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The soliton solutions are obtained by using extended rational sin/cos and sinh-cosh method. The methods are powerful and have ease of use. Applying wave transformation to the nonlinear partial differential equations (NLPDEs) and the considered equation turns into a nonlinear differential equation (NODE). According to the methods, the solution sets of the NODE are supposed to the form of the rational terms as sinh/cosh and sin/cos and the trial solutions are substituted into the NODE. Collecting the same power of the trigonometric functions, a set of algebraic equations is derived.

The main purpose of this paper is to obtain soliton solutions of the modified equal width (MEW) equation. MEW is a form of regularized-long-wave (RLW) equation that represents one-dimensional wave propagation in nonlinear media with dispersion processes. This is also used to simulate the undular bore in a long shallow water canal.

Thus, the solution of the main PDE is reduced to the solution of a set of algebraic equations. In this paper, the kink, singular and singular periodic solitons have been successfully obtained.

Illustrative plots of the solutions have been presented for physical interpretation of the obtained solutions. The methods are powerful and might be used to solve a broad class of differential equations in real-life problems.

This study aims to reveal consumers' internal and external motivations to prefer online food shopping. The paper proposes an integrated model including aspirations, capabilities, subjective norms (divided into online resources and offline resources), perceived value and traditionalism to examine their effects on consumers' intention to do online food shopping.

A cross–sectional design was used to understand which factors affect consumers' intention to do online food shopping. The data were collected from a total of 400 people via an online survey. The conceptual model was tested using structural equational modeling to understand the relationships between the factors.

The results suggest that the conceptual framework can be used to have a better understanding of consumers' internal and external motivations to do online food shopping. The study proves that aspirations have a considerable direct effect on and a mediating role between capabilities, subjective norms from online resources, traditionalism and the effect of COVID-19 pandemics and the intention. Also, traditionalism was found to be an antecedent for consumers to prefer online food shopping.

This study reveals better insights for the sellers, marketers and system providers dealing with supplying food products through online channels. The findings suggest that the stakeholders take into consideration aspirations, capabilities, subjective norms, perceived value and traditionalism to organize their activities in food marketing in the online area.

In this study, aspirations–capabilities framework was adopted and confirmed within consumers' online food shopping domain. Also, it was proved that traditionalism was a driver of individuals' intention to do online shopping for food products.

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).

The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.

The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

This paper aims to suggest the approximate solution of time fractional heat-like and wave-like (TFH-L and W-L) equations with variable coefficients. The proposed scheme shows that the results are very close to the exact solution.

First with the help of some basic properties of fractional derivatives, a scheme that has the capability to solve fractional partial differential equations is constructed. Then, TFH-L and W-L equations with variable coefficients are solved by this scheme, which yields results very close to the exact solution. The derived results demonstrate that this scheme is very effective. Finally, the convergence of this method is discussed.

A traditional method is combined with the Laplace transform to construct this scheme. To decompose the nonlinear terms, this paper introduces the homotopy perturbation method with He’s polynomials and thus the solution is provided in the form of a series that converges to the exact solution very quickly.

The proposed approach is original and very effective because this approach is, to the authors’ knowledge, used for the first time very successfully to tackle the fractional partial differential equations, which are of great interest.

The purpose of this study is to test the impact of time and price sensitivity on consumer satisfaction and purchase intention on online-to-offline (O2O) takeout platforms and explore the moderating effect of purchase preference on time sensitivity and satisfaction, as well as price sensitivity and satisfaction, in order to guide market pricing.

A structural equation model (SEM) of customer purchase intention was constructed, and the relationships between the variables (time sensitivity, price sensitivity, satisfaction and purchase intention) were examined. The completed questionnaires of 349 respondents were collected from the Questionnaire Star platform in China. The research model and hypotheses were then tested. Analytic hierarchy procedure was used to determine the moderating effect of purchase preference. Finally, the study proposes a pricing strategy for customer-active selective services.

Satisfaction positively influences purchase intention, and price sensitivity significantly increases satisfaction and further increases purchase intention; however, time sensitivity negatively affects satisfaction. Specifically, purchase preference has strongly moderated the relationship between time, price sensitivity and satisfaction. In addition, the findings show that when purchase preference is high, the effect of price sensitivity on satisfaction is stronger, suggesting the importance of purchase preference in strengthening purchase intentions. The research work recommends a pricing strategy involving value-added pricing primarily for time-sensitive customers, which can help build a high-end brand image and reduce price competition. Reduced pricing is mainly for price-sensitive customers, which is conducive to stimulating consumption within a specific time. This pricing strategy is important for adjusting market sensitivity and flexibility.

This research provides new ideas for related disciplines and guidance for the differentiated pricing and promotion of takeout platforms, as well as a theoretical basis for the diversified development of takeout platforms, improvement of personalized service quality and enhancement of customer stickiness. This study fills gaps in the existing literature on the moderating effect of purchase preference on time sensitivity and satisfaction and price sensitivity and satisfaction.

Studies on the performance of agribusiness cooperatives in Brazil focus on economic and financial aspects. The purpose of this paper is to further delve into such studies by investigating which commonly measurable structural production factors (horizontal, vertical and lateral diversification; operating area; number of associates; and time in operation) have greater impacts on the financial performance of such cooperatives.

To achieve such a goal, a survey was conducted with a sampling pool divided by size (annual net revenues of US$ 50 million or higher), and the questionnaire was employed as a method of data collection. The sample was concentrated in the southern, south-eastern and mid-western regions of Brazil; classified by size; and deemed adequate after several adequacy tests.

The results were analysed using Spearman’s correlation, which showed that there were no significant correlations between the structural production factors considered in this study and the economic-financial performance of agricultural cooperatives, which leads to questions about the effectiveness of employing diversification strategies with a conjoint approach. Nonetheless, it was possible to identify several relationships not mentioned in the original hypotheses that might be addressed further in future studies.

The data obtained should be interpreted with caution because heteroscedasticity was detected. Although the cause could not be clearly identified, the presence of heteroscedasticity could mean that smaller and similar cooperatives present similar variation in their diversification and production base strategies.

This work sought to generate knowledge regarding operations management, which was achieved by demonstrating that production diversification in a dynamic and relevant economic sector, that is, agricultural cooperatives, is limited in terms of financial return when performed in an isolated mode. Hence, cooperatives’ production managers should take into account the totality of structural production factors during their planning activities.

Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems.

In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Kármán non-linearity and CFD definition.

The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio.

A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The aim of this research is to examine the public leadership (PL) behaviors of principals working in public schools and its effect on teacher motivation (M) and job satisfaction (JS). Moreover, the mediating role of JS in the relationship between PL and M is also explored.

This research is quantitative and designed in relational survey model conducted with 327 teachers working in Siirt/Turkey in 2020. In the research, Public Leadership Scale, Teacher Motivation Scale and Minnesota Satisfaction Questionnaire were used. Descriptive analyses were used in data analysis. Moreover, mediating role of job satisfaction between public leadership and teacher motivation was tested.

According to the results, the public leadership behaviors of school principals, motivation and job satisfaction of teachers are high according to teacher opinions. Additionally, public leadership behaviors of school principals have an effect on teacher motivation and job satisfaction. On the other hand, this study found a negative effect between public leadership and motivation when the effect of job satisfaction is controlled. The possible reasons for this situation were discussed in term of cultural differences.

The results of this study imply that the leadership behaviors of school principals have cultural elements. Future research should be careful in measuring the political loyalty dimension of the public leadership and should take cultural element into consideration.

Although there are many types of leadership, the type of leadership differs depending on the purpose of the organization, environmental conditions and culture. The lifestyle of the society, current developments and the structure of the organization are effective in interpreting the leadership needed in the organization. When looking at the models created about leadership in organizations, the effect of this type of leadership on organizational behavior is generally tried to be explained. This is also the case for motivation or job satisfaction. Therefore, this study also focuses on the effect of public leadership in explaining the job satisfaction and motivation of employees in educational organizations. However, another distinctive aspect of this research is that the cultural structure of the society is emphasized in the model to be created.

Catastrophe of steel-structured bridges due to progressive localized corrosion may lead to a major loss in terms of life and cost if not monitored continuously or periodically. The purpose of this paper is to present a vibration-based strategy to assess the severity and monitor the deterioration caused by corrosion-induced localized damage in a simply-supported steel beam.

The threshold damage level is defined up to the yield limit of a simply supported steel beam of size ISMB 150 × 8 × 5 under three-point bending test and the progressive damage is induced through a continuous accelerated corrosion test. Change in the fundamental natural frequency due to localized damage in the experimental beam and the modulus of elasticity (E) in the corroded zone of an updated finite element (FE) model is evaluated.

The updated FE model of the damaged beam shows a clear trend with the progressive damage of the beam and, hence, can be used to monitor the severity of damage and remaining capacity assessment of the monitored beam.

Steel-structured bridges are prone to localized corrosion attack, and there are no standardized process or predictive model available by international steel design codes on how to consider corrosion damage in the condition assessment analysis. The vibration-based methods have gained popularity for condition assessment, and are mostly confined to damage assessment of corroded reinforced concrete (RC) beams. In this work, a vibration-based approach is presented for degradation assessment of steel beam due to progressive localized corrosion using modal hammer test.