We study the structure of length three polynomial automorphisms of R[X, Y ] when R is a UFD. These results are used to prove that if SLm(R[X1, X2, . . . , Xn]) = Em(R[X1, X2, . . . , Xn]) for all n,≥ 0 and for all m ≥ 3 then all length three polynomial automorphisms of R[X, Y ] are stably tame. 1. Introducton Unless otherwise specified R will be a commutative ring with 1 and R = R[X ] = R[X1, ....

BACKGROUND Ginsenoside F1, a pharmaceutical component of ginseng, is known to have antiaging, antioxidant, anticancer, and keratinocyte protective effects. However, the usage of ginsenoside F1 is restricted owing to the small amount found in Korean ginseng. METHODS To enhance the production of ginsenoside F1 as a 10 g unit with high specificity, yield, and purity, an enzymatic bioconversion m...

One can prove the following propositions: (1) For all functions f , g, h such that dom f ∩ dom g ⊆ domh holds f+·g+·h = g+·f+·h. (2) For all functions f , g, h such that f ⊆ g and rng h ∩ dom g ⊆ dom f holds g · h = f · h. (3) For all functions f , g, h such that dom f ⊆ rng g and dom f misses rng h and g domh misses dom f holds f · (g+·h) = f · g. (4) For all functions f1, f2, g1, g2 such that...

29 2 Suresh Dara, S.M. Hegde, V. Deva, S.B. Rao and T. Zaslavsky In 1966, Cummins introduced the “tree graph”: the tree graph T(G) 30 of a graph G (possibly infinite) has all its spanning trees as vertices, and 31 distinct such trees correspond to adjacent vertices if they differ in just one 32 edge, i.e., two spanning trees T1 and T2 are adjacent if T2 = T1 − e+ f for 33 some edges e ∈ T1 and ...

Let α(G), α(G), κ(G) and κ (G) denote the independence number, the matching number, connectivity and edge connectivity of a graph G, respectively. We determine the finite graph families F1 and F2 such that each of the following holds. (i) If a connected graph G satisfies κ (G) ≥ α(G) − 1, then G has a spanning closed trail if and only if G is not contractible to a member of F1. (ii) If κ (G) ≥ ...

Let E/F be a Galois extension of number fields with Galois group G. The purpose of this paper is to place limitations on the structure of a Sylow 2-subgroup of G in the case when the extension E/F is a minimal counterexample to Artin’s Conjecture on the holomorphy of L-series. More specifically, assume for some s0 ∈ C − {1} and some irreducible character χ of G that the Artin L-series L(s, χ,E/...

A review of the publications in traditional medicine indicates that the root of Glycyrrhiza glabra L., Fabaceae, is recommended for treatment of epilepsy. As a renewable source, the leaves of G. glabra var. glandulifera growing in Iran were examined for possible anticonvulsant activity. The anticonvulsant activity of the leaves' ethanol extract and dichloromethane, f1, n-Hexane, f1A, and methan...

Given two images f1 , f2 representing the same object, we want to identify geometric correspondences between homologous features in both images. Specifically, we want to find a correspondence function (also called deformation function or deformation field) g(x1)=x2 , where x1 ,x2 are matching coordinates in images f1 , f2 . Here, we intend to concentrate on a non-linear registration (also calle...

If G is an n-dimensional joint distribution function with 1-dimensional margins F1,...,Fn, then there exists a function C (called an "w-copula") from the unit »-cube to the unit interval such that G(xx, ..., xn) = C(F1(x1), ..., Fn(xn)) for all real n-tuples (xlt ..., xn). The paper is devoted to an investigation of the structure and properties of n-copulas and their connection with random vari...