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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。

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.

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.

Considering the impact of the Free Trade Zone (FTZ) policy on forecasting the port cargo throughput, this paper constructs a fractional grey multivariate forecasting model to improve the prediction accuracy of port cargo throughput and realize the coordinated development of FTZ policymaking and port construction.

Considering the effects of data randomization, this paper proposes a novel self-adaptive grey multivariate prediction model, namely FDCGM(1,N). First, fractional-order accumulative generation operation (AGO) is introduced, which integrates the policy impact effect. Second, the heuristic grey wolf optimization (GWO) algorithm is used to determine the optimal nonlinear parameters. Finally, the novel model is then applied to port scale simulation and forecasting in Tianjin and Fujian where FTZs are situated and compared with three other grey models and two machine learning models.

In the Tianjin and Fujian cases, the new model outperforms the other comparison models, with the least mean absolute percentage error (MAPE) values of 6.07% and 4.16% in the simulation phase, and 6.70% and 1.63% in the forecasting phase, respectively. The results of the comparative analysis find that after the constitution of the FTZs, Tianjin’s port cargo throughput has shown a slow growth trend, and Fujian’s port cargo throughput has exhibited rapid growth. Further, the port cargo throughput of Tianjin and Fujian will maintain a growing trend in the next four years.

The new multivariable grey model can effectively reduce the impact of data randomness on forecasting. Meanwhile, FTZ policy has regional heterogeneity in port development, and the government can take different measures to improve the development of ports.

Under the background of FTZ policy, the new multivariable model can be used to achieve accurate prediction, which is conducive to determining the direction of port development and planning the port layout.

Examining the role of women on board (WoB) toward corporate sustainable growth (CSG) through leverage policy (LP). This research also investigates the interaction effect of WoB and LP on improving CSG.

This study uses a moderated mediation model to examine the impact of WoB on CSG, mediated by LP. Data from 48 KEHATI IDX ESG Sector Leaders Index companies observed from 2015 to 2021 were analyzed using the structural equation model partial least square (SEM-PLS) Warp.PLS 8.0. The research applies instrumental variables (IV) to test and control endogeneity due to nonrandom sample selection.

We found evidence that LP acts as a full mediator between the presence of WoB and CSG. The presence of WoB plays a moderate role by slightly weakening the influence of LP on CSG. Furthermore, we obtained evidence showing that the relationship between WoB and CSG is J-curve-shaped, a nonlinear relationship related to critical mass. Where the WoB ratio is at least 8.35% or higher, it will increase CSG in companies that have implemented the concept of environment social governance (ESG) in Indonesia.

This model uses a moderated mediation model and J-curve analysis; there is an interaction between WoB and LP on different paths of the mediator to CSG. This model examines the role of WoB as a moderator of the effect of LP on CSG. A nonlinear J-curve test was conducted to determine the minimum level of WoB that can influence the increase of CSG.