We prove the following result: If G is a nite irreducible reeection group deened over a base eld k, then the invariant eld of G is purely transcendental over k, even if jGj is divisible by the characteristic of k. It is well known that in the above situation the invariant ring is in general not a polynomial ring. So the question whether at least the invariant eld is purely transcendental (Noeth...

We show that if f is a transcendental meromorphic function with a finite number of poles and f has a cycle of Baker domains of period p, then there exist C > 1 and r0 > 0 such { z : 1 C r < |z| < Cr } sing(f−p) ∅, for r r0. We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles.

We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular K3 surfaces associated with an arithmetic Zariski pair of maximizing sextics of type A10 + A9 that are defined over Q( √ 5) and are conjugate to each other by the action of Gal(Q( √

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incremen...

lnjlammaiion of the gingiva (margins of the gums) is altered by local and systemic stressfactors.lt precedes resorption of underlying bone (periodontal disease), which occurs in a vast majority of the population, ultimately resulting in loss of teeth and nutritional imbalance. Forty-six people practicing the Transcendental Meditation technique and 26 controls were examined clinically and repeat...

Let k(~x) := k(x1, . . . , xn) be a finitely generated extension field of some field k, and denote by k(~g) := k(g1, . . . , gr) an intermediate field of k(~x)/k generated over k by some elements g1, . . . , gr ∈ k(~x). So geometrically, we may take ~g for rational functions on the variety determined by the generic point (~x). To determine whether the extension k(~x)/k(~g) is transcendental or ...

The study was designed to investigate the influence of the Transcendental Meditation (TM) technique on hearing threshold, and to compare the relative influence of Transcendental Meditation and rest. A group of 29 volunteers aged between 16 and 6/ were tested, all of whom were practising TM regularly. The experiment was conducted in two phases: 15 subjects rested in the first phase and meditated...