On ML-Certificate Linear Constraints for Rank Modulation with Linear Programming Decoding and its Application to Compact Graphs

Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of matrices, new classes of such polytopes are obtained from known small polytopes. This concept, called "consolidation", is applied to find a new compact graph which is known as an approach for the graph isomorphism problem. Encoding and decoding algorithms for our new permutation codes are obtained from existing algorithms for small polytopes. The minimum distances associated with Kendall-tau distance and the minimum Euclidean distance of a code obtained by changing the basis of a permutation code may be larger than the original one.Comment: Submitted to ISIT 201

Study of the gluon polarization in the proton with a silicon vertex upgrade at RHIC/PHENIX

PHENIX has a well defined program for measuring the polarized gluon distribution in the nucleon. We measure the gluon polarization in the proton with polarized $p$-$p$ collisions at PHENIX. The measurements of gluon polarization $via$ the direct-photon production and the heavy-flavor production can be significantly improved by the silicon vertex tracker upgrade. We have studied the possible improvements of the gluon polarization measurements using Monte Carlo simulation and they are shown and discussed in this paper.Comment: 4pp. To appear in the proceedings of 16th International Spin Physics Symposium (SPIN 2004), Trieste, Italy, 10-16 Oct 200

Remark on the Alexander polynomials of periodic knots

We will show that if $K$ is a knot of prime period $p>2$ and whose Alexander polynomial $\Delta_K(t)$ is monic and of degree $p-1$, then $\Delta_K(t)$ is uniquely determined only by $p$

Invariants and discriminant ideals of orthogonal complements in a quadratic space

This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of such a complement in the sense of Shimura. The other is to investigate an ideal of the base field, which may be viewed as a difference between the genus of maximal lattices and an integral lattice in the complement. We shall discuss about the class number of the genus of maximal lattices as an application.Comment: We have revised several typographical errors and grammatical flows of the first versio

An ultrametric space of Eisenstein polynomials and ramification theory

We give a criterion whether given Eisenstein polynomials over a local field K define the same extension over K in terms of a certain non-Archimedean metric on the set of polynomials. The criterion and its proof depend on ramification theory.Comment: 11 page

On the genera of certain integral lattices in ternary quadratic spaces

This paper treats certain integral lattices with respect to ternary quadratic forms, which are obtained from the data of a non-zero element and a maximal lattice in a quaternary quadratic space. Such a lattice can be described by means of an order associated with the lattice in the even Clifford algebra of the ternary form. This provides a correspondence between the genus of the lattice and that of the order.Comment: We have reduced the length of several proofs of the first versio

On the abelian groups which occur as Galois cohomology groups of global unit groups

For any finite group G and integer i, let $\mathcal{H}^i(G)$ be the set of all the isomorphism classes of the Galois cohomology groups $\hat{H}^i(K/k,E_K)$, where K/k runs over all the unramified G-extension of number fields and E_K denotes the global unit group of K. We will determine $\mathcal{H}^i(G)$ for i=0,1,2, and 4 in the case where G is a finite p-group

Three-dimensional transport theory via one-dimensional transport theory

In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained

The time-fractional radiative transport equation -- Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion

A duality of a twisted group algebra of the hyperoctahedral group and the queer Lie superalgebra

We establish a duality relation between one of the twisted group algebras of the hyperoctahedral groupf H_k and a Lie superalgebra q(n_0) \oplus q(n_1) for any integers k and n_0, n_1, where q(n_0) and q(n_1) denote the ``queer'' Liesuperalgebras. Note that this twisted group algebra \B'_k belongs to a different cocycle from the one \B_k used by A. N. Sergeev in [8] and by the present author in [11]. We will use the supertensor product \C_k \otimes \B'_k of the 2^k-dimensional Clifford algebra \C_k and \B'_k, as an intermediary for establishing our duality. We show that the algebra \C_k \otimes B'_k and q(n_0) \oplus q(n_1) act on the k-fold tensor product W=V^{\otimes k} of the natural representation V of q(n_0+n_1) ``as mutual centralizers of each other'' (Theorem 4.1). Moreover, we show that \B'_k and q(n_0) \oplus q(n_1) act on a subspace W' of W ``as mutual centralizers of each other'' (Theorem 4.2). This duality relation gives a formula for character values of simple B'_k-modules. This formula is di fferent from a formula (Theorem D) obtained by J. R. Stembridge (cf. [10, Lem 7.5]).Comment: AMS-TeX, 22 pages, submitted to Advanced Studies in Pure Mat