Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

Coupling of Biomolecular Logic Gates with Electronic Transducers: From Single Enzyme Logic Gates to Sense/Act/Treat Chips

The integration of biomolecular logic principles with electronic transducers allows designing novel digital biosensors with direct electrical output, logically triggered drug‐release, and closed‐loop sense/act/treat systems. This opens new opportunities for advanced personalized medicine in the context of theranostics. In the present work, we will discuss selected examples of recent developments in the field of interfacing enzyme logic gates with electrodes and semiconductor field‐effect devices. Special attention is given to an enzyme OR/Reset logic gate based on a capacitive field‐effect electrolyte‐insulator‐semiconductor sensor modified with a multi‐enzyme membrane. Further examples are a digital adrenaline biosensor based on an AND logic gate with binary YES/NO output and an integrated closed‐loop sense/act/treat system comprising an amperometric glucose sensor, a hydrogel actuator, and an insulin (drug) sensor.     

关于左完全幺半群

设Ｓ是左完全幺半群．本文讨论了左，右Ｓ－系的链条件，特别地证明了右Ｓ－系的Ｂｊｏｒｋ定理．     

一类循环系的平坦性

设Ｓ是幺半群,ｘ_１,ｘ₂,…∈Ｓ且满足ｘ_i+１ｘ_i＝ｘ_i,ｉ＝１,２……ｙ是S中的任意元素,记H={(yx_i,x_i)|i=1,2,…}.设ρ(H)是S的由Ｈ生成的最小右同余,本文证明了S／ρ（Ｈ）是平坦右Ｓ－系．     

占座效应的数学建模与统计分析

利用因果图模型及其可识别性理论对占座效应 ,即占座行为对座位使用率的影响进行了建模 .并利用这一模型对实际例子中的占座效应进行了分析 ,最终得出占座行为对实例中座位使用率的影响程度     

TO LEARN OR TO CHANGE: OPTIMAL R&D INVESTMENTS UNDER UNCERTAINTY IN THE CASE OF CLIMATE CHANGE

When studying R&D investments in technologies that address potential damage from climate change (termed as “research to change” or RTC), current literature overlooks the effects of purchased learning (i.e., learn through scientific research, termed as “research to learn” or RTL) about climate change. We investigate interactions between optimal R&D investments in RTC and RTL under uncertainty in climate change and research outcomes, while accounting for the positive impact that successful RTL may have on RTC outcome. We find that simultaneously investing in both RTL and RTC may be optimal when the probability that climate change imposes a specific level of damage is either moderate or very high and when RTL cost is relatively low. Whenever RTL and RTC are conducted simultaneously, then they substitute. However, when it is not optimal to conduct RTC and RTL simultaneously, then an increase in RTC cost decreases, at least weakly, RTL investment (i.e., RTL and RTC complement). When the probability that climate change imposes damage increases, then the optimal RTL investment may first decrease and then increase. Moreover, we identify conditions under which either the precautionary principle or the learn‐then‐act principle should be followed regarding R&D investments.     

Some homological characterizations of semigroups and semirings

In this paper we characterize semirings all of whose p-injective semimodules are injective. We also classify monoids all of whose p-injective acts are injective.     

C(P)系对幺半群的刻画

设S是幺半群.本文介绍并研究了正则右系的一个推广.一个右S-系A称为C(P)系,如果A的所有循环子系满足条件(P).本文证明了右C(P)系形成了右S-系的一个新的类,同时,C(P)性质为幺半群同调分类研究提供了新思路.     

p-内射半模

给出p-内射半模的概念,并在此基础上刻划了p-内射半模与Hom函子的关系.接下来证得p-内射半模的直积与直和仍保持是p-内射半模。以及讨论了在无零因子半环中,p-内射半模与可除半模的关系。最后由于p-内射半模定义的条件比内射半模弱,证明了在任意真半环上存在非零的p-内射半模。     

氮杂环化合物对苄醇电氧化的催化媒介作用研究进展

将芳香醇选择性地氧化为相应的羰基化合物(醛或酮)一直是化学研究人员面临的挑战之一。有机电合成技术中的间接电氧化法是进行芳香醇电氧化反应的常用方法,其中通过调控有机媒质结构是提高醇氧化选择性的一种有效途径。本文综述了几类含不同框架的有机媒质及其在醇的电化学氧化转化中的应用,介绍了这几类有机媒质的结构及其在间接电氧化反应中的作用机制,并进一步阐述了如何提高有机媒质的稳定性、溶解性和催化活性,实现醇的可控氧化转化。