In this study we investigated the structures of 11 neutral oligosaccharides released from bovine submaxillary mucin by alkaline borohydride treatment and isolated by h.p.l.c. One hexa-, one penta-, three tetra-, four tri- and two di-saccharides containing core types 1, 2, 3 or 4 were obtained. We report their structures, determined by a combination of one- and two-dimensional 1H n.m.r. spectros...

Let Γ be a co-compact Fuchsian group of isometries on the Poincaré disk D and ∆ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction f of ∆, equivariant by Γ with real eigenvalue λ = −s(1 − s), where s = 1 2 + it, admits an integral representation by a distribution D f,s (the Helgason distribution) which is equivariant by Γ and supported at infinity ∂D = S 1. The geodesic flo...

We determine the Shimura modular curve X0(3) and the Jacobian of the Shimura modular curve X1(3) associated with the congruence subgroups Γ0(3), Γ1(3) of the (2, 3, 7) triangle group. This group is known to be arithmetic and associated with a quaternion algebra A/K ramified at two of the three real places of K = Q(cos 2π/7) and at no finite primes of K. Since the rational prime 3 is inert in K,...

is a Hessenberg matrix and its determinant is F2n+2. Furthermore, a Hessenberg matrix is said to be a Fibonacci-Hessenberg matrix [2] if its determinant is in the form tFn−1 + Fn−2 or Fn−1 + tFn−2 for some real or complex number t. In [1] several types of Hessenberg matrices whose determinants are Fibonacci numbers were calculated by using the basic definition of the determinant as a signed sum...