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In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

The framework of this paper is financial mathematics and, more specifically, the control of data fraud and manipulation with their subsequent economic effects, namely, in financial markets. The purpose of this paper is to calculate the global loss or gain, which supposes, for the borrower, a change of the interest rate while the contracted loan is in force or, in another case, the loan has finished.

The methodology used in this work has been, in the first place, a review of the existing literature on the topic of manipulability and abusiveness of the loan interest rates applied by banks; in the second place, the introduction of a mathematical-financial analysis to calculate the interests paid in excess; and, finally, the compilation of several sentences issued on the application of the so-called mortgage loan reference index (MLRI) to mortgage loans in Spain.

There are three main contributions in this paper. First, the calculation of the interests paid in excess in the amortization of mortgage loans referenced to an overvalued interest rate. Second, an empirical application shows the amount to be refunded to a Spanish consumer when amortizing his/her mortgage loan referenced to the MLRI instead of the Euro InterBank Offered Rate (EURIBOR). Third, consideration has been made to the effects and the possible solutions to the legal problems arising from this type of contract.

This research is a useful tool capable of implementing the financial calculation needed to find out overpaid interests in mortgage loans and to execute the sentences dealing with this topic. However, a limitation of this study is the lack of enough sentences on mortgage loans referenced to the MLRI to get some additional information about the number of borrowers affected by these legal sentences and the amount refunded by the financial institutions.

To the best of the authors’ knowledge, this is the first time that deviations in the payment of interests have been calculated when amortizing a mortgage.

This study aims to explore the relationship between chief executive officer (CEO) power and stock price crash risk in India. Furthermore, it seeks to analyse how insider trades may moderate the impact of CEO power on stock price crash risk.

A study of 236 companies from the S&P BSE 500 Index (2014–2023) have been analysed through pooled ordinary least square (OLS) regression in the baseline analysis. To enhance the results' reliability, robustness checks include alternative methodologies, such as panel data regression with fixed-effects, binary logistic regression and Bayesian regression. Additional control variables and alternative crash risk measure have also been utilised. To address potential endogeneity, instrumental variable techniques such as two-stage least squares (IV-2SLS) and difference-in-difference (DiD) methodologies are utilised.

Stakeholder theory is supported by results revealing that CEO power proxies like CEO duality, status and directorship reduce one-year ahead stock price crash risk and vice versa. Insider trades are found to moderate the link between select dimensions of CEO power and stock price crash risk. These findings persist after addressing potential endogeneity concerns, and the results remain consistent across alternative methodologies and variable inclusions.

This study significantly advances research on stock price crash risk, especially in emerging economies like India. The implications of these findings are crucial for investors aiming to mitigate crash risk, for corporations seeking enhanced governance measures and for policymakers considering the economic and welfare consequences associated with this phenomenon.

Based on relationship marketing theory, this study aims to test the effect of social customer relationship management (social CRM) on customer satisfaction (CS) and loyalty (CL).

To assess the proposed framework, structural equation modeling was performed on the data of 314 automotive customers surveyed online.

Social CRM dimensions [traditional CRM (TCRM) and social media (SM) technology use] have a direct and positive effect on CS. On the other hand, only TCRM has a direct and significant influence on CL, while the SM technology use effect seems to be indirect rather than direct. Indeed, the findings have provided empirical support for the contention that CS plays a mediating role between social CRM dimensions and CL.

In the automotive sector and developing countries in particular, companies’ managers could increase CS and CL and consequently enhance their competitiveness and market share by adopting an effective social CRM strategy. From this perspective, companies should focus their social CRM campaigns on the most SM used by customers, offer personalized choices and improve customer experience, interaction and value co-creation.

This paper enriches the understanding of how social CRM can affect CS and CL. The scales of social CRM, CS and CL were validated in the context of developing countries and the automotive sector. Furthermore, the direct and mediating effect of CS between social CRM (TCRM and SM) and CL was also confirmed.

Basándose en la teoría del marketing relacional, este estudio pretende comprobar el efecto de la gestión social de las relaciones con los clientes (CRM social) sobre la satisfacción y la fidelidad de los clientes.

Para evaluar el marco propuesto, se realizó un modelado de ecuaciones estructurales sobre los datos de 314 clientes de automoción encuestados online.

Las dimensiones del CRM social (CRM tradicional y uso de tecnología de medios sociales) tienen un efecto directo y positivo en la satisfacción del cliente. Por otro lado, solamente el CRM tradicional tiene una influencia directa y significativa en la fidelidad del cliente, mientras que el efecto del uso de la tecnología de medios sociales parece ser más indirecto que directo. De hecho, los resultados han proporcionado apoyo empírico a la afirmación de que la satisfacción del cliente desempeña un papel mediador entre las dimensiones del CRM social y la fidelidad del cliente.

Este artículo enriquece la comprensión de cómo el CRM social puede afectar a la satisfacción y la fidelidad de los clientes. Las escalas de CRM social, satisfacción del cliente y fidelidad del cliente se validaron en el contexto de países en vías de desarrollo y del sector automovilístico. Además, también se confirmó el efecto directo y mediador de la satisfacción del cliente entre el CRM social (CRM tradicional y medios sociales) y la fidelidad del cliente.

En el sector de la automoción y en los países en desarrollo en particular, los directivos de las empresas podrían aumentar la satisfacción y fidelidad de sus clientes y, en consecuencia, mejorar su competitividad y cuota de mercado adoptando una estrategia eficaz de CRM social. Desde esta perspectiva, las empresas deberían centrar sus campañas de CRM social en los medios más utilizados por los clientes, ofrecer opciones personalizadas y mejorar la experiencia del cliente, la interacción y la cocreación de valor.

基于关系营销理论, 本研究旨在检验社会化客户关系管理（social CRM）对客户满意度和忠诚度的影响。

为评估所提出的框架, 对 314 名汽车客户的在线调查数据进行了结构方程建模。

社交客户关系管理维度（传统客户关系管理和社交媒体技术使用）对客户满意度有直接的积极影响。另一方面, 只有传统客户关系管理对客户忠诚度有直接和显著的影响, 而社交媒体技术使用的影响似乎是间接而非直接的。事实上, 研究结果为客户满意度在社交客户关系管理维度和客户忠诚度之间发挥中介作用的论点提供了实证支持。

本文丰富了人们对社交客户关系管理如何影响客户满意度和忠诚度的认识。本文以发展中国家和汽车行业为背景, 对社会化客户关系管理、客户满意度和客户忠诚度的量表进行了验证。此外, 还证实了客户满意度在社会化客户关系管理（传统客户关系管理和社会化媒体）与客户忠诚度之间的直接和中介效应。

尤其是发展中国家, 企业管理者可以通过采取有效的社交客户关系管理战略, 提高客户满意度和忠诚度, 进而增强竞争力和市场份额。从这个角度来看, 企业应将社交客户关系管理活动的重点放在客户使用最多的社交媒体上, 提供个性化选择, 改善客户体验、互动和价值共创。

The purpose of this study is to develop a novel general mathematical model to find the optimal product mix of commercial graphite products, which has a complex production process with alternative sub-processes in the graphite mining production process.

The network optimization was adopted to model the complex graphite mining production process through the optimal allocation of raw graphite, byproducts, and saleable products with comparable sub-processes, which has different processing capacities and costs. The model was tested on a selected graphite manufacturing company, and the optimal graphite product mix was determined through the selection of the optimal production process. In addition, sensitivity and scenario analyses were carried out to accommodate uncertainties and to facilitate further managerial decisions.

The selected graphite mining company mines approximately 400 metric tons of raw graphite per month to produce ten types of graphite products. According to the optimum solution obtained, the company should produce only six graphite products to maximize its total profit. In addition, the study demonstrated how to reveal optimum managerial decisions based on optimum solutions.

This study has made a significant contribution to the graphite manufacturing industry by modeling the complex graphite mining production process with a network optimization technique that has yet to be addressed at this level of detail. The sensitivity and scenario analyses support for further managerial decisions.

The paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.

The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.

The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion.

The author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation.

The author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views.

The authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.

Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series.

Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform.

Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions.

This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results.

Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.

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.

Although scholars have been studying human resource management (HRM) and open innovation (OI), yet there is less attention to this relationship in the context of small-and medium-sized enterprises (SMEs). This paper aims to bring some insights about the human side of inbound open innovation (INOI) in SMEs. The goal is to better understand the role of organizational trust (OT) and developmental culture (DC) in the interactions between commitment-based HRM (C-HRM) and INOI.

The present study employs partial least squares-structural equation modeling to investigate the interrelationships among constructs, utilizing data gathered from a sample of 206 SMEs.

The study's empirical results indicate that the presence of OT serves as a complementary factor in mediating the relation between C-HRM and INOI. Furthermore, the analysis shows that there exists a moderating influence of DC in the relationship between C-HRM and INOI.

The role of HRM practices is important in developing OT and consequently foster INOI in SMEs. To achieve INOI, SMEs need a DC that induces C-HRM toward an OI approach.

This study adds to the understanding of the interactions between C-HRM practices and INOI in SMEs. The comprehension of the mediating function of OT and the moderating effect of DC serve to enhance the scholarly understanding of the human dimension of OI research.