Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q → k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k(x, y). Although the value groups correspondi...

in this paper we study right $n$-engel group elements‎. ‎by modifying a group constructed by newman and nickel‎, ‎we construct‎, ‎for each integer $ngeq 5$‎, ‎a 2-generator group $g =langle a‎, ‎brangle$ with the property that $b$ is a right $n$-engel‎ ‎element but where $[b^k,_n a]$ is of infinite order when $knotin {0‎, ‎1}$‎.

The asymmetric unit of the enanti-omerically pure title compound, C18H18N2O3S, comprises two independent mol-ecules (A and B) having almost identical conformations. When overlayed, the alignment-r.m.s. deviation value is 0.30 Å. The six-membered heterocycle has a twisted half-chair conformation in both mol-ecules. The O atom on the S atom of the ring is pseudo-axial on the thia-zine ring and tr...

Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q → k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k(x, y). Although the value groups correspondi...

Minimal pairs of definition were introduced by Alexandru, Popescu and Zaharescu [3], [4], [5] to study residue transcendental extensions. In this paper we obtain analogous results in the value case. We introduce notion minimal fields for valuation extensions show that they share some common ramification theoretic properties. The connection between implicit constant is also investigated. Further...

We determine all homogeneous pseudo-embeddings of the affine space AG(n, 4) and the projective space PG(n, 4). We give a classification of all pseudo-hyperplanes of AG(n, 4). We also prove that the two homogeneous pseudo-embeddings of the generalized quadrangle Q(4, 3) are induced by the two homogeneous pseudo-embeddings of AG(4, 4) into which Q(4, 3) is fully embeddable.

abstract introduction: the purpose of present project was to examine the distinctive indicators in self-figure drawings in three groups of children with internalizing problems, those with externalizing problems, and the normal children. method: a total of 4000 child behavior checklist were administered in 34 boys and girls elementary schools in six different tehran school districts .using a pur...

Let S be a compact orientable surface, and Mod(S) its mapping class group. Then there exists a constant M(S), which depends on S, with the following property. Suppose a, b ∈ Mod(S) are independent (i.e., [a, b] 6= 1 for any n,m 6= 0) pseudo-Anosov elements. Then for any n,m ≥ M , the subgroup 〈a, b〉 is free of rank two, and convex-cocompact in the sense of Farb-Mosher. In particular all nontriv...

The title compound, C(9)H(9)N(3)O(6), was synthesized by the condensation of methyl 3,5-dinitro-benzoate and 2-amino-ethanol. The non-centrosymmetric space group results in the formation of pseudo-chiral helices in the crystal structure, which exhibits a layer packing structure involving intra-molecular N-H⋯O and O-H⋯O inter-actions.