Abstract. In this article, we consider the group F∞ 1 (N) of modular units on X1(N) that have divisors supported on the cusps lying over∞ of X0(N), called the ∞-cusps. For each positive integer N , we will give an explicit basis for the group F∞ 1 (N). This enables us to compute the group structure of the rational torsion subgroup C∞ 1 (N) of the Jacobian J1(N) of X1(N) generated by the differe...

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: testicular torsion is a medical emergency with catastrophic sequelae that deserves the same treatment considerations and concerted efforts in research as any other complicated medical condition. the aim of this study was to investigate the effect of pausinystalia macroceras (pm) bark extract on sperm quality and serum testosterone levels in testicular torsion in a rat model. methods...

Given an odd prime p and a representation % of the absolute Galois group of a number field k onto PGL2(Fp) with cyclotomic determinant, the moduli space of elliptic curves defined over k with p-torsion giving rise to % consists of two twists of the modular curve X(p). We make here explicit the only genus-zero cases p = 3 and p = 5, which are also the only symmetric cases: PGL2(Fp) ' Sn for n = ...

  Torsion of the gallbladder is a relatively rare surgical disease which mimics acute cholecystitis' symptoms that usually would not be respondable to medical therapies. The torsion would mostly be diagnosed intra-operatively. Cholecystectomy is the treatment of choice. In general in our centre, General Surgery department, Imam Reza hospital, Mashhad, Iran, since 1986 over 14000 cholecystect...

In the title compound, C(26)H(19)N(3)O, the dimethyl-ene hydrazine (-C=N-N=C-) unit is approximately planar, the torsion angle around the N-N bond being 162.2 (6)°. The phenyl and benzoyl-phenyl rings at one end of the hydrazine unit are aligned at angles of 9.5 (5) and 88.5 (4)°, respectively, with respect to the hydrazine unit, whereas the benzene ring at the other end is twisted by an angle ...

We show that there is an exact sequence of biset functors over p-groups 0 → Cb j −→B∗ Ψ −→D → 0 where Cb is the biset functor for the group of Borel-Smith functions, B ∗ is the dual of the Burnside ring functor, D is the functor for the subgroup of the Dade group generated by relative syzygies, and the natural transformation Ψ is the transformation recently introduced by the first author in [5]...

Abstract. In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 2 of the group Γ of positive units of the Lorentzian quadratic form x 1 + · · ·+ x 5 − x 6 . We also show that Γ 2 is a reflection group with respect to a 5-dimensional right-angled convex po...

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

In conjugated polymers the concept of spectroscopic units belonging to different spatial segments of the chain, which are responsible for the spectroscopic properties of the polymer, has been used to explain the spectral heterogeneity and the excitation migration by (Förster type) hopping transfer. In the present work we study the possible mechanism of segmentation of polythiophene into spectro...