Green's function for a third-order generalized right focal problem

We determine the Green's function for the third-order three-point generalized right focal boundary value problem

     

Continuity in G

For a discrete group G, we consider βG, the Stone– ech compactification of G, as a right topological semigroup, and G^*=βGG as a subsemigroup of βG. We study the mappings λ_p^* :G^*→G^*and μ^* :G^*→G^*, the restrictions to G^* of the mappings λ_p :βG→βG and μ :βG→βG, defined by the rules λ_p(q)=pq, μ(q)=qq. Under some assumptions, we prove that the continuity of λ_p^* or μ^* at some point of G^* implies the existence of a P-point in ω^*.     

非光滑多目标规划的最优性

本文给出了一种新的右上导数定义,利用这一右上导数定义了几类广义凸性条件,进而讨论了非光滑多目标规划的最优性．包括Ｆｒｉｔｚ－Ｊｏｈｎ条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ条件．     

彭罗斯对广义相对论和黑洞理论的贡献

这篇文章列出了2020年诺贝尔物理学奖获得者彭罗斯对广义相对论和黑洞理论做出的重要贡献.它包括著名的奇点定理、彭罗斯图、彭罗斯过程和宇宙监督假设等.介绍了彭罗斯和霍金之间的友谊和合作.也简要介绍了另两位2020年诺贝尔物理学奖获得者根泽尔和盖兹对存在于银河系中心的超大质量致密天体的发现.     

Non-associative algebras containing the matrix ring

The Lie admissible non-associative algebra is defined in the papers [Seul Hee Choi, Ki-Bong Nam, Derivations of a restricted Weyl type algebra I, Rocky Mountain J. Math. 37 (6) (2007) 1813–1830; Seul Hee Choi, Ki-Bong Nam, Weyl type non-associative algebra using additive groups I, Algebra Colloq. 14 (3) (2007) 479–488; Ki-Bong Nam, On Some Non-associative Algebras using Additive Groups, Southeast Asian Bull. Math., vol. 27, Springer-Verlag, 2003, 493–500]. We define in this work the algebra which generalizes the previous one and is not Lie admissible. We prove that the antisymmetrized Lie algebra is simple and contains the simple Lie algebra . We also prove that the matrix ring is embedded in .     

Groupoids with quasigroup and Latin square properties

Connections of some groupoid identities with the quasigroup and Latin square properties are investigated using combinatorial methods.     

Amarts: A class of asymptotic martingales B. Continuous parameter

A continuous-parameter ascending amart is a stochastic process (X_t)_{t +} such that E[X_τn] converges for every ascending sequence (τ_n) of optional times taking finitely many values. A descending amart is a process (X_t)_{t +} such that E[X_τn] converges for every descending sequence (τ_n), and an amart is a process which is both an ascending amart and a descending amart. Amarts include martingales and quasimartingales. The theory of continuous-parameter amarts parallels the theory of continuous-parameter martingales. For example, an amart has a modification every trajectory of which has right and left limits (in the ascending case, if it satisfies a mild boundedness condition). If an amart is right continuous in probability, then it has a modification every trajectory of which is right continuous. The Riesz and Doob-Meyer decomposition theorems are proved by applying the corresponding discrete-parameter decompositions. The Doob-Meyer decomposition theorem applies to general processes and generalizes the known Doob decompositions for continuous-parameter quasimartingales, submartingales, and supermartingales. A hyperamart is a process (X_t) such that E[X_τn] converges for any monotone sequence (τ_n) of bounded optional times, possibly not having finitely many values. Stronger limit theorems are available for hyperamarts. For example: A hyperamart (which satisfies mild regularity and boundedness conditions) is indistinguishable from a process all of whose trajectories have right and left limits.     

Essay: Cosmic Censorship: The Role of Quantum Gravity

The cosmic censorship hypothesis introduced by Penrose thirty years ago is still one of the most important open questions in classical general relativity. In this essay we put forward the idea that cosmic censorhip is intrinsically a quantum gravity phenomena. To that end, we construct a gedanken experiment in which cosmic censorship is violated within the purely classical framework of general relativity. We prove, however, that quantum effects restore the validity of the conjecture. This suggests that classical general relativity is inconsistent and that cosmic censorship might be enforced only by a quantum theory of gravity.     

关于空间型中的正螺面

将正螺面引入到一般的空间型中,在Beltrami-Klein坐标系下统一加以表示,并一致地详尽考察其度量、法向、第二基本形式及主曲率,推出正螺面是极小曲面.     

左截断右删失下乘积限过程的振动模的强极限定理

本文在左截断右删失模型下获得了乘积限过程和累积失效率过程的振动模和Ｌｉｐｓｃｈｉｔｚ－１２模的强一致收敛的精确速度．作为定理的应用，推导了各种核密度估计和失效率估计的强一致收敛的精确速度．