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Hoping to uncover the physical principles of the vibration of the functionally graded material (FGM) microplate, by which the authors can make contributions to the design and manufacturing process in factories like micro-electro-mechanical system (MEMS) and other industries.

The authors design a method by establishing a reasonable mathematical model of the physical microplate composed of a porous FGM.

The authors discover that the porosity, the distributions of porosity, the power law of the FGM and the length-to-thickness ratio all affect the natural frequency of the vibration of the microplate, but in different ways.

Originally proposed a model of the micro FGM plate considering the different distributions of the porosity and scale effect and analyzed the vibration frequency of it.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

This study aims to introduce and define the concept of phygital brand community (PBC). It discusses the potential conflicts that can arise from engaging in multiple PBCs and propose an enriched netnographic methodological approach to explore the role of PBC engagement overlap and its influence on the phygital experience.

Following a critical analysis of the inherent limitations of netnographic methodological approaches in the context of PBCs, this study develops an enriched netnographic research protocol that accounts for the challenges of engagement overlap among PBCs.

This study proposes two methods of analysis, namely, “participatory netnography” and “witness netnography,” which are derived from a mixed-methodology approach that integrates elements of netnography.

The findings of this study underscore the requisite methodological refinements imperative for enhancing netnographic analysis, particularly in its application for a better comprehension of individual behaviors within the realm of PBCs. In pursuit of this objective, the identified adjustments encompass ethical considerations, evaluation methods and their application in a digital milieu, where intricate mechanics and technologies frequently elude conventional methodologies.

In this study, the authors present a novel conceptualization of PBCs, highlighting their role and development, as well as the challenges they pose. To adequately capture the impact of PBC engagement overlap, the authors propose the need for an enriched mixed-methodological approach.

The purpose of this paper is twofold: (1) to map and analyze existing complexity typologies and (2) to develop a framework for characterizing complexity-based approaches.

This study was conducted in three stages: (1) initial identification of typologies related to complexity following a structured procedure based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol; (2) backward and forward review to identify additional relevant typologies and (3) content analysis of the selected typologies, categorization and framework development.

Based on 17 selected typologies, a comprehensive overview of complexity studies is provided. Each typology is described considering key concepts, contributions and convergences and differences between them. The epistemological, theoretical and methodological diversity of complexity studies was explored, allowing the identification of the main schools of thought and authors. A framework for characterizing complexity-based approaches was proposed including the following perspectives: ontology of complexity, epistemology of complexity, purpose and object of interest, methodology and methods and theoretical pillars.

This study examines the main typologies of complexity from an integrated and multidisciplinary perspective and, based on that, proposes a novel framework to understanding and characterizing complexity-based approaches.

This paper aims to explore how traditional industries revert the trend of decline in sales through rebranding by analyzing the extended case study of the fountain pen industry.

This study analyzes the marketing in case study of the fountain pen industry through two coordinates – symbolizing status and branding nostalgia. The division of analyses in these categories is supplanted by data, such as linear regression to analyze changes in product characteristics.

This study finds that the rebranding of the fountain pen in multiple fitting images – status symbol, object of nostalgia and something scarce and unique – is successful in capturing consumer demand, shaping consumer perceptions and help the mature industry locate as well as enter a niche market.

To the best of the authors’ knowledge, this paper is the first one to explore the business development of traditional industry as a case study of fountain pens from the perspective of marketing and consumer behavior.

The purpose is to explore the free vibration behaviour of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The goal of this study is to gain a better knowledge of the dynamic response of nanoscale structures made of functionally graded materials and porous features. The Rayleigh-Ritz approach is used in this study to generate realistic mathematical models that take elastic foundation support into account. This research can contribute to the design and optimization of advanced nanomaterials with potential applications in engineering and technology by providing insights into the influence of material composition, porosity and foundation support on the vibrational properties of nanoplates.

A systematic methodology is proposed to evaluate the free vibration characteristics of elastic foundation-supported porous functionally graded nanoplates using the Rayleigh-Ritz approach. The study began by developing the mathematical model, adding material properties and establishing governing equations using the Rayleigh-Ritz approach. Numerical approaches to solve the problem are used, using finite element methods. The results are compared to current solutions or experimental data to validate the process. The results are also analysed, keeping the influence of factors on vibration characteristics in mind. The findings are summarized and avenues for future research are suggested, ensuring a robust investigation within the constraints.

The Rayleigh-Ritz technique is used to investigate the free vibration properties of elastic foundation-supported porous functionally graded nanoplates. The findings show that differences in material composition, porosity and foundation support have a significant impact on the vibrational behaviour of nanoplates. The Rayleigh-Ritz approach is good at modelling and predicting these properties. Furthermore, the study emphasizes the possibility of customizing nanoplate qualities to optimize certain vibrational responses, providing useful insights for engineering applications. These findings expand understanding of dynamic behaviours in nanoscale structures, making it easier to build innovative materials with specific features for a wide range of industrial applications.

The novel aspect of this research is the incorporation of elastic foundation support, porous structures and functionally graded materials into the setting of nanoplate free vibrations, utilizing the Rayleigh-Ritz technique. Few research have looked into this complex combo. By tackling complicated interactions, the research pushes boundaries, providing a unique insight into the dynamic behaviour of nanoscale objects. This novel approach allows for a better understanding of the interconnected effects of material composition, porosity and foundation support on free vibrations, paving the way for the development of tailored nanomaterials with specific vibrational properties for advanced engineering and technology applications.

Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

This study employed self-determination theory (SDT) and the “Motivational affordance–Psychological outcomes–Behavioral outcomes” framework to investigate the relationship between gamification features and knowledge-sharing behavior in online communities.

A theoretical model was tested with 281 Chinese users from an online social question and answer (Q&A) community. Partial least square structural equation modeling was applied to analyze the data.

The empirical results revealed that competence mediated the effects of immersion and achievement-related gamification features on knowledge sharing. Moreover, relatedness mediated the effects of immersion, achievement and social-related gamification features on knowledge sharing.

This study was conducted on a Chinese Q&A platform, and the results may not be generalizable to other cultures or service providers with different goals.

The study's findings indicate that gamification could serve as an effective toolkit for incentivizing and promoting knowledge sharing in online communities. The findings thus provide strategic insights for administrators of online communities seeking to leverage gamification designs to encourage user participation in knowledge-sharing activities.

Research on the role of gamification in promoting knowledge sharing has been limited in scope and has focused on tourism comment communities. Little evidence exists on the effect of gamification within social Q&A communities. Further, the finding of gamification's positive role in motivating knowledge sharing indicates the need for the knowledge-sharing field to focus on contextual factors.