Linear Operators That Strongly Preserve Nilpotent Matrices over Antinegative Semirings

Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

Discussion on the Complex Structure of Nilpotent Lie Groups Gk

Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.

THE CLASSIFICATION OF NILPOTENT LEIBNIZ 3-ALGEBRAS

The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.

深水采油树Spring-Seal密封圈接触模型构建与实验测试

为提高深水采油树在高压、高温、低温等工况下长时间工作的稳定性,对采油树密封圈进行重新设计,提出Spring-Seal密封圈(以下简称S密封圈);基于赫兹接触理论、填料密封接触理论,重新构建S密封圈接触力学模型;建立有限元仿真分析模型,分析不同条件下S密封圈的密封性能,同时验证新建接触模型的合理性;利用实验测试S密封圈的实际密封效果。研究结果表明:S密封圈在高压、高温、低温等工况下能够长时间稳定工作且密封性能良好。研究结果可为S密封圈的接触研究及工程运用提供理论参考。

Generalized Derivations with Skew Nilpotent Values on Lie Ideals

This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.

Using Normal Form of Nilpotent Matrices over Finite Fields to Construct Cartesian Authentication Codes

Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.

Finitely Generated Torsion-free Nilpotent Groups Admitting an Automorphism of Prime Order

Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.

Limit Cycle Bifurcations in a Class of Cubic System near a Nilpotent Center

In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.

一种构造高维Nilpotent正规型的方法

正规型方法是一种有效的简化一类非线性方程的方法．今提出了一种简便的代数方法去构造高维非线性系统的Ｎｉｌｐｏｔｅｎｔ范式．通过引入一系列简单的变换和代数运算，而无需求解任何偏微分方程，即可得到高维非线性系统的Ｎｉｌｐｏｔｅｎｔ范式．以四维非线性系统为例介绍这个方法，该方法完全适用于分析高于四维的非线性系统的Ｎｉｌｐｏｔｅｎｔ范式．

MAXIMAL NILPOTENT IDEALS AND ISOMORPHISMS OF LARGE SUBALGEBRAS OF NEST ALGEBRAS

Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.

关于Qnilpotent环（英文）

对于环R中的一个元素a,如果存在p^2=p∈comm^2(a)使得a+p∈R^(qnil),则称a为qnilpotent的,一个环称为qnilpotent的如果环中每一个元素都是qnilpotent的.文章证明了qnilpotent环是quasipolar的,若一个环R是qnilpotent的,则eRe也是qnilpotent的.同时给出了一些qnilpotent环与其相关的环之间的充分必要条件.证明了若R是一个局部环,则n×n阶上三角矩阵环是qnilpotent当且仅当R是唯一bleached的并且R/J(R)■Z_2.

A Note on Nilpotent Operators

We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤(||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup and Harpe in [1] is suggested. We establish an upper bound for the numerical radius of nilpotent operators.

Two Theorems about Nilpotent Subgroup

In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.

The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H^n×R^k

In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.

A characteristic condition of finite nilpotent group

This paper gives a characteristic condition of finite nilpotent group under the assumption that all minimal subgroups of G are well-suited in G.

Rising utilization of stable isotopes in tree rings for climate change and forest ecology

Analyses of stable isotopes(C,O,H)in tree rings are increasingly important cross-disciplinary programs.The rapid development in this field documented in an increasing number of publications requires a comprehensive review.This study includes a bibliometric analysis-based review to better understand research trends in tree ring stable isotope research.Overall,1475 publications were selected from the Web of Science Core Collection for 1974-2023.The findings are that:(1)numbers of annual publications and citations increased since 1974.From 1974 to 1980,there were around two relevant publications per year.However,from 2020 to 2022,this rose sharply to 109 publications per year.Likewise,average article citations were less than four per year before 1990,but were around four per article per year after 2000;(2)the major subjects using tree ring stable isotopes include forestry,geosciences,and environmental sciences,contributing to 42.5%of the total during 1974-2023;(3)the top three most productive institutions are the Chinese Academy of Sciences(423),the Swiss Federal Institute for Forest,Snow and Landscape Research(227),and the University of Arizona(204).These achievements result from strong collaborations;(4)review papers,for example,(Dawson et al.,Annu Rev Ecol Syst 33:507-559,2002)and(McCarroll and Loader,Quat Sci Rev 23:771-801,2004),are among the most cited,with more than 1000 citations;(5)tree ring stable isotope studies mainly focus on climatology and ecology,with atmospheric CO_(2) one of the most popular topics.Since 2010,precipitation and drought have received increasing attention.Based on this analysis,the research stages,key findings,debated issues,limitations and direc-tions for future research are summarized.This study serves as an important attempt to understand the progress on the use of stable isotopes in tree rings,providing scientific guid-ance for young researchers in this field.

Herz Spaces on Nilpotent Lie Groups and Its Applications

In this paper, we define Herz type spaces on nilpotent Lie groups and give the boundedess of heat kernel and Riesz transform on Herz spaces.

Atoms of Lattices of Supernilpotent and Special Radicals

In this paper we define pure-supernilpotent radical and show that the class of all pureaupernilpotent radicals forms a complete lattice. We discuss some open questions on lattices of supernilpotent and special radicals [5, 6] and obtain some new results.