This paper introduces two new representations for real-parameter spaces—the Dedekind and Isodedekind representations. Point mutation and uniform crossover—in their generalised, representation-independent form—are shown, when instantiated with respect to these representations, to give rise to familiar operators for continuous domains, such as gaussian mutation, blend crossover and line recombina...

Various contributors to recent philosophy of mathematics have taken Richard Dedekind to be the founder of structuralism in mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining...

In 1977 Hartwig and Luh asked whether an element a in a Dedekind-finite ring R satisfying aR = a2R also satisfies Ra = Ra2. In this paper, we answer this question in the negative. We also prove that if a is an element of a Dedekind-finite exchange ring R and aR = a2R, then Ra = Ra2. This gives an easier proof of Dischinger’s theorem that left strongly π-regular rings are right strongly π-regula...

Phosphate (Pi) and its analog phosphite (Phi) are acquired by plants via Pi transporters. Although the uptake and mobility of Phi and Pi are similar, there is no evidence suggesting that plants can utilize Phi as a sole source of phosphorus. Phi is also known to interfere with many of the Pi starvation responses in plants and yeast (Saccharomyces cerevisiae). In this study, effects of Phi on pl...

The locus of all points in the complex plane of the dielectric function ?[?(r) + j?(i) = |?| exp(jtheta)], that represent all possible interfaces characterized by the same pseudo-Brewster angle theta(p)B of minimum p reflectance, is derived in the polar form: |?| = l cos(zeta/3), where l = 2(tan(2)Phi(p)B)k, zeta = arccos(- costheta cos(2)Phi(p)B/k(3)), and k = (1 - 2/3 sin(2)Phi(p)B)(1/2). Fam...