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Considering two types of subsidies for producers (supplier and manufacturer) and one for consumers based on product greenness and sales quantity, this study aims to formulate optimal supply chain green innovation and subsidy strategies, and to achieve this goal with the support of information systems.

This study introduces a composite green-product supply chain where suppliers focus on green innovation for component greenness and manufacturers focus on green innovation for manufacturing process greenness. Game theory modeling is applied to investigate the differences of product greenness, supply chain members’ profit and social welfare under different government subsidy strategies.

Increasing the unit greenness subsidy coefficient can boost product greenness and supply chain members’ profits, but does not always raise social welfare. When the government exclusively offers subsidies to producers, subsidies should be allocated to suppliers when there is a significant disparity in supply chain green innovation costs. Conversely, it is more beneficial to subsidize manufacturers. Consumer subsidies have the potential to enhance both environmental and economic performance in the supply chain compared with producer-exclusive subsidies, but may not always maximize social welfare when supply chain members have low unit costs associated with green innovation.

This study examines the optimal decisions for green supply chain innovation and government subsidy strategies. Supply chain members and the government can use the information system to collect and evaluate the cost of upstream and downstream green innovation, and then develop reasonable collaborative green innovation and subsidy strategies.

This study aimed to analyze the free vibration of a radially graded Ni-Al2O3-based functionally graded (FG) disk with uniform thickness.

Using the energy method, natural frequencies of rotating and non-rotating disks were determined at the limit elastic angular speed. Material properties were estimated using a modified rule of mixture. Both even and uneven porosity variation effects were considered in the material modeling. Finite element analysis validated the analytical approach.

The study explored limit angular speeds and natural frequencies across various grading indices, investigating the impact of porosity types and grading indices on these parameters.

Insights from this research are valuable for researchers and design engineers involved in modeling and fabricating porous FG disks, aiding in more effective design and manufacturing processes.

This study contributes to the field by providing a comprehensive analysis of free vibration behavior in radially graded Ni-Al2O3-based FG disks. The incorporation of material modeling considering both even and uneven porosity variation adds originality to the research. Additionally, the validation through finite element analysis enhances the credibility of the findings.

Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid.

The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles.

Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios.

The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.

The goal of this article is to introduce the notion of a grey relation between grey sets using grey numbers.

This study uses the grey number to create novel ideas of grey sets. We suggest several operations that can be performed on it, including the union, intersection, join, merge, and composition of grey relations. In addition, we present the definitions of reflexive, symmetric, and transitive grey relations and analyze certain characteristics associated with them. Furthermore, we formulate the concept of the grey equivalence relation, apply it to the study of the grey equivalence class over the grey relation, and go over some of its features.

We present new algebraic aspects of grey system theory by defining grey relations and then analyzing their characteristic features.

This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. As such, it can be applied to create rough approximations as well as congruences in algebras, topologies, and semigroups.

The presented notions are regarded as new algebraic approaches in grey system theory for the first time. Additionally, some fundamental operations on grey relations are also investigated. Consequently, different types of grey relations, such as reflexive, symmetric, and transitive relations, are discussed. Then, the grey equivalence class derived from the grey equivalence relation is demonstrated, and its properties are examined.

The purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is connected. Also, the purpose is to generalize some of the known results proved by Duric et al. on the total zero-divisor graph of R.

We use the methods from commutative ring theory on primary decomposition and strong primary decomposition of ideals in commutative rings. The structure of ideals, the primary ideals, the prime ideals, the set of zero-divisors of the finite direct product of commutative rings is used in this paper. The notion of maximal Nagata prime of the zero-ideal of a commutative ring is also used in our discussion.

For a commutative ring R with identity, ZT(R) is the intersection of the zero-divisor graph of R and the total graph of R induced by the set of all non-zero zero-divisors of R. The zero-divisor graph of R and the total graph of R induced by the set of all non-zero zero-divisors of R are well studied. Hence, we determine necessary and sufficient condition so that ZT(R) agrees with the zero-divisor graph of R (respectively, agrees with the total graph induced by the set of non-zero zero-divisors of R). If Z(R) is an ideal of R, then it is noted that ZT(R) agrees with the zero-divisor graph of R. Hence, we focus on rings R such that Z(R) is not an ideal of R. We are able to characterize R such that ZT(R) is connected under the assumptions that the zero ideal of R admits a strong primary decomposition and Z(R) is not an ideal of R. With the above assumptions, we are able to determine the domination number of ZT(R).

Duric et al. characterized Artinian rings R such that ZT(R) is connected. In this paper, we extend their result to rings R such that the zero ideal of R admits a strong primary decomposition and Z(R) is not an ideal of R. As an Artinian ring is isomorphic to the direct product of a finite number of Artinian local rings, we try to characterize R such that ZT(R) is connected under the assumption that R is ta finite direct product of rings R1, R2, … Rn with Z(Ri) is an ideal of Ri for each i between 1 to n. Their result on domination number of ZT(R) is also generalized in this paper. We provide several examples to illustrate our results proved.

The implication of this paper is that the existing result of Duric et al. is applicable to large class of commutative rings thereby yielding more examples. Moreover, the results proved in this paper make us to understand the structure of commutative rings better. It also helps us to learn the interplay between the ring-theoretic properties and the graph-theoretic properties of the graph associated with it.

The results proved in this paper are original and they provide more insight into the structure of total zero-divisor graph of a commutative ring. This paper provides several examples. Not much work done in the area of total zero-divisor graph of a commutative ring. This paper is a contribution to the area of graphs and rings and may inspire other researchers to study the total zero-divisor graph in further detail.

The present work focuses on the primality and the Cartesian product of graphs.

Given a graph G, a subset M of V (G) is a module of G if, for a, b ∈ M and x ∈ V (G) \ M, xa ∈ E(G) if and only if xb ∈ E(G). A graph G with at least three vertices is prime if the empty set, the single-vertex sets and V (G) are the only modules of G.

Motivated by works obtained on “the Cartesian product of graphs” and “the primality,” this paper creates a link between the two notions.

In fact, we study the primality of the Cartesian product of two connected graphs minus k vertices, where k ∈ {0, 1, 2}.

The objective of this paper is to formulate the precise meanings of grey graphs and examine some of their properties.

This article introduces innovative concepts of grey sets based on the grey number. We establish the grey graphs and examine their essential properties as isomorphisms of these graphs. Additionally, we explore the notion of a grey-complete graph and demonstrate certain properties of self-complementary grey-complete graphs.

We showcase novel facets of grey system theory through the establishment of the structures of grey graphs, and the subsequent analysis of their distinctive traits.

This article provides us with a new theoretical direction for grey system theory according to grey numbers. Thus, we present test examples that explain the routes between cities and the electrical wires between homes. Furthermore, the concept of grey graphs can be applied in several areas of engineering, computer science, neural networks, artificial intelligence, and medical diagnosis.

The proposed concepts are considered novel mathematical directions in grey system theory for the first time. Some operations of grey graphs are also explored.

The management issues of this article, and the author is attempting to address these issues, are as follows: What is the optimal decision of each entity in the closed-loop supply chain for the cascading utilization of power batteries under three government measures: no subsidies, subsidies and rewards and punishments? How do different measures affect the process of cascading the utilization of power batteries? Which measures will help incentivize cascading utilization and battery recycling efforts?

The paper uses game analysis methods to study the optimal decisions of various stakeholders in the supply chain under the conditions of subsidies, non-subsidies and reward and punishment policies. The impact of various parameters on the returns of game entities is tested through Matlab numerical simulation.

The analysis discovered that each party in the supply chain will see an increase in earnings if the government boosts trade-in subsidies, which means that the degree of recycling efforts of each entity will also increase; under the condition with subsidies, the recycling efforts and echelon utilization rates of each stakeholder are higher than those under the incentive and punishment measure. In terms of the power battery echelon’s closed-loop supply chain incentive, the subsidy policy exceeds the reward and punishment policy.

The article takes the perspective of differential games and considers the dynamic process of exchanging old for new, providing important value for the practice of using old for new behavior in the closed-loop supply chain of power battery cascading utilization.

A new model for two-sided platforms is presented, incorporating both the original business and an expanded (new) business. Previous studies have neglected the impact of technology R & D on the new business aspect of two-sided platforms. This study addresses this gap by examining the technology R & D effect on the new business while also considering the congestion effect on the original business. It investigates the optimal pricing and user scales for both the original and new businesses. Additionally, the profits of the original business, the new business, and the overall two-sided platform are analyzed.

Previous studies have overlooked the technology R & D effect on the new business aspect of two-sided platforms. Therefore, this study focuses on examining the technology R & D effect on the new business. Additionally, the congestion effect on the original business is considered. To determine the optimal prices for both sides of the original and new businesses, a game sequence model is introduced.

The optimal price on the service buyers (defined b side) of new business increases only with regard to technology R & D effect on b side of new business increasing. The optimal price on b side of new business is equal to half of the b-side R & D effect. The optimal profit of original business decreases with regard to the technology R & D effect of new business and cross-market network effect on the services provider (defined s side) between original business and new business increasing, respectively. To gain optimal profit of two-sided platform, the two-sided platform adopts some strategies to improve the congestion.

A new two-sided platform model is stated, in which the technology R & D effect is embraced. The expanded business scenario of two-sided platform is considered, that is, the two-sided platform has one business firstly and a new business is developed or improved of two-sided platform. To solve the prices strategy of original business and new business, a game sequence of the original business and new business is presented.

Due to the important and extensive use of graphene in the engineering structures, the purpose of this paper is to investigate the low-velocity impact (LVI) response of a graphene-reinforced plate with a rectangular central hole.

In this paper, Halpin-Tsai theory is used to model the mechanical properties of the plate made of polymethyl methacrylate (PMMA) resin and graphene particles. First, the plate displacement field is presented, and then the strains and stresses are obtained. The motion equations are extracted using energy equations, Ritz method and generalized Lagrange equations. The verification of theoretical formulation shall be carried out using the ABAQUS finite element software suite.

The effects of graphene volume fraction, approaching the impact point to the corner of the rectangular plate, and different boundary conditions of the plate are studied for LVI of impactor with spherical tip on the rectangular central hole reinforced by graphene. Important responses of the impact, such as the contact force between the impactor and the plate as well as the displacement of the plate at the impact place, are investigated and analyzed in this research.

Considering the wide application of graphene in the engineering structures, the simulation of the LVI on the graphene-reinforced plate made of PMMA resin with a rectangular central hole is carried out in this paper using numerical and theoretical modeling.