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This study aims to examine the perceptions of students about learning science and physics using the engineering design process (EDP).

The study employed a mixed-methods research design: The quantitative session features a pre–post-test control group study. In the qualitative aspect, the study conducted semistructured interviews for data collection. In the experimental group, the flipped classroom (FC) model and an instructional design are combined to design, develop and implement a physics course using the steps of the EDP, while the conventional method was applied to the control group. The respondents are students of the Department of Mechanical Engineering at Cao Thang Technical College in Vietnam for the academic year 2022–2023. The control and experimental groups are composed of 80 students each. An independent sample Mann–Whitney U test is applied to the quantitative data, while thematic analysis is employed for the qualitative data.

The results demonstrate a statistically significant difference between the experimental and control groups in terms of perceptions about learning science and physics using the EDP, which, when combined with a FC, enhances physics learning for engineering students.

This study implemented the EDP in teaching physics to first-year engineering students in the Department of Mechanical Engineering using the combined FC and instructional design models. The results revealed that a difference exists in the perception of the students in terms of integrating the EDP into learning physics between the experimental and control groups. The experimental group, which underwent the EDP, obtained better results than did the control group, which used the conventional method. The results demonstrated that the EDP encouraged the students to explore and learn new content knowledge by selecting the appropriate solution to the problem. The EDP also helped them integrate new knowledge and engineering skills into mechanical engineering. This research also introduced a new perspective on physics teaching and learning using the EDP for engineering college students.

The research findings are important for teaching and learning physics using EDP in the context of engineering education. Thus, educators can integrate the teaching and learning of physics into the EDP to motivate and engage student learning.

Using the EDP combined with a FC designed under stages of the analyze, design, develop, implement and evaluate (ADDIE) model has enhanced the learning of physics for engineering college students.

Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L²_α (K), where K=0,+∞×0,+∞[.

The author has employed the results developed by Titchmarsh, of reference number [1].

In this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform.

To the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.

The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations x(6)+(1+p2+q2)x… .+(p2+q2+p2q2)x¨+p2q2x=εF(x,ẋ,x¨,x…,x… .,x(5)), where p and q are rational numbers different from 1, 0, −1 and p ≠ q, ε is a small enough parameter and F ∈ C² is a nonlinear autonomous function.

The authors shall use the averaging theory to study the periodic solutions for a class of perturbed sixth-order autonomous differential equations (DEs). The averaging theory is a classical tool for the study of the dynamics of nonlinear differential systems with periodic forcing. The averaging theory has a long history that begins with the classical work of Lagrange and Laplace. The averaging theory is used to the study of periodic solutions for second and higher order DEs.

All the main results for the periodic solutions for a class of perturbed sixth-order autonomous DEs are presenting in the Theorem 1. The authors present some applications to illustrate the main results.

The authors studied Equation 1 which depends explicitly on the independent variable t. Here, the authors studied the autonomous case using a different approach.

The aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles.

Using the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles.

Findings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles.

To the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.

The paper attempts to discuss the optimal pricing decisions under the decentralized and centralized decision and analyze the influence of online reviews and in-sale service on dual-channel supply chain. Finally, the authors design a two-part tariff coordination mechanism.

To deal with this pricing conflict problems of dual-channel supply chain consisting of dominant manufacturer and a retailer, considering the fact that online reviews and in-sale service are important factors on consumers’ purchase decisions, the authors establish some basic models and exploit them to discuss the optimal pricing decisions under the decentralized and centralized decision and analyze the influence of online reviews and in-sale service on dual-channel supply chain. Finally, the authors design a profit-sharing coordination mechanism.

The results show that the optimal online direct selling price is positively correlated with product perceived quality obtained from online reviews and negatively correlated with the in-sale service. The traditional retail price is positively correlated with the in-sale service and weakly correlated with online reviews. For the manufacturer and retailer, whether decentralized decision or coordination contract, their profits increase with the increase of the in-sale service in a certain range and quality perceived from spontaneous online reviews. Online reviews and in-sale service are important factors on consumers’ purchase decisions. Positive in-sale services and online reviews can provide consumers with a better shopping experience, thereby promoting their enthusiasm for shopping and improving their quality of life. The two-part tariff coordination mechanism improves the profits of the manufacturer and the traditional retailer, respectively, through the transfer fee.

The proposed approach can well analyze the channel conflicts and pricing problems between retailers and manufacturers with respect to product offline price and online price. The analysis and results can inform decision-making for manufacturers and retailers.

The author studies forms over finite fields obtained as the determinant of Hermitian matrices and use these determinatal forms to define and study the base polynomial of a square matrix over a finite field.

The authors give full proofs for the new results, quoting previous works by other authors in the proofs. In the introduction, the authors quoted related references.

The authors get a few theorems, mainly describing some monic polynomial arising as a base polynomial of a square matrix.

As far as the author knows, all the results are new, and the approach is also new.

The purpose of this paper is to develop optimal estimation procedures for the stress-strength reliability (SSR) parameter R = P(X > Y) of an inverse Pareto distribution (IPD).

We estimate the SSR parameter R = P(X > Y) of the IPD under the minimum risk and bounded risk point estimation problems, where X and Y are strength and stress variables, respectively. The total loss function considered is a combination of estimation error (squared error) and cost, utilizing which we minimize the associated risk in order to estimate the reliability parameter. As no fixed-sample technique can be used to solve the proposed point estimation problems, we propose some “cost and time efficient” adaptive sampling techniques (two-stage and purely sequential sampling methods) to tackle them.

We state important results based on the proposed sampling methodologies. These include estimations of the expected sample size, standard deviation (SD) and mean square error (MSE) of the terminal estimator of reliability parameters. The theoretical values of reliability parameters and the associated sample size and risk functions are well supported by exhaustive simulation analyses. The applicability of our suggested methodology is further corroborated by a real dataset based on insurance claims.

This study will be useful for scenarios where various logistical concerns are involved in the reliability analysis. The methodologies proposed in this study can reduce the number of sampling operations substantially and save time and cost to a great extent.

This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.

This paper considered theoretical and numerical methodologies.

This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.

The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

This study aims to investigate the effects and implications of overconfidence in a competitive game involving multiple newsvendors. This study explores how overconfidence influences system coordination, optimal stocking strategies and competition among newsvendors in the context of the well-known newsvendor stocking problem.

The study applies robust optimization theory and the absolute regret minimization criterion to analyze the competitive game of overconfident newsvendors. This study considers the asymmetric information held by newsvendors regarding market demand and obtains a closed-form solution for the competing game. The effects of overconfidence on system coordination and optimal stocking strategies are examined.

The results of the study indicate that overconfidence can act as a positive force in reducing the effects of overstocking caused by competition and asymmetric information among newsvendors. The analysis reveals that there exists an optimal level of overconfidence that coordinates the ordering system of multiple overconfident newsvendors, leading to first-best outcomes under certain conditions. Additionally, numerical examples confirm the obtained results. Furthermore, considering newsvendors' expected profit, the study finds that a higher degree of overconfidence does not necessarily result in lower actual expected profit.

Despite the significant contributions of this study to theoretical and managerial insights, this study does have certain limitations. First, in the establishment of the belief demand function, the substitution ratio, which quantifies the transfer, is assumed to be an exogenous variable. However, in reality, this is often influenced by factors such as the price of goods and the distance between stores. Therefore, one direction worth studying in the future is to explore the uncertainty associated with the demand substitution ratio and integrate that as an endogenous variable into the optimization model. Second, this study does not address the type of product and solely focuses on quantitatively analyzing the effect of salvage value on the optimal stocking strategy. Future studies can explore the effect of degree of perishability and selling period of the product on the stocking. Third, the focus of uncertainty in this study revolves around market demand, and the implications of this uncertainty are significant. A recent study (Rahbari et al., 2023) addressed an innovative robust optimization problem related to canned foods during pandemic crises. The recent study's findings highlighted the effectiveness of expanding canned food exports to neighboring countries with economic justification as the best strategy for companies amidst the disruptions caused by the coronavirus disease 2019 (COVID-19) pandemic. Incorporating the issue of disruptions into the authors' research would be interesting and challenging.

From a managerial perspective, the authors' study provides a research paradigm for game-theoretic inventory problems in scenarios where the market demand distribution is unknown. While most inventory problems are analyzed and solved based on expectation-based optimization criteria, which rely on an accurate distribution of market demand, obtaining this information in practice can often be challenging or expensive for decision-makers. Consequently, a discrepancy arises between real-world observations and theoretical identifications. This study aimed to complement previous research and address the inconsistency between observations and theoretical identification.

The authors' research contributes to the existing understanding of overconfidence and assists individuals in making appropriate stocking strategies based on the individuals' level of overconfidence. Diverging significantly from the traditional view of overconfidence as a negative bias, the authors' results show the view's potential positive impact within a competitive environment, resulting in greater actual expected profits for newsvendors.

This study contributes to the existing literature by examining the effects of overconfidence in a competitive game of newsvendors. This study extends the analysis of the well-known newsvendor stocking problem by incorporating overconfidence and considering the implications for system coordination and competition. The application of robust optimization theory and the absolute regret minimization criterion provides a novel approach to studying overconfidence in this context.