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This paper aims to investigate the reciprocal nonlinear relationship between corporate social responsibility (CSR) and firm performance (FP).

The authors used a sample of 814 European firms over the period 2008–2017. The Panel Smooth Transition Regression (PSTR) model was performed as an econometric approach.

Firstly, results show a threshold effect in the CSR–FP relationships within the two directions. More specifically, the authors found that firms are more likely to engage in CSR by surpassing a threshold of 1.231% for return on assets (ROA) and 0.821% for Tobin’s Q ratio. Secondly, the authors also found that the impact of CSR on FP is positive and significant only if the environment, social and governance score surpasses the threshold of 56.780% when the dependent variable is ROA and 41.02% when Tobin’s Q ratio measures performance.

A significant part of the literature supports the linear relationship between CSR and FP from the unique direction (CSR → FP). This study comes to fill this gap by assessing the possible nonlinear relationship. In addition, this nonlinear relationship is tested under the two directions. Therefore, defining the threshold of FP that allows companies to engage in CSR, on the one hand, and the threshold of engagement in CSR that improves FP, on the other hand, could be an exciting topic.

To get the full benefit from CSR effects, firms should be with better financial performance to be socially responsible.

To the best of our knowledge, few studies have explored the nonlinear relationship between CSR and FP. In addition, this study raises the question of whether this relation is causal. The authors assess the two nonlinear relationships between CSR ? FP and FP ? CSR by determining the optimal thresholds.

本文旨在探究企業社會責任 (以下簡稱企社責) 與公司業績之間的相互非線 性關係。

研究所採用的樣本為814間歐洲公司, 涵蓋期為2008年至2017年。研究人 員使用縱橫平滑轉換模型、作為經濟計量方法和工具去進行研究。

研究結果顯示、在有關的兩個方向內, 企社責與公司業績之間的關聯上是 存在著閾值效應的。更具體地說, 研究人員發現, 若企業的資產報酬率超過1.231%的 水平, 以及托賓的Q比率 (Tobin’s Q Ratio) 0.821%的水平的話, 它們會更願意承擔企 社責。其次, 研究結果亦顯示, 企社責對企業的業績會產生積極的影響; 另外, 只有 當資產報酬率是因變數、而環境、社會和公司治理的分數 (ESGS) 超過56.780%, 以 及當托賓的Q比率用來測量績效、而數值為41.02%時, 企社責對企業的業績所產生的 影響會較為顯著。

過去的學術文獻、大部份都是以唯一的方向 (企社責 ->公司業績) 去確認 企社責與企業業績之間的線性關係。本研究評估了兩者之間可能存在的非線性關係; 而且, 這非線性關係是在有關的兩個方向下而進行測試的; 因此, 本研究一方面給可 讓公司以企社責的精神和理念去營運的企業業績的閾值下了定義; 另一方面, 又給參 與企社責為公司帶來業績的改善的閾值下了定義。這均為令人興奮的課題。

企業若想取得因參與企社責而帶來的完全好處, 它們必須擁有更佳 的財務績效、以能盡其社會責任。

盡我們所知, 探究企社責與企業業績之間的非線性關係的研究實在不 多; 而且, 本研究對這兩者的關係是否是因果關係提出了質疑; 就此, 我們藉著釐定 最佳的相對閾值、來評估企社責 ->企業業績與企業業績 ->企社責之間的兩個非線性的 關係。

This paper aims to investigate the nonlinear effects of bank regulation stringency on bank lending in 23 sub-Saharan African (SSA) countries over the period 1997–2017.

This study employs the dynamic panel threshold regression (PTR) model, which addresses endogeneity and heterogeneity problems within a nonlinear framework. It also uses indices of entry barriers, mixing of banking and commerce restrictions, activity restrictions and capital regulatory requirements from the updated databases of the World Bank's Bank Regulation and Supervision Surveys as measures of bank regulation.

The linearity test results support the existence of nonlinear effects in the relationship between bank lending and entry barriers or capital regulations in the selected SSA economies. The dynamic PTR estimation results reveal that bank lending responds positively when the stringency of entry barriers is below the threshold of 62.8%. However, once the stringency of entry barriers exceeds that threshold level, bank credit reacts negatively and significantly. By contrast, changes in capital regulation stringency do not affect bank lending, either below or above the obtained threshold value of 76.5%.

These results can help policymakers design bank regulatory measures that will promote the resilience and safety of the banking system but at the same time not bring unintended effects to bank lending.

To the best of the authors’ knowledge, this is the first study to examine the nonlinear effects of bank regulatory measures on bank lending using the dynamic PTR model and SSA context.

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.

In this paper we examine the validity of the J-curve hypothesis in four Southeast Asian economies (Indonesia, Malaysia, the Philippines and Thailand) over the 1980–2017 period.

We employ the linear autoregressive distributed lags (ARDL) model that captures the dynamic relationships between the variables and additionally use the nonlinear ARDL model that considers the asymmetric effects of the real exchange rate changes.

The estimated models were diagnostically sound, and the variables were found to be cointegrated. However, with the exception of Malaysia, the short- and long-run relationships did not attest to the presence of the J-curve effect. The trade flows were affected asymmetrically in Malaysia and the Philippines, suggesting the appropriateness of nonlinear ARDL in these countries.

The previous research tended to examine the effects of the real exchange rate changes on the agricultural trade balance and specifically the J-curve effect (deterioration of the trade balance followed by its improvement) in the developed economies and rarely in the developing ones. In this paper, we address this omission.

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.

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 purpose of this study is to explore the role of gold as a hedge against inflation in the case of the United Arab Emirates.

The study utilizes monthly data on the local sharia-compliant spot gold contract traded on the Dubai Gold and Commodity Exchange (DGCX) and the corresponding consumer price index series over the period December 2015 to January 2021. The econometric approach employed by the study involves a unit root testing procedure that allows the timing of significant breaks to be estimated. A cointegration analysis is then conducted using a nonlinear autoregressive distributed lag (NARDL) model, taking into consideration the presence of structural breaks in addition to short- and long-run asymmetries.

The results reveal that consumer and gold prices are cointegrated, which implies that investing in gold can hedge against inflation in the long run. No sufficient evidence, nonetheless, is found in support of the ability of gold to serve as a hedge against inflation in the short run.

The findings have several important policy implications for policymakers and investors that are further discussed in the study.

This paper aims to investigate the impact of combining grain-oriented electrical steel (GOES) grades on specific iron losses and the flux density distribution within a single-phase magnetic core.

This paper presents the results of finite-element method (FEM) simulations investigating the impact of mixing two different GOES grades on losses of a single-phase magnetic core. The authors used different models: a 3D model with a highly detailed geometry including both saturation and anisotropy, as well as a simplified 2D model to save computation time. The behavior of the flux distribution in the mixed magnetic core is analyzed. Finally, the results from the numerical simulations are compared with experimental results.

The specific iron losses of a mixed magnetic core exhibit a nonlinear decrease with respect to the GOES grade with the lowest losses. Analyzing the magnetic core behavior using 2D and 3D FEM shows that the rolling direction of the GOES grades plays a critical role on the nonlinearity variation of the specific losses.

The novelty of this research lies in achieving an optimum trade-off between the manufacturing cost and the core efficiency by combining conventional and high-performance GOES grade in a single-phase magnetic core.

This study aims to provide insight into the determinants of wellness tourism satisfaction, thereby taking a nonlinear approach regarding the relationships between attribute-level performance of wellness facility attributes, on the one hand, and wellness destination attributes, on the other hand, and global wellness tourist satisfaction. In addition, scores of impact range are calculated to reveal the potentially most determinant wellness facility and destination attributes.

This study uses data from a survey-based study conducted among 1,331 wellness tourists who have engaged in wellness tourism activities at one of 28 hotels with wellness offerings and 10 spas in Croatia. Impact-asymmetry analysis and impact-range analysis are used to quantify the potential of individual wellness attributes to generate satisfaction and dissatisfaction among wellness tourists and to perform a classification of wellness attributes according to the three-factor theory of customer satisfaction.

Operators of wellness tourism facilities, as well as managers of wellness destinations, must not make any compromises in quality levels because most wellness attributes have significantly higher potential to frustrate than please tourists. Basic factors such as cleanliness, punctuality or safety turned out to have the strongest influence on global satisfaction levels. Moreover, in line with previous research, wellness tourists have large expectations from destinations to have a preserved and beautiful nature, which is by far the most influential destination attribute. In addition to a safe environment and high-quality accommodation, wellness tourists further prefer rich cultural offerings.

To the best of the authors' knowledge, this is the first study to apply a nonlinear analysis approach to the quality–satisfaction relationship in a wellness tourism setting. Moreover, to the knowledge of the authors, this is the only study that used separate attribute models for wellness facilities, on the one hand, and wellness destinations, on the other hand, based on a nation-wide sample that covers multiple cases (i.e. multiple facilities and destinations).

本研究旨在深入了解养生旅游满意度的决定因素, 从而采用非线性方法来研究（i）养生设施属性和 （ii）养生目的地属性对国际养生游客满意度的关系。此外, 本文还计算了影响范围的分数, 以揭示潜在的最具决定性的养生设施和目的地属性。

本研究使用了基于对 1,331 名养生游客进行调查问卷的数据, 这些游客曾在克罗地亚 28 的酒店以及10个水疗中心进行了养生旅游活动。本文采用影响不对称分析（IAA）和影响范围分析（IRA）来量化个体养生属性在健康游客中产生满意度和不满意的潜力, 并根据顾客三因素满意度理论对健康属性进行分类。

养生旅游设施的运营商以及养生目的地的管理者不能在质量水平上做出任何妥协, 因为大多数养生属性很可能使游客感到沮丧, 而不是取悦游客。事实证明, 清洁、准时及安全等基本因素对全球满意度影响最大。此外, 根据之前的研究, 健康游客对目的地抱有很大的期望, 希望拥有保存完好且美丽的自然风光, 这是最具影响力的目的地属性。除了安全的环境和高品质的住宿外, 养生游客更看重丰富的文化产品。

这是第一项将非线性分析方法应用于养生旅游环境中的质量与满意度关系的研究。此外, 据作者所知, 这是唯一一项基于涵盖多个案例（即多个设施及目的地）的国家样本, 一方面对养生设施使用单独的属性模型, 另一方面对养生目的地使用单独的属性模型的研究。

Este estudio tiene como objetivo proporcionar información sobre los determinantes de la satisfacción del turismo de bienestar, adoptando así un enfoque no lineal con respecto a las relaciones entre el rendimiento a nivel de atributos de (i) atributos de instalaciones de bienestar, por un lado, y (ii) atributos de destino de bienestar, por otro lado, y la satisfacción del turista de bienestar global. Además, se calculan puntajes de rango de impacto para revelar las instalaciones de bienestar y los atributos de destino potencialmente más determinantes.

este estudio utiliza datos de un estudio basado en encuestas realizado entre 1,331 turistas de bienestar que participaron en actividades de turismo de bienestar en uno de los 28 hoteles con ofertas de bienestar y diez spas en Croacia. El análisis de asimetría de impacto (IAA) y el análisis de rango de impacto (IRA) se utilizan para cuantificar el potencial de los atributos de bienestar individuales para generar satisfacción e insatisfacción entre los turistas de bienestar y para realizar una clasificación de los atributos de bienestar de acuerdo con la teoría de los tres factores del cliente. satisfacción.

Los operadores de instalaciones de turismo de bienestar, así como los administradores de destinos de bienestar, no deben comprometer los niveles de calidad porque la mayoría de los atributos de bienestar tienen un potencial significativamente mayor para frustrar que para complacer a los turistas. Los factores básicos, como la limpieza, la puntualidad o la seguridad, resultaron ser los que más influyeron en los niveles de satisfacción global. En consecuencia, estos atributos no deben verse como fuentes potenciales de satisfacción y deleite del cliente, sino que deben otorgarse altos niveles de desempeño para evitar una fuerte insatisfacción. Además, en línea con investigaciones anteriores, los turistas de bienestar tienen grandes expectativas de que los destinos tengan una naturaleza preservada y hermosa, que es, con mucho, el atributo de destino más influyente. Además de un entorno seguro y un alojamiento de alta calidad, los turistas de bienestar prefieren una rica oferta cultural. Aplicando la teoría de los tres factores, una visión más matizada de la formación de la satisfacción del turista de bienestar mostró que estos atributos del destino tienen un potencial mucho mayor para crear una fuerte insatisfacción que satisfacción.

Este es el primer estudio que aplica un enfoque de análisis no lineal a la relación calidad-satisfacción en un entorno de turismo de bienestar. Además, según el conocimiento de los autores, este es el único estudio que utilizó modelos de atributos separados para instalaciones de bienestar, por un lado, y destinos de bienestar, por el otro, en base a una muestra nacional que cubre múltiples casos (es decir, múltiples instalaciones y destinos).

The purpose of this study is to analyze how sentiment affects economic activity in Brazil.

Based on a nonlinear autoregressive distributed lag (NARDL) model, this study examines in detail the short-term and long-term asymmetric impacts between the variables during the period from January 2007 to December 2020.

There are three main results of this study. First, sentiment is an important factor for economic activity in Brazil, and its effect possibly occurs through the channels of consumption and investment, which are the two main components of economic growth. Second, sentiment affects economic activity in different ways in the short and the long term: in Brazil, although in the short-term, immediate shocks of sentiment may be confusing, the negative shocks from previous periods have a negative impact on economic activity. Third, the effect of shocks of optimism and pessimism on economic activity is asymmetric, and in the long run, only shocks of optimism have a significant and positive impact.

The relationship between sentiment and economic activity is still a controversial issue in the literature and this study seeks to advance its understanding in Brazil.