfaces and c = n−2 nr . In particular, we o...

A theory of nonassociative measurement structures is developed which produces a natural generalization of associative measurement (i.e., extensive structures), and representation and uniqueness theorems are established for these generalized structures, and it is shown that in many cases these representations are ratio scales. The methods of proof strongly relate the structure of the automorphis...

The identification of nutrients and the study of their bioactivity were significant developments in the evolution of contemporary nutrition science. This review argues for shifting the focus towards food in order to better understand the nutrition-health interface. It begins by introducing the concept of food synergy (a perspective that more information can be obtained by looking at foods than ...

The molecular/genetic era has seen the discovery of a staggering number of molecules implicated in pain mechanisms [18,35,61,69,96,133,150,202,224]. This has stimulated pharmaceutical and biotechnology companies to invest billions of dollars to develop drugs that enhance or inhibit the function of many these molecules. Unfortunately this effort has provided a remarkably small return on this inv...