Notes on the Frobenius test exponents

In this article, we show that the Frobenius test exponent for parameter ideals of a local ring of prime characteristic is always bigger than or equal to its Hartshorne–Speiser–Lyubeznik number. Our argument is based on an isomorphism of Nagel and Schenzel on local cohomology for which we will provide an elementary proof.     

论微分约束系统的d-δ对易关系

利用Frobenius可积性定理,研究微分约束系统一个重要的变分法问题：微分运算与变分运算的对易关系. 文中以微分约束的Frobenius可积性理论为依据,在分析线性稳定微分约束系统和仿射微分约束系统的d-δ对易关系基础上,简要论证了微分与变分的非对易子与微分约束的非完整性之间的关系. 对非线性微分约束系统的微分与变分运算的对易关系作了讨论. 给出了三个实例来验证结论. 关键词： 非完整约束 Frobenius可积性 d-δ对易关系     

Neutron transfer dynamics and doorway to fusion in time-dependent Hartree-Fock theory

We analyze the details of mass exchange in the vicinity of the Coulomb barrier for heavy-ion collisions involving neutron-rich nuclei using the time-dependent Hartree-Fock (TDHF) theory. We discuss the time dependence of transfer and show that the potential barriers seen by individual single-particle states can be considerably different than the effective barrier for the two interacting nuclei having a single center of mass. For this reason we observe a substantial transfer probability even at energies below the effective barrier.     

Une Famille Infinie d'Extensions Faiblement Ramifiées

We study weakly ramified extensions of ℚ with Galois group C ⋊ C_p, where p is an odd prime. In particular, we describe an infinite family of such extensions when p = 3.     

Products of Random Rectangular Matrices

We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron‐Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate recurrence problems.     

Quantifier elimination on some pseudo-algebraically closed valued fields

In this article, some theories of pseudo-algebraically closed non-trivially valued fields are shown to admit quantifier elimination in the language obtained by adjoining to the language of rings the function symbols for splitting coefficients, the function symbols for relative p-coordinate functions, and the division predicate for a valuation.     

Vector bundles on flag varieties

We study vector bundles on flag varieties over an algebraically closed field k. In the first part, we suppose $G=G_k(d,n)$ $(2\le d\le n-d)$ to be the Grassmannian parameterizing linear subspaces of dimension d in $k^n$, where k is an algebraically closed field of characteristic $p>0$. Let E be a uniform vector bundle over G of rank $r\le d$. We show that E is either a direct sum of line bundles or a twist of the pullback of the universal subbundle $H_d$ or its dual $H_d^{\vee }$ by a series of absolute Frobenius maps. In the second part, splitting properties of vector bundles on general flag varieties $F(d_1,\text{…},d_s)$ in characteristic zero are considered. We prove a structure theorem for bundles over flag varieties which are uniform with respect to the ith component of the manifold of lines in $F(d_1,\text{…},d_s)$. Furthermore, we generalize the Grauert–M$\ddot{\mathrm{u}}$lich–Barth theorem to flag varieties. As a corollary, we show that any strongly uniform i-semistable $(1\le i\le n-1)$ bundle over the complete flag variety splits as a direct sum of special line bundles.     

余半单Hopf代数的Frobenius性质

设k是特征为0的代数闭域,H为其上的余半单Hopf代数,本文证明了当H有型:l:1 m:p 1:q(其中p~2相似文献