Recent work has shown that every 3D root system allows the construction of a correponding 4D via an `induction theorem'. In this paper, we look at icosahedral case $H_3\rightarrow H_4$ in detail and perform calculations explicitly. Clifford algebra is used to group theoretic based on versor theorem Cartan-Dieudonn\'e theorem, giving simple Pin Spin covers. Using connection with $H_3$ induction ...

In a constructive setting, the formula ∀n ∃r r2≤n ∧ n<(r+1) specifies an algorithm for computing the integer square root r of a natural number x. A proof for this formula implicitly contains an integer square root algorithm that mirrors the way in which the formula was proven correct. In this note we describe the formal derivation of several integer square root algorithms within the Nuprl proof...

Functional screening of an Arabidopsis cDNA library enabled the identification of a novel cDNA, ESR1 (for Enhancer of Shoot Regeneration), that can confer cytokinin-independent shoot formation when overexpressed in Arabidopsis root explants. Neither callus induction nor root formation was affected by ESR1 overexpression. ESR1 encodes a putative transcription factor with an AP2/EREBP domain. Sur...

This study was conducted to assessthe preventive effect of aqueous extract of Berberis integerrima Bge. root (AEBIR) on liver damage and oxidative stress induced by diabetes mellitus in rats. Forty male rats were divided into 5 groups as follows: 1- normal (N); 2- normal + barberry (N+B) (they received barberry root extract for 6 weeks); 3- diabetic (D) (they received Streptozotocin (STZ), 65 m...

ROOT HAIR DEFECTIVE SIX-LIKE4 (RSL4) is necessary and sufficient for root hair elongation in Arabidopsis thaliana. Root hair length is determined by the duration for which RSL4 protein is present in the developing root hair. The aim of this research was to identify genes regulated by RSL4 that affect root hair growth. To identify genes regulated by RSL4, we identified genes whose expression was...

The invariance of the Artin root number under induction can be proved without special effort. In fact if one develops the properties of Artin Lfunctions in the usual way, then the inductivity of the root number is obvious. In barest outline the argument is as follows. First one proves the inductivity of Artin L-functions themselves, and then one combines Brauer’s induction theorem with the anal...