Let q be a power of an odd prime number and Fq be the finite field with q elements. We will construct a binary spherical code from an algebraic curve C defined over Fq and a rational divisor G on C, as the twist by the quadratic character 11 of the Goppa code L(G). The computation of the parameters of this code is based on the study of some character sums. 0. Introduction. In a previous paper (...

There are embeddings of complex abelian surfaces in P but it was shown by Van de Ven in [17] that no abelian d-fold can be embedded in P if d ≥ 3. Hulek [9], Lange [13], Birkenhake [4] and Bauer and Szemberg [3] have all investigated the possibility of replacing P with a product of projective spaces. Furthermore, Lange [14] studies the rank 2 bundle on P × P that arises from the abelian surface...

1. Introduction Pfeffermann (1994) has proposed a solution to the long-standing problem of variance measures for time series seasonally adjusted by the X-11 method (Ladiray & Quenneville, 2001). Pfeffermann's approach builds from a method suggested by Wolter & Monsour (1981), using sampling error information and the linear approximation to X-11. The present paper pulls together results across t...

LetM be an n-dimensional Riemannian manifold. ThenM is a differentiable manifold with a smoothly varying inner product 〈, 〉x on each tangent space TxM . An orthonormal frame at the point x ∈ M is an orthonormal basis {e1, . . . , en} of the tangent space TxM . The set of orthonormal frames at each point is isomorphic to the Lie group O(n), and the set of orthonormal frames on M forms a principa...

Let (M, g) be a compact Kähler-Einstein manifold with c1 > 0. Denote by K → M the canonical line-bundle, with total space X, and X0 the singular space obtained by blowing down X along its zero section. We employ a construction by Page and Pope and discuss an interesting multi-parameter family of Poincaré–Einstein metrics on X. One 1-parameter subfamily {gt}t>0 has the property that as t ց 0, gt...

1.1 Preliminaries In this chapter we focus on what Rabiner in his popular tutorial (Rabiner, 1989) calls “uncovering the hidden part of the model” or “Problem 2”, that is, hidden path inference. We consider a hidden Markov model (X,Y) = {(Xt,Yt)}t∈Z, where Y = {Yt}t∈Z is an unobservable, or hidden, homogeneous Markov chain with a finite state space S = {1, . . . ,K}, transition matrix P = (pi,j...

Sr 2 IrO 4 is predicted to be a new superconductor in theory, and its electric transport properties have attracted much attention the field of physics. Here we prepared series polycrystalline samples doped with 2-x Bi x (x=0,0.02,0.04,0.06,0.08) 2-y Dy y (y=0,0.02,0.04,0.06) respectively. The influence two ions on lattice structure electronic after substitution Ir site very similar, which makes...

and Applied Analysis 3 Our main result is as follows. Theorem 2.3. Suppose a x , b x , and F satisfy A , F1 – F3 . Then System 1.2 has infinitely many distinct pairs of solutions zn un, vn , which are critical points of the functional I : X → R, and I zn → ∞ as n → ∞. In this paper, the existence of periodic solutions of a single equation in System 1.1 are extended to the case of equations, and...

In section 6.2, we learnt how to count the number of r-permutations from an n-element set (recall that an r-permutation is an ordered selection of r elements from a set containing n elements). Note that a permutation depends upon ordering that is, if x, y ∈ S, a set, then the permutation x, y is different to that of y, x. In this section, we introduce a similar notion to a permutation called a ...

Fix a smooth very ample curve C on a K3 or abelian surface X . Let M denote the moduli space of pairs of the form (F, s), where F is a stable sheaf over X whose Hilbert polynomial coincides with that of the direct image, by the inclusion map of C in X , of a line bundle of degree d over C, and s is a nonzero section of F . Assume d to be sufficiently large such that F has a nonzero section. The...