ACTA MATHEMATICA VIETNAMICA 是一份经过同行评审的数学期刊。该杂志在数学的所有分支中发表高质量的原创论文，重点关注代数几何和交换代数、代数拓扑、复分析、动力系统、优化和偏微分方程。

Acta Mathematica Vietnamica is a peer-reviewed mathematics journal that covers all branches of mathematics. The journal publishes high-quality original research papers, with a focus on algebraic geometry, commutative algebra, algebraic topology, complex analysis, dynamical systems, optimization, and partial differential equations.

《Acta Mathematica Vietnamica》是一本经过同行评审的数学期刊，涵盖数学的各个分支。该期刊发表高质量的原创研究论文，重点关注代数几何、交换代数、代数拓扑、复分析、动力系统、优化及偏微分方程等领域。

Acta Mathematica Vietnamica

Dinh Nho Hào

Preface

前言

Nguyen Ngoc Trong

Bui Le Trong Thanh

Tan Duc Do

A Degenerate Forward-backward Problem Involving the Spectral Dirichlet Laplacian

涉及谱狄利克雷拉普拉斯算子的退化前向后向问题

Abstract A differential 1-form $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> on a manifold of odd dimension $$2n+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , which satisfies the contact condition $$\alpha \wedge (d\alpha )^n \ne 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∧</mml:mo> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>d</mml:mi> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> almost everywhere, but which vanishes at a point O , i.e., $$\alpha (O) = 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>(</mml:mo> <mml:mi>O</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , is called a singular contact form at O . The aim of this paper is to study local normal forms (formal, analytic and smooth) of such singular contact forms. Our study leads naturally to the study of normal forms of singular primitive 1-forms of a symplectic form $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> in dimension 2 n , i.e., differential 1-forms $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> which vanish at a point and such that $$d\gamma = \omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>γ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> , and their corresponding conformal vector fields. Our results are an extension and improvement of previous results obtained by other authors, in particular Lychagin (1975), Webster (Amer. J. Math. 109 , 807–832 (1987)) and Zhitomirskii (1986, 1992). Besides the classical normalization techniques, such as the step-by step normalization methods based on the cohomological equations and the Moser path method, we also use the toric approach to the normalization problem for dynamical systems (Jiang et al. 2019; Zung, Ann. Math. 161 , 141–156 2005; Zung 2016; Zung, Arch. Rational Mech. Anal. 229 , 789–833 (2018)).

Kai Jiang

Hong Minh Truong

Nguyen Tien Zung

Normalization of Singular Contact Forms and Primitive 1-forms

奇异接触形式与原1-形式的标准化

Liguo Jiao

Jae Hyoung Lee

Tiến-Sơn Phạm

Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations

广义半无限多项式优化与半定规划松弛

Duc Quang Si

General Form of Second Main Theorem on Generalized p-Parabolic Manifolds for Arbitrary Closed Subschemes

短名	Acta Math. Vietnam.
Journal Impact	0.24
国际分区	MATHEMATICS(Q4)

ISSN	0251-4184, 2315-4144
h-index	15

涉及主题	数学纯数学数学分析物理计算机科学组合数学离散数学量子力学几何学哲学生物化学认识论工程类应用数学经济
出版信息	出版商: Springer Verlag，出版周期: 4 issues per year，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 2011，原创研究文献占比: 100.00%，自引率:0.00%， Gold OA占比: 5.79%

Acta Mathematica Vietnamica

期刊引文格式

有 1 位以上作者的期刊

有 2 位作者的期刊

有 3 位作者的期刊

有 5 位以上作者的期刊

书籍引用格式

学位论文引用格式

网页引用格式

专利引用格式

手工熬夜修改参考文献？研飞自动匹配期刊，一键轻松成稿，支持 Word/WPS

投稿经验分享

Preface

A Degenerate Forward-backward Problem Involving the Spectral Dirichlet Laplacian

Normalization of Singular Contact Forms and Primitive 1-forms

Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations

General Form of Second Main Theorem on Generalized p-Parabolic Manifolds for Arbitrary Closed Subschemes

Preface

Integral Closure of Powers of Edge Ideals of Weighted Oriented Graphs

General Form of Second Main Theorem on Generalized p-Parabolic Manifolds for Arbitrary Closed Subschemes

Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations

Normalization of Singular Contact Forms and Primitive 1-forms