Class Of Groups Research Articles

Radical Difunctionalization of Unsaturated Hydrocarbons Employing the Same Functional Reagent

AbstractThe radical difunctionalization of unsaturated hydrocarbons serves as an efficient means to rapidly construct molecular skeletons and synthesize‐highly valuable compounds. In this transformational process, diverse positions within unsaturated hydrocarbons are sequentially functionalized by a single radical precursor reagent, thereby achieving highly efficient and selective transformations that promote atom economy. Furthermore, this approach minimizes the generation of numerous byproducts stemming from cross‐coupling reactions between reactants, owing to the reduction of the number of participating components. Therefore, this review provides an in‐depth analysis of the radical difunctionalization of unsaturated hydrocarbons utilizing a single functional reagent in recent decades. The discussion is based on eight different radical classes (carbon‐, nitrogen‐, phosphine‐, oxygen‐, sulfur‐, selenium‐, tellurium‐, and chlorine‐centered radicals), emphasizing the mechanism of specific radical difunctionalization. It also analyzes in detail the regulation of key factors such as regional selectivity, and provides unique insights into reaction transformations.

A generalization of the lower radical type construction for strict and base radical classes

Regarding the construction of strict and base radical classes for the variety of associative rings, we show that “subring” and “accessible subring” are two of a number of substructures that can be used in constructing a radical class. The substructures we focus on are set properties that are transitive across accessible subrings. These substructures allow us to look beyond those that are related by the binary operations of the ring itself, to ones that may only be related by containment. The lower radical type construction defined by these substructures include those of Yu-lee Lee, McDougall and Stewart.

Towards a new progressive labour culture? Industry-oriented channels, bitter and precarious structure of feeling and worker solidarity in China

This article explores the progressive potential of commercial industry-oriented channels (IoCs), an emerging form of media produced by and addressed to workers of specific industries, on China’s digital platforms. Juxtaposing textual analysis with worker-audience interviews and participant observation, I found that despite the collusion of state surveillance and platform governance, IoCs prove instrumental in fostering resistive labour subjects and collectives among ordinary workers. This is due to IoCs’ genre convention and discourses, but more importantly, to worker-audience’s bitter and precarious structure of feeling that mediates their collective reception processes. The findings complicate our understanding of the potential of media/cultural production for labour resistance, highlighting the role of worker-audience in the circuit of progressive labour culture and the potential of commercial media in fostering radical class subjects. Drawing on the analysis, I further advance a model of worker media as double articulation, to open up more hermeneutic and action space for cultural labour activism.

Generalization of primary ideal associated with a special radical class

Generalization of primary ideal associated with a special radical class

On the Baer–Suzuki Width of Some Radical Classes

On the Baer–Suzuki Width of Some Radical Classes

Sets of radical classes

Sets of radical classes

Characterizations of the Baer radical class by almost nilpotent rings

Characterizations of the Baer radical class by almost nilpotent rings

Correction and remark to my paper: "Characterisations of the Baer radical class by almost nilpotent rings"

Correction and remark to my paper: "Characterisations of the Baer radical class by almost nilpotent rings"

Characterization of radicals in polysorbate 80 using electron paramagnetic resonance (EPR) spectroscopy and spin trapping

Polysorbates are an important class of nonionic surfactants that are widely used to stabilize biopharmaceuticals. The degradation of polysorbate 20 and 80 and the related particle formation in biologics are heavily discussed in the pharmaceutical community. Although a lot of experimental effort was spent in the detailed study of potential degradation pathways, the underlying mechanisms are only sparsely understood. Besides enzymatic hydrolysis, another proposed mechanism is associated with radical-induced (auto)oxidation of polysorbates. To characterize the types and the origin of the involved radicals and their propagation in bulk material as well as in diluted polysorbate 80 solutions, we applied electron paramagnetic resonance (EPR) spectroscopy using a spin trapping approach. The prerequisite for a meaningful experiment using spin traps is an understanding of the trapping rate, which is an interplay of (i) the presence of the spin trap at the scene of action, (ii) the specific reactivity of the selected spin trap with a certain radical as well as (iii) the stability of the formed spin adducts (a slow decay rate). We discuss whether and to which extent these criteria are fulfilled regarding the identification of different radical classes that might be involved in polysorbate oxidative degradation processes. The ratio of different radicals for different scenarios was determined for various polysorbate 80 quality grades in bulk material and in aqueous solution, showing differences in the ratio of present radicals. Possible correlations between the radical content and product parameters such as the quality grade, the manufacturing date, the manufacturer, the initial peroxide content according to the certificate of analysis of polysorbate 80 are discussed.

Radicals and idempotents II

Continuing the study of interactions between radical theory and corners, subrings of the form eAe, where e is an idempotent of a ring A, we examine radicals characterized by the presence or absence of idempotents of various types, relative versions of corner-hereditary and corner-strict radicals corresponding to various types of idempotents, and discuss the smallest corner-strict radical class containing a given class.

Brown-McCoy Radical in Restricted Graded Version

Some conjectures related to the radical theory of rings are still open. Hence, the research on the radical theory of rings is still being investigated by some prominent authors. On the other hand, some results on the radical theory of rings can be implemented in another branch or structure. In radical theory, it is interesting to bring some radical classes into graded versions. In this chance, we implement a qualitative method to conduct the research to bring the Brown-McCoy radical class to the restricted graded Brown-McCoy radical class as research objective. We start from some known facts on the Brown-McCoy radical class and furthermore, let G be a group, we explain the Brown-McCoy radical restricted with respect to the group G. The result of this paper, we describe the Brown-McCoy radical in restricted graded version and it is denoted by G^G. Furthermore, we also give the fact by explaining G^G (A)=(〖G(A))〗_G, for any ring A, as the final outcome of this paper.

On the restricted graded Jacobson radical of rings of Morita context

The class of rings $\mathcal{J}=\{A (A,\circ)$ forms a group$\}$ forms a radical class and it is called the Jacobson radical class. For any ring $A$, the Jacobson radical $\mathcal{J}(A)$ of $A$ is defined as the largest ideal of $A$ which belongs to $\mathcal{J}$. In fact, the Jacobson radical is one of the most important radical classes since it is used widely in another branch of abstract algebra, for example, to construct a two-sided brace. On the other hand, for every ring of Morita context $T=\begin{pmatrix} R & V \\ W & S \end{pmatrix}$, we will show directly by the structure of the Jacobson radical of rings that the Jacobson radical $\mathcal{J}(T)= \begin{pmatrix} \mathcal{J}(R) & V_0\\ W_0 & \mathcal{J}(S) \end{pmatrix}$, where $\mathcal{J}(R)$ and $\mathcal{J}(S)$ are the Jacobson radicals of $R$ and $S$, respectively, $V_0=\{v \in V vW \subseteq \mathcal{J}(R)\}$ and $W_0=\{w \in W wV \subseteq \mathcal{J}(S)\}$. This clearly shows that the Jacobson radical is an $N-$radical. Furthermore, we show that this property is also valid for the restricted $G-$graded Jacobson radical of graded ring of Morita context.

On reduced rings with prime factors simple

We obtain a common generalization of the results by Wong and Birkenmeier-Kim-Park, respectively, which say that a reduced ring with unity is strongly (respectively, weakly) regular if and only if all of its prime homomorphic images are division rings (respectively, simple domains). Our arguments are different from those in the known proofs and are quite simple. They also give a characterization of weakly regular reduced rings without unity. This characterization implies in particular that the class of weakly regular reduced rings forms a radical class. However, even if a weakly regular reduced ring has no unity, its prime homomorphic images must be simple domains with unity. In the second part of the paper, we study reduced rings whose prime homomorphic images are simple domains (not necessarily with unity).

A Need or a Force? Shadow Education in Hong Kong From Secondary School Parent’s Perspective

It is becoming more common for students in Hong Kong to take extra lessons after school. Several surveys indicate that more than 70% of students need to take private tutoring classes after school in their final year of secondary school (Bray, 2013). This indicates that “shadow education” has become a trend in Hong Kong. There are different types of private tutoring classes in Hong Kong, such as one-on-one tutoring or tutorial classes for groups of five to eight students. These classes aim to help students to perform better in public examination, but it has become more competitive in recent years. Even if students have satisfactory results at school, they may be expected to take extra classes, since doing so has become a societal trend. However, do students really need to take so many classes after school? Does the quantity of private tutoring lessons taken correlate with good academic results? This study investigates why parents in Hong Kong are sending their children to learning centers after school. Do these children really need extra classes, or are they being affected by the surrounding area?

Connectednesses of graphs and congruences

A connectedness of graphs is the analogue of the radical class of algebraic structures. The similarities (and differences) between these two theories and other radical theories have been explored at many different levels of generality. The recent development of a theory of congruences for graphs has opened up the possibility to explore and further strengthen this analogy. It is shown that a graph connectedness can be characterized with the use of congruences in an exact analogous way as the radical classes of associative rings using ideals.

О максимальных подформациях n-кратно Ω-расслоенных формаций конечных групп

Only finite groups are considered in the article. Among the classes of groups the central place is occupied by classes closed regarding homomorphic images and subdirect products which are called formations. We study Ω-foliateded formations constructed by V. A. Vedernikov in 1999 where Ω is a nonempty subclass of the class I of all simple groups. Ω-Foliated formations are defined by two functions — an Ω-satellite f : Ω ∪ {Ω 0} → {formations} and a direction ϕ : I → {nonempty Fitting formations}. The conception of multiple locality introduced by A. N. Skiba in 1987 for formations and further developed for many other classes of groups, as applied to Ω-foliated formations is as follows: every formation is considered to be 0-multiple Ω-foliated with a direction ϕ; an Ω-foliated formation with a direction ϕ is called an n-multiple Ω-foliated formation where n is a positive integer if it has such an Ω-satellite all nonempty values of which are (n − 1)-multiple Ω-foliated formations with the direction ϕ. The aim of this work is to study the properties of maximal n-multiple Ω-foliated subformations of a given n-multiple Ω-foliated formation. We use classical methods of the theory of groups, of the theory of classes of groups, as well as methods of the general theory of lattices. In the paper we have established the existence of maximal n-multiple Ω-foliated subformations for the formations with certain properties, we have obtained the characterization of the formation ΦnΩϕ (F) which is the intersection of all maximal n-multiple Ω-foliated subformations of the formation F, and we have revealed the relation between a maximal inner Ω-satellite of 1-multiple Ω-foliated formation and a maximal inner Ω-satellite of its maximal 1-multiple Ω-foliated subformation. The results will be useful in studying the inner structure of formations of finite groups, in particular, in studying the maximal chains of subformations and in establishing the lattice properties of formations.

О влиянии свойств минимальных не F-групп на классы групп

О влиянии свойств минимальных не F-групп на классы групп

Algebraic Structure of Supernilpotent Radical Class Constructed from a Topology Thychonoff Space

A radical class of rings is called a supernilpotent radicals if it is hereditary and it contains the class for some positive integer In this paper, we start by exploring the concept of Tychonoff space to build a supernilpotent radical. Let be a Tychonoff space that does not contain any isolated point. The set of all continuous real-valued functions defined on is a prime essential ring. Finally, we can show that the class of rings is a supernilpotent radical class containing the matrix ring .

Reinterpreting the Chinese Revolution: The Balance between Radical and Moderate Approaches, 1937–1945

The success of the Chinese Communist Party (CCP) by the end of the Sino-Japanese War (1937–1945) has generally been credited to its moderate approach to mobilizing the local peasantry through appeals to anti-Japanese nationalism and programs of social justice. However, the evidence presented in this article demonstrates that during late 1939 and early 1940 in some counties of the Southwest Shanxi Base Area and other major North China base areas the CCP abandoned its moderate approach and promoted a radical and violent class struggle. Based on its experiences in 1939–1940, the CCP created a model for mobilization in early 1942 that balanced radical and moderate approaches, which was then gradually applied to all Communist base areas. This article argues that the CCP relied on a combination of two contrasting and complementary approaches—radical and moderate—both of which played an indispensable role in its success by 1945.

A comparison of Kurosh–Amitsur and base radical classes

In this paper we use class operators to compare and contrast Kurosh-Amitsur radical classes and base radical classes in a setting where they do not coincide to highlight some of the consequences of changing ‘ideal’ to ‘accessible’ in the construction. We show the result of Puczylowski that the largest hereditary subclass of a Kurosh–Amitsur radical class is a Kurosh–Amitsur radical class does not extend to the largest hereditary subclass of a base radical class being base radical and uncover a class of algebras which are not Kurosh–Amitsur radical-semisimple, nor base radical-semisimple, but rather Kurosh–Amitsur radical-base semisimple.