We generalize Dirichlet’s S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a Q-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, a...

Background: When a large number of protein conformations are generated and screened, as in protein structure prediction studies, it is often advantageous to change the conformation in units of four consecutive residues at a time. The internal geometry of a chain of four consecutive Ca atoms is completely described by means of the three angles u1, t, and u2, where t is the virtual torsion angle ...

We present the first upper limit on gravitational wave (GW) backgrounds at an unexplored frequency of 0.2 Hz using a torsion-bar antenna (TOBA). A TOBA was proposed to search for low-frequency GWs. We have developed a small-scaled TOBA and successfully found Ω(gw)(f)<4.3×10(17) at 0.2 Hz as demonstration of the TOBA's capabilities, where Ω(gw)(f) is the GW energy density per logarithmic frequen...

We show that every virtually torsion-free subgroup of the outer au-tomorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is residually finite. We also generalise the main result for relatively hyperbolic groups.

Consider the space of ‘long knots’ in Rn Kn,1 . This is the space of knots as studied by V. Vassiliev. Based on previous work [5, 12], it follows that the rational homology of K3,1 is free Gerstenhaber-Poisson algebra. A partial description of a basis is given here. In addition, the mod-p homology of this space is a ‘free, restricted Gerstenhaber-Poisson algebra’. Recursive application of this ...

In this paper, we introduce a sequence of invariants of a knot K in S3 : the knot Floer homology groups ĤFK(Σm(K); K̃, i) of the preimage of K in the m–fold cyclic branched cover over K . We exhibit ĤFK(Σm(K); K̃, i) as the categorification of a well-defined multiple of the Turaev torsion of Σm(K)− K̃ in the case where Σm(K) is a rational homology sphere. In addition, when K is a two-bridge knot, ...

We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers of S branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold bran...

Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K . The anti-automorphism g 7→ g of G can be extended linearly to an anti-automorphism a 7→ a∗ of KG . Let S∗(KG) = {x ∈ U(KG) | x∗ = x} be the set of all symmetric units of U(KG) . We consider the following question: for which groups G and commutative rings K it is true that S∗(KG) is a subgroup in U(KG...

For a torsion unit u of the integral group ring ZG of a finite group G, and a prime p which does not divide the order of u (but the order of G), a relation between the partial augmentations of u on the p-regular classes of G and Brauer character values is noted, analogous to the obvious relation between partial augmentations and ordinary character values. For non-solvable G, consequences concer...

Notations /3, Prest a outer radius of the tube A apparatus constant t b distance to screen (in App. B) Tliq Bn 3 dB-bandwith B l o n g longitudinal magnetization of RL the tube gin, Vout C O ~ ]~Ni~ONi l velocity of propX agation of torsional waves in a XL tube without losses y C, C~, C2, C3 constants z deff thickness of "immobilized Z liquid layer" Z L f frequency a fn resonance frequency /~ F...