We provide an application of the theory group actions to study musical scales. For any G, finite G-set S, and real number t, we define t-power diameter diamt(G,S) be size maximal orbit S divided by mean elements S. The symmetric S11 acts on set all tonic scales, where a scale is subset Z12 containing 0. show that for t∈[−1,1], among subgroups G S11, heptatonic scales largest subgroup Γ, its con...

Let Homeo(S) represent the full group of homeomorphisms of the unit circle S, and let A represent the set of subgroups of Homeo(S) satisfying the two properties that if G ∈ A then 1) G contains only orientationpreserving homeomorphisms of S and 2) G contains no non-abelian free subgroups. In this article we use classical results about homeomorphisms of the circle and elementary dynamical method...

We describe the subgroups of the group Zm × Zn × Zr and derive a simple formula for the total number s(m,n, r) of the subgroups, where m,n, r are arbitrary positive integers. An asymptotic formula for the function n 7→ s(n, n, n) is also deduced.

BACKGROUNDS Segmental and circumferential pulmonary vein isolations (SPVI and CPVI) have been demonstrated to be effective therapies for paroxysmal atrial fibrillation (PAF). PVI is well established as the endpoint of different ablation techniques, whereas it may not completely account for the long-term success. METHODS 181 drug-refractory symptomatic PAF patients were referred for segmental ...

In this paper, we introduce the notion of (i-v) fuzzy (weakly) completely regular subsemigroup of a semigroup S and study their different properties. We show that every (i-v) fuzzy completely regular subsemigroup of a semigroup S is a union of (i-v) fuzzy subgroups of S. We also characterize (i-v) fuzzy completely regular subsemigroup by (i-v) fuzzy semilattice of (i-v) fuzzy subgroups. 2010 AM...

In this note we give examples of a ring that has no maximal ideals. Recall that, by a Zorn’s lemma argument, a ring with identity has a maximal ideal. Therefore, we need to produce examples of rings without identity. To help motivate our examples, let S be a ring without identity. We may embed S in a ring R with identity so that S is an ideal of R. Notably, set R = Z⊕S, as groups, and where mul...

In the theory of one-relator groups, Magnus subgroups, which are free subgroups obtained by omitting a generator that occurs in the given relator, play an essential structural role. In a previous article, the author proved that if two distinct Magnus subgroups M and N of a one-relator group, with free bases S and T are given, then the intersection of M and N is either the free subgroup P genera...

Silvestri, L. G. (Università Statale, Milan, Italy), and L. R. Hill. Agreement between deoxyribonucleic acid base composition and taxometric classification of gram-positive cocci. J. Bacteriol. 90:136-140. 1965.-It had been previously proposed, from taxometric analyses, that gram-positive, catalase-positive cocci be divided into two subgroups. Thirteen strains, representative of both subgroups,...

The third Conway group Co3 is one of the twenty-six sporadic finite simple groups. The cohomology of its Sylow 2-subgroup S is computed, an important step in calculating the mod 2 cohomology of Co3. The spectral sequence for the central extension of S is described and collapses at the sixth page. Generators are described in terms of the Evens norm or transfers from subgroups. The central quotie...