On Self-Aggregations of Min-Subgroups

Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

How Does Tie Strength Dispersion within Inter-Organizational Networks Affect Agricultural Technological Innovation? Evidence from China

Agricultural technology is key to ensuring food security. Innovation in agricultural technology plays a vital role in increasing national food production. Collaborative innovation has become an essential form of technological innovation in the new era. Although there has been a large body of literature exploring the influencing factors on technological innovation, how tie strength dispersion within inter-organizational networks affects agricultural technological innovation has not been systematically studied. In this research, we use a cooperative network to investigate how relational divisive faultlines caused by the uneven distribution of the strength of inter-organizational relationships affects agricultural technological innovation through the subgroup structure, and the moderating role of position embeddedness. This article uses the Derwent Innovations Index to select agricultural technology joint patent applications from 2000 to 2018 to build a cooperation network, and uses multiple linear regression to conduct an empirical analysis. The empirical results show that the relational divisive faultlines have a positive effect on the subgroup structure. There is an inverted U-shaped relationship between the subgroup structure and agricultural technological innovation. The initial stage of subgroup formation can transmit the information between the subgroups in time and promote the efficiency of agricultural technological innovation. However, as the degree of subgroup cohesion increases, the phenomenon of “in-group” and “out-of-group” will be formed, which will inhibit information exchange, having a negative impact on agricultural technological innovation. In addition, positional embeddedness has a significant positive moderating effect between relational divisive faultlines and agricultural technological innovation. This research provides a theoretical basis for understanding how the overall network relationship strength distribution affects technological innovation by exploring the micro-process of the structural changes of the cooperation network. Moreover, it has specific guiding significance for the organization to participation in a cooperation network to improve the efficiency of agricultural technological innovation.

Electric Vehicle Battery Disassembly Sequence Planning Based on Frame-Subgroup Structure Combined with Genetic Algorithm

Since the electric vehicle battery (EVB) is wildly recycled in industry, the disassembly procedures of variable EVBs is so important that can influence the efficiency and environmental impacts in remanufacturing. To improve disassembly efficiency in EVB remanufacturing, a disassembly sequence planning method based on frame-subgroup structure is proposed in this paper. Firstly, the improved disassembly relation hybrid graph and disassembly relation matrix are proposed to identify the disassembly precedence relationship and connection relationship between the components in EVB. Secondly, the frame - subgroup structure is given, and the method for solving disassembly sequence planning with frame-subgroup structure and genetic algorithm is introduced. In this method, to simplify the series of processes such as encoding, decoding, crossover and mutation, the solution space composed of all disassembly sequences is transformed into the positive integer sequence for the disassembly efficiency in battery remanufacturing. Finally, the case study of EVB disassembly sequence planning is presented to validate the feasibility of this proposed method. Comparing with other traditional methods, the advantage and application of this proposed method are introduced.

Finite groups with given non-nilpotent maximal subgroups of prime index

The subgroup structure of a finite group, under the assumption that its every non-nilpotent maximal subgroup has prime index, is studied in the paper.

-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS

Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p>0$ and let $X=\text{PSL}_{2}(p)$ be a subgroup of $G$ containing a regular unipotent element $x$ of $G$. By a theorem of Testerman, $x$ is contained in a connected subgroup of $G$ of type $A_{1}$. In this paper we prove that with two exceptions, $X$ itself is contained in such a subgroup (the exceptions arise when $(G,p)=(E_{6},13)$ or $(E_{7},19)$). This extends earlier work of Seitz and Testerman, who established the containment under some additional conditions on $p$ and the embedding of $X$ in $G$. We discuss applications of our main result to the study of the subgroup structure of finite groups of Lie type.