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In user-oriented websites, e.g. in news websites or in seller websites, it is important to take the user’s preferences into account when deciding which items to place in higher-exposure locations. The traditional approach to solving this problem, based on maximizing the average user utility, leads to unfair solutions, and this eventually hurts the company’s bottom line. Because of this, researchers have proposed complex schemes that explicitly add fairness to the formulation of this problem. But since utilities already describe human preferences, it is strange that it is necessary to add something beyond utilities.

In this paper, the authors analyze the problem of selecting exposure level for different items from the viewpoint of decision theory, the basic theory underlying all our activities, including economic ones.

The authors show that a more adequate use of utilities, namely, taking into account that Nash’s bargaining solution is a proper way to make group decisions, not maximizing average utility, already leads to fair solutions.

The idea to apply Nash’s bargaining solution to the problem of assigning exposure level to different items is new, as well as the analysis that shows that this application restores the fairness, which is missing in the current solutions.

This study aims to propose a consensus model that considers dynamic trust and the hesitation degree of the expert's evaluation, and the model can provide personalized adjustment advice to inconsistent experts.

The trust degree between experts will be affected by the decision-making environment or the behavior of other experts. Therefore, based on the psychological “similarity-attraction paradigm”, an adjustment method for the trust degree between experts is proposed. In addition, we proposed a method to measure the hesitation degree of the expert's evaluation under the multi-granular probabilistic linguistic environment. Based on the hesitation degree of evaluation and trust degree, a method for determining the importance degree of experts is proposed. In the feedback mechanism, we presented a personalized adjustment mechanism that can provide the personalized adjustment advice for inconsistent experts. The personalized adjustment advice is accepted readily by inconsistent experts and ensures that the collective consensus degree will increase after the adjustment.

The results show that the consensus model in this paper can solve the social network group decision-making problem, in which the trust degree among experts is dynamic changing. An illustrative example demonstrates the feasibility of the proposed model in this paper. Simulation experiments have confirmed the effectiveness of the model in promoting consensus.

The authors presented a novel dynamic trust consensus model based on the expert's hesitation degree and a personalized adjustment mechanism under the multi-granular probabilistic linguistic environment. The model can solve a variety of social network group decision-making problems.

This study explores the perceptions of the leadership team on knowledge creation in lesson study (LS) using P. Gronn's concept of hybrid leadership.

This study included teachers from a public elementary school in Japan that has been engaged in autonomous LS for several years. Teachers (n = 8) from the leadership team of the LS practice for four years (2016–2019) were interviewed for the study.

The findings are threefold. First, teachers in the leadership team most often referred to teachers' leadership practices as occurring in the phases of externalisation and combination, which are the important phases in the organisational knowledge creation process. Second, in the context of LS, the study found that teachers in the leadership team used three approaches to take the lead in knowledge creation, approaching the individual and the groups using tools. Third, using the concept of hybrid leadership helped detail the complexity of the leadership practices performed by the leadership team in LS.

This study focusses on teachers in the leadership team in LS, which has been an overlooked topic in this field of research. In many Japanese schools where LS has been practiced for many years, leadership teams have been set up with certain expectations. The findings of this study highlight certain leadership team practices that will contribute to the development of a sustainable LS.

The purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.

For ceteris paribus, the constitutive relations of the resistor and inductor have been reformulated by following the novel constitutive relation of capacitor. The responses of RL, RC, LC and RLC circuits defined on the fractal set described by these definitions have been derived by means of the fractal calculus and fractal Laplace transformation. A comparative Hamiltonian formalism-based analysis has been performed where the circuits described by the conventional and the formerly proposed revisited constitutive relations have also been considered.

This study has found that the novel constitutive relations give unreasonable results unlike the conventional ones. Like such previous revisited constitutive relations, an odd Hamiltonian has been obtained. On the other hand, the conventional constitutive relations give a reasonable Hamiltonian.

To the best of the author’s knowledge, for the first time, the analysis of fractal set defined electrical circuits by means of unconventional constitutive relations has been performed where the deficiency of the tested capacitive constitutive relation has been pointed out.

The aim is the introduction of lesson study (LS) in geometry in Malawi secondary schools supported by a teaching framework that includes a focus on language responsive teaching.

The study reports an LS on geometry for professional development (PD) of secondary teachers. Data analysed includes lesson plans, transcripts of lessons, reflective discussions. The analytical approach is qualitative content analysis.

Teachers' lexicalisation of an exterior angle of a triangle evolved as a function of a teaching framework that guided their participation in planning, teaching and reflecting through LS cycle, and that was derived from networking between theories.

This is both a small-scale study, and a limited content focus in the lesson, a function of LS being a new practice, and teachers simultaneously learning ideas about geometry teaching, those embedded in the framework and doing LS.

The paper includes a description of how LS might contribute to teachers' learning of language responsive teaching, and so is useful for others working on LS and language practices.

This paper fulfils an identified need to learn more about how networking theories to inform and support LS can create learning opportunities for teachers, particularly about language responsive teaching, an interest and concern worldwide.

Let p_[1,r;t] be defined by ∑n=0∞p[1,r;t](n)qn=(E1Er)t, where t is a non-zero rational number, r ≥ 1 is an integer and Er=∏n=0∞(1−qr(n+1)) for |q| < 1. The function p_[1,r;t](n) is the generalisation of the two-colour partition function p_[1,r;−1](n). In this paper, the authors prove some new congruences modulo odd prime ℓ by taking r = 5, 7, 11 and 13, and non-integral rational values of t.

Using q-series expansion/identities, the authors established general congruence modulo prime number for two-colour partition function.

In the paper, the authors study congruence properties of two-colour partition function for fractional values. The authors also give some particular cases as examples.

The partition functions for fractional value is studied in 2019 by Chan and Wang for Ramanujan's general partition function and then extended by Xia and Zhu in 2020. In 2021, Baruah and Das also proved some congruences related to fractional partition functions previously investigated by Chan and Wang. In this sequel, some congruences are proved for two-colour partitions in this paper. The results presented in the paper are original.

The context of the case presents an account of how corporate social responsibility (CSR) initiated by Lawrence & Mayo (L&M), a company dealing in optical frames for 140 years, helped to build brand equity, image and identity, creating a strategic advantage against competition. The case had a deep-rooted theoretical association with a theory such as the triple bottom line theory (three Ps: profit, people and planet) on CSR. The case helps to understand and clarify the role of CSR in brand equity. It also gives an insight into the value and culture of L&M, and its impact on various stakeholders, namely, employees and customers.

This case is related to the CSR orientation of L&M and its impact on brand equity. As a brand, L&M is over 140 years old and has a dynamic and trending optics market in India. There is a dilemma in the company around the impact of CSR on brand equity, customer engagement and company goodwill. This case focuses on maintaining and improving brand equity, identity and image through CSR initiatives.

Undergraduate and postgraduate students, essential for students focusing on Marketing and CSR disciplines.

Teaching notes are available for educators only.

CSS 8: Marketing.

The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.

In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.

The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.

This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.

Lesson study (LS) is a collaborative form of action research. Collaboration is central to LS methodology, therefore exploring and expanding the understanding of the collaborative features that occur in LS is a priority. This paper explores the features of collaboration in existing publications on LS to consider if, as Quaresma (2020) notes, collaboration is simplistically referred to within LS research.

Utilising a qualitative review of LS literature to explore LS collaboration through Mynott's (2019) outcome model and Huxham and Vangen's (2005) theory of collaborative advantage and inertia. 396 publications using “lesson study” and “collaboration” as key words were considered and reviewed, with 26 articles further analysed and coded, generating a collaborative feature matrix.

While collaboration in LS is referred to generically in the articles analysed, the authors found examples where collaboration is considered at a meta, meso and micro level (Lemon and Salmons, 2021), and a balance between collaborative advantage and inertia. However, only a small proportion of LS publications discuss collaboration in depth and, while the matrix will support future research, more focus needs to be given to how collaboration functions within LS.

Through answering Robutti et al.'s (2016) question about what can be learnt from the existing LS research studies on collaboration, this paper builds on Mynott's (2019) outcome model by providing a detailed matrix of collaborative features that can be found in LS work. This matrix has applications beyond the paper for use by facilitators, leaders of LS, and researchers to explore their LS collaborations through improved understanding of collaboration.

Researchers often stress the predictive goals of their partial least squares structural equation modeling (PLS-SEM) analyses. However, the method has long lacked a statistical test to compare different models in terms of their predictive accuracy and to establish whether a proposed model offers a significantly better out-of-sample predictive accuracy than a naïve benchmark. This paper aims to address this methodological research gap in predictive model assessment and selection in composite-based modeling.

Recent research has proposed the cross-validated predictive ability test (CVPAT) to compare theoretically established models. This paper proposes several extensions that broaden the scope of CVPAT and explains the key choices researchers must make when using them. A popular marketing model is used to illustrate the CVPAT extensions’ use and to make recommendations for the interpretation and benchmarking of the results.

This research asserts that prediction-oriented model assessments and comparisons are essential for theory development and validation. It recommends that researchers routinely consider the application of CVPAT and its extensions when analyzing their theoretical models.

The findings offer several avenues for future research to extend and strengthen prediction-oriented model assessment and comparison in PLS-SEM.

Guidelines are provided for applying CVPAT extensions and reporting the results to help researchers substantiate their models’ predictive capabilities.

This research contributes to strengthening the predictive model validation practice in PLS-SEM, which is essential to derive managerial implications that are typically predictive in nature.