自反函数与自反变换

这篇论文的主题是研究由自反函数导出自反级数变换与自反积分变换的一般方法。方法的基本思想来源于著者1964年发表的一篇文章(美国数学家9H.W.Gould曾在德国的Zentralblatt杂志上介绍了该文的主要结果,见该刊1973年254卷#44003)。现在这个工作较系统地发展了早先提出的思想方法,建立了若干一般性定理,有些定理可以作为构造各种级数变换互反公式的方法原则。文中除定理1,2,8之外大部份结果是属于初次发表。值得指出的是,本文中探讨的方法与概念,都是根据对某些特例的分析形成的,积分自反变换方面的结果是以级数变换为借镜,通过类比法得到的。(本文基本内容曾在1981年4月20日大连工学院举办的科学报告会上报告过)。     

鸽笼原理的一个注记

Let d. b be fixed positive integers, d1,s₂,…,s_d) is called a game sum sequence if it is a strictly increasing sequence and s_d≤b. Further, if there exist two positive integers m,n(1≤nm -s_n=k or some term s₁=k(1≤i≤d). S is said to have the property k.     

Structural diversification of phenylspirodrimane lactams by employing a biosynthetic intermediate

Phenylspirodrimanes are a kind of meroterpenoids with structural diversity and complexity, exhibiting a wide of biological properties, especially for the lactam derivatives consisting a γ-lactam moiety and N-linked side chains. These compounds were derived from multi-step combination of enzymatic and non-enzymatic conversions of intermediates in their biosynthetic pathways. Stachbotrydial (2) with an o-phthalaldehyde unit was supposed as the high-reactivity intermediate of phenylspirodrimane lactams via nonenzymatic reaction with amines. In the present work, an effective and non-enzymatic diversification strategy was developed for the structural diversification of phenylspirodrimane lactams including monomers and dimers from 2 by feeding structurally various mono- and diamines in the fungus Stachybotrys chartarum cultures. In total, 24 phenylspirodrimane lactams (1, 3–25) including 18 new compounds were synthesized. Among them, stachybocin A (1), a bioactive phenylspirodrimane lactam dimer, was produced with the yield of 18.7 mg/g of cell dry weight. The structures of these compounds were elucidated by extensive spectroscopic data, single-crystal X-ray diffraction (Cu Kα), and calculated electronic circular dichroism (ECD) analyses. Bioassay revealed that compounds 1, 17, and 24 displayed significant inhibitory effect on the inactivated state of hNa_V 1.2 channels with IC₅₀ values of 0.22, 2.08, and 0.53 µmol/L, respectively. In addition, 1 showed potent protein tyrosine phosphatase 1B (PTP1B) inhibitory, N-methyl-d-aspartate (NMDA) receptor antagonistic, and anti-inflammatory activities.