In Theorem 2.5 in previous paper [4], we determined the Fourier coefficients of the image of Shimura correspondence of modular forms f of half integral weight over arbitrary algebraic number fields in terms of those of f. It seems that there is a gap in the proof. We give a correct proof of Theorem 2.5 in [4]. Moreover, we deduce useful formulas between the product of Fourier coefficients of f and the central value of quadratic twisted L-series associated with the image of Shimura correspondence of f .

We will give an efficient bimodule projective resolution of the generalized quaternion Z algebra Γ. As a main result, we will determine the ring structure of the Hochschild cohomology HH*(Γ) by calculating the Yoneda products using this resolution.

In [2] we investigated independent infinite Markov particle systems as measure-valued Markov processes with jumps, and we gave sample path properties and martingale characterizations. In particular, we investigated the exponent of Hölder-right continuity in case that the motion process is absorbing α-stable motion on (0,∞) with 0 < α < 2, that is, time-changed absorbing Brownian motions on (0,∞) by the increasing α/2-stable Lévy processes.In the present paper we shall extend the results to the case of simple interactive infinite Markov particle systems. We also consider the absorbing stable motion on a half space H = R^d−1 × (0,∞) as a motion process.

We extend the notion of a max-plus algebra and study periodicity and eigenvalues of matrices over this new structure thereby generalizing some well-known results on matrices over a max-plus algebra.

We prove that a σ-compact metric space having the compact extension property is an AR. This solves the problem ANR 13 of West's list [5].

Let J¹ be the real form of a complex simple Jordan algebra such that the automorphism group is F₄₍₋₂₀₎. By using some orbit types of F₄₍₋₂₀₎ on J¹, for F₄₍₋₂₀₎, explicitly, we give the Iwasawa decomposition, the Oshima-Sekiguchi's K_ε-Iwasawa decomposition, the Matsuki decomposition, and the Bruhat and Gauss decompositions.

The aim of this paper is to study the location and the geometrical properties of the double points of the slowness surface associated to the system of linear crystal-elasticity in three space dimensions for tetragonal crystals. It will turn out that compared with the case of cubic crystals, the location of these double points is more involved. Moreover, for some specific choices of the “so-called” stiffiness constants, a new type of singularities namely “biplanar” ones, will appear.

Happel and Unger defined a partial order on the set of basic tilting modules. The tilting quiver is the Hasse diagram of the poset of basic tilting modules. We determine the number of arrows in the tilting quiver over a path algebra of Dynkin type.