Let p be a prime number. We introduce a sparseness condition on the supports of p-adic Hahn series, and prove that this condition implies transcendence over 𝐐̆_p, the completed maximal unramified extension of 𝐐_p. As an application, we prove the order-type conjecture of 𝐐_p-algebraic p-adic Hahn series with bounded support under the condition that the support has only finitely many accumulation points. All results in this paper have been fully formalized in the Lean theorem prover (v 4.31.0), building over Mathlib.

Let p≥ 3 be a prime. The hyper-algebraic elements in the p-adic Mal'cev-Neumann field 𝕃_p form an algebraically closed subfield 𝕃_p^ha. In this article, we clarify the relations among the fields 𝕃_p^ha, ℚ_p and ℂ_p. We introduce two arithmetic invariants (hyper-tame index and hyper-inertia index) of hyper-algebraic elements and study the relation between these invariants and classical arithmetic invariants of p-adic algebraic numbers. Finally, we give a criterion for hyper-algebraic elements to be tamely ramified over ℚ_p.

Let p be a prime number. In this article, we prove that the p-adic Hahn series ∑_k=1^∞ p^-1/p^k, which is the mixed-characteristic analogue of Abhyankar's solution ∑_k=1^∞ t^-1/p^k to the Artin-Schreier equation X^p-X-t^-1=0 over 𝐅_p((t)), is a p-adic complex number, but not a p-adic algebraic number. Based on this result, we formulate a conjecture about the possible order type of the support of an algebraic p-adic Hahn series and prove that it is implied by a tentative observation of Kedlaya.

In this note, we make explicit the correspondence between Harish-Chandra parameters and Langlands-Vogan parameters for symplectic groups and orthogonal groups of equal rank over reals. As an application, we reformulate Moeglin's results and Paul's work on the Howe correspondence for symplectic-orthogonal dual pairs using Langlands-Vogan parameters.

We extend the dictionary between Fontaine rings and $p$-adic functionnal analysis, and we give a refinement of the $p$-adic local Langlands correspondence for principal series representations of ${\rm GL}_2(\mathbf{Q}_p)$.

In this note, we show that the metaplectic theta correspondence is compatible with the tempered condition by directly estimating the matrix coefficients, without using the classification theorem.

. In this note, we show that the metaplectic theta correspondence is compatible with the tempered condition by directly estimating the matrix coefficients, without using the classification theorem.

We show that the modular symbol (0,∞), considered as an element of the dual of Emerton's completed cohomology, interpolates Kato's Euler system at classical points, and we deduce from this a factorisation of Beilinson-Kato's system as a product of two symbols (0,∞) (an algebraic analog of Rankin's method). The proof uses the p-adic local Langlands correspondence for 𝐆L_2(𝐐_p) and Emerton's factorization of the completed cohomology of the tower of modular curves for which we provide a new proof resting upon the construction of a Kirillov model for the completed cohomology, and which we refine by imposing conditions at classical points; the existence of such a refinement is a manifestation of an analyticity property for p-adic periods of modular forms.

Fix an odd prime $p$. In this article, we provide a $\mathrm{mod}\ p$ harmonic number identity, which appears naturally in the canonical expansion of a root $\zeta_{p^n}$ of the $p^n$-th cyclotomic polynomial $\Phi_{p^n}(T)$ in the $p$-adic Mal'cev-Neumann field $\mathbb{L}_p$. We establish a $\frac{2}{(p-1)p^{n-2}}$-truncated expansion of $\zeta_{p^n}$ via a variant of the transfinite Newton algorithm, which gives the first $\aleph_0^2$ terms of the canonical expansion of $\zeta_{p^n}$. The harmonic number identity simplifies the expression of this expansion.

In this article, we investigate the explicit formula for the uniformizers of the false-Tate curve extension of $\mathbb{Q}_p$. More precisely, we establish the formula for the fields ${\mathbb{K}}_p^{m,1}={\mathbb{Q}}_p(\zeta_{p^m}, p^{1/p})$ with $m\geq 1$ and for general $n\geq 2$, we prove the existence of the recurrence polynomials ${\mathcal{R}}_p^{m,n}$ for general field extensions ${\mathbb{K}}_p^{m, n}$ of ${\mathbb{Q}}_p$, which shows the possibility to construct the uniformizers systematically.

This article is the second article on the generalization of Kato’s Euler system. The main subject of this article is to construct a family of Kato’s Euler systems over the cuspidal eigencurve, which interpolate the Kato’s Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato’s Euler system to construct a family of distributions on ℤp over the cuspidal eigencurve; this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.

在总结分析近十年来我国重特大生产安全事故统计数据基础上,归纳提出重特大生产安全事故发生的阶段规律.通过进一步的研究发现,重特大生产安全事故的发生与国家GDP增长速率、产业结构布局情况和从业人员安全生产意识等要素之间存在着非常密切的关联性.依据重特大生产安全事故发生规律,从加强风险控制、提高技术保障、提升应急能力、社会安全文化建设等方面,提出了遏制重特大生产安全事故的对策措施.

This article is the second article on the generalization of Kato's Euler system. The main subject of this article is to construct a family of Kato's Euler systems over the cuspidal eigencurve, which interpolate the Kato's Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato's Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve; this distribution gives us a two variable p-adic L function which interpolate the p-adic L function of modular forms.

This article is devoted to Kato's Euler system, which is constructed from modular unites, and to its image by the dual exponential map (so called Kato's reciprocity law). The presentation in this article is different form Kato's original one, and dual exponential map in this article is a modification of Colmez's construction in his Bourbaki talk.

1 研究目标 课题组从我国安全生产工作的整体需求出发,建立和完善我国安全生产重点领域标准体系,研究制修订一批急需的安全生产关键技术标准,最终实现全面促进和提升我国安全生产标准化水平的目标.

<正>美国职业安全与卫生研究所(NIOSH)主要从事职业安全与卫生科学研究,就与工作有关的伤害和疾病的预防提出建议。该所隶属于美国卫生与人力服务部疾病预防控制中心。

<正> 美国一家SAN JOAQUINVAL-LEY(SJV)商业集团公司员工约为1000人,同时还有250名经常在公司使用电脑的签约员工。由于技术的改进,公司员工将花更多的时间在电脑或控制面板上,这样他们患上与电脑相关的重复性肌肉损伤(RSIs)的可能性也就大大增加。 SJVBU公司的领导层在几年前就开始对RSIs采取了措施,但公司的员工仍长期受到RSIs的困扰。公司领导已经意识到:要想使公司的人机工程学研究达到世界的水平,必须着重降低RSIs的

<正> 骇人听闻——生命毁于一夜间死亡之夜1984年12月3日凌晨,坐落在印度中部博帕尔市北郊的一家农药厂,突然传出尖利刺耳的汽笛声,紧接着一声巨响,一股巨大的气柱冲向天空,形成一个