Issue 2, Volume 38, June 2013

2013

1. Sur une question de capitulation Abdelmalek Azizi , Mohammed Talbi PDF

   ▸ Abstract

   Pour certains corps quartiques cycliques $\mathbb K$, on va étudier le problème de capitulation des 2-classes d’idéaux de $\mathbb K$ et nous déterminons la structure du groupe de Galois du deuxième 2-corps de classes de Hilbert de $\mathbb K$ sur $\mathbb K$.

   207-212
2. Mixed invariant subspaces over the bidisk II Kou Hei Izuchi , Kei Ji Izuchi PDF

   ▸ Abstract

   For a mixed invariant subspace $N$ of $H^2$ under $T_z$ and $T^∗_w$, in the previous paper we studied the case $\mathrm{rank}[V_z ,V_w ]=1$ and either $\dim(N\ominus zN)=0$ or $1$. In this paper, we study the structure of $N$ satisfying $\mathrm{rank}[V_z ,V_w ]=1$ and $\dim(N\ominus zN)=2$. Our study is deeply concerned with the structure of nonextreme points in the closed unit ball of the space of one variable bounded analytic functions.

   213-239
3. Remarks on parameter estimation for the drift of fractional brownian sheet Junfeng Liu PDF

   ▸ Abstract

   Let $\{B_{z}^{\alpha, \beta},z\in[0,T]^{2} \}$ be a $d$-dimensional fractional Brownian sheet with Hurst parameters $(\alpha, \beta)\in(0,\frac{1}{2})^{2}$. We consider the problem of parameter estimation for the drift of fractional Brownian sheet $B^{\alpha,\beta}$ and construct superefficient James–Stein estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

   241-253
4. Pseudodifferential operators on localized Besov spaces Madani Moussai , Salah Eddine Allaoui PDF

   ▸ Abstract

   We study the boundedness of pseudodifferential operators $\sigma(x,D)$ of order $m$ and symbols $\sigma(x,\xi)$ which satisfy a condition of Dini-type, on localized Besov spaces $(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))_{\ell^{r}}$. In the case $s > n/p$ and $p \le q$, we deduce the boundedness of such an operator $\sigma(x, D)$ on pointwise multipliers Besov space $M(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))$.

   255-278
5. On a nonconvex separation theorem and the approximate extremal principle in Asplund spaces T. Q. Bao PDF

   ▸ Abstract

   In this paper we establish a revised version of the nonconvex separation theorem established in J. M. Borwein and A. Jofré (Math. Meth. Oper. Res. 48:169–179, 1996). Our new separation theorem is formulated in terms of Fréchet normal cones in Asplund spaces while their result was formed with an abstract kind of generalized differentiation enjoying a good calculus. It is, indeed, shown to be equivalent to the known approximate extremal principle in B. Mordukhovich (Variational analysis and generalized differentiation, I: Basic theory, Grundlehren series 330, Springer, Berlin, 2006). In addition, we discuss several efficient conditions ensuring the extremality property of a system of nonconvex sets.

   279-291
6. Torsion functors with monomial support Fred Rohrer PDF

   ▸ Abstract

   The dependence of torsion functors on their supporting ideals is investigated, especially in the case of monomial ideals of certain subrings of polynomial algebras over not necessarily Noetherian rings. As an application it is shown how flatness of quasicoherent sheaves on toric schemes is related to graded local cohomology.

   293-301
7. On some $L_1$-finite type Euclidean surfaces A. Mohammadpouri , S. M. B. Kashani , F. Pashaie PDF

   ▸ Abstract

   In this paper, we study some revolution, spiral and tube surfaces to see if they are of $L_1$-finite type. When they are of $L_1$-finite type, we characterize them completely.

   302-316
8. Stochastic dynamic equations on time scales Nguyen Huu Du , Nguyen Thanh Dieu PDF

   ▸ Abstract

   The aim of this paper is to consider the $\nabla$-stochastic dynamic equation on time scales. We give a condition for the existence and uniqueness of solutions, study Markovian property of the solutions concerning its time-dependent generator. This work can be considered as a unification and a generalization of similar results in random difference equation and stochastic differential one.

   317-338