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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 purpose of this study is to introduce the top-level design ideas and the overall architecture of earthquake early-warning system for high speed railways in China, which is based on P-wave earthquake early-warning and multiple ways of rapid treatment.

The paper describes the key technologies that are involved in the development of the system, such as P-wave identification and earthquake early-warning, multi-source seismic information fusion and earthquake emergency treatment technologies. The paper also presents the test results of the system, which show that it has complete functions and its major performance indicators meet the design requirements.

The study demonstrates that the high speed railways earthquake early-warning system serves as an important technical tool for high speed railways to cope with the threat of earthquake to the operation safety. The key technical indicators of the system have excellent performance: The first report time of the P-wave is less than three seconds. From the first arrival of P-wave to the beginning of train braking, the total delay of onboard emergency treatment is 3.63 seconds under 95% probability. The average total delay for power failures triggered by substations is 3.3 seconds.

The paper provides a valuable reference for the research and development of earthquake early-warning system for high speed railways in other countries and regions. It also contributes to the earthquake prevention and disaster reduction efforts.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

Artificial intelligence (AI) models are demonstrating day by day that they can find long-term solutions to improve wastewater treatment efficiency. Artificial neural networks (ANNs) are one of the most important of these models, and they are increasingly being used to forecast water resource variables. The goal of this study was to create an ANN model to estimate the removal efficiency of biological oxygen demand (BOD), total nitrogen (TN), total phosphorus (TP) and total suspended solids (TSS) at the effluent of various primary and secondary treatment methods in a wastewater treatment plant (WWTP).

The MATLAB App Designer model was used to generate the data set. Various combinations of wastewater quality data, such as temperature(T), TN, TP and hydraulic retention time (HRT) are used as inputs into the ANN to assess the degree of effect of each of these variables on BOD, TN, TP and TSS removal efficiency. Two of the models reflect two different types of primary treatment, while the other nine models represent different types of subsequent treatment. The ANN model’s findings are compared to the MATLAB App Designer model. For evaluating model performance, mean square error (MSE) and coefficient of determination statistics (R2) are utilized as comparative metrics.

For both training and testing, the R values for the ANN models were greater than 0.99. Based on the comparisons, it was discovered that the ANN model can be used to estimate the removal efficiency of BOD, TN, TP and TSS in WWTP and that the ANN model produces very similar and satisfying results to the APPDESIGNER model. The R-value (Correlation coefficient) of 0.9909 and the MSE of 5.962 indicate that the model is accurate. Because of the many benefits of the ANN models used in this study, it has a lot of potential as a general modeling tool for a range of other complicated process systems that are difficult to solve using conventional modeling techniques.

The objective of this study was to develop an ANN model that could be used to estimate the removal efficiency of pollutants such as BOD, TN, TP and TSS at the effluent of various primary and secondary treatment methods in a WWTP. In the future, the ANN could be used to design a new WWTP and forecast the removal efficiency of pollutants.

This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.

The functional analysis method is the a priori estimate method or energy inequality method.

The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.

The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.

The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.

Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and △-convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT(0) spaces and Hilbert spaces as special cases.

The relevance of present consumption bias on personal finance has been confirmed in several studies and has important theoretical and practical implications. It has important, measurable implications when analyzing commitment or self-control, adherence to healthy habits (e.g. exercising or dieting), procrastination tendencies or savings. The purpose of this paper is to contribute to our understanding of these issues by postulating a model of income uncertainty within a hyperbolic discounting framework that measures the cost of financial intertemporal inconsistencies related to this bias. The emphasis is on the analysis of this cost. We also propose experimental designs and consistent estimation methods, as well as agent-based modelling extensions.

The authors develop a finite-horizon model with hyperbolic preferences. Individuals have a present bias distinct from their discount rate so their choices face intertemporal inconsistencies. The authors further extend the analysis with uncertainty about future incomes. Specifically, individuals live for three periods, and the authors find the optimal consumption levels in the perfect-information benchmark by backward induction. They then proceed to add biases and uncertainty to characterize their implications and measure the costs of the intertemporal inconsistencies they cause.

The authors measure how an agent's utility is greater when they “tie their hands” than when they are free to re-evaluate and change their consumption schedule. This “cost of being vulnerable to falling into temptation” only depends (increasingly) on the measure of the present bias and (decreasingly) on the discount factor. They analyze the varying effects on utility and consumption of changes in impatience and optimism. They conclude by discussing theoretical and practical implications; they also propose agent-based simulations, as well as empirical and experimental designs, to further test the relevance and applications of the results.

This model has important, measurable implications when analyzing commitment or self-control, adherence to healthy habits (e.g. exercising or dieting), procrastination tendencies or savings.

The results enhance the estimation of the costs of present biases such that employers can better identify the incentives required to acquire and retain human capital. The authors provide evidence that workers are vulnerable to contract renegotiations and about the need for a regulator that restores ex-ante efficiency. Similarly, in the private sector, firms could recognize the postulated consumer profiles and focus their resources on anxious, too-optimistic or potentially addictive consumers; this, again, provides some justification about the need for a regulator.

In traditional exponential discounting, the marginal rate of substitution of consumption between two points depends only on their distance; thus, it allows none of the intertemporal inconsistencies we often observe in real life. Therefore, hyperbolic discounting better fits the data. The authors model choice under uncertainty and focus on the costs caused when present biases (ex-post) push behaviour away from ex-ante optimality. They conclude by proposing experimental designs to further enhance the estimation and implications of these costs. The postulated refinements have the potential to improve previous analyses on commitment devices and commitment-related regulation.

The main purpose of this paper is to determine the discount function which better fits the individuals' preferences through the empirical analysis of the different functions used in the field of intertemporal choice.

After an in-depth revision of the existing literature and unlike most studies which only focus on exponential and hyperbolic discounting, this manuscript compares the adjustment of data to six different discount functions. To do this, the analysis is based on the usual statistical methods, and the non-linear least squares regression, through the algorithm of Gauss-Newton, in order to estimate the models' parameters; finally, the AICc method is used to compare the significance of the six proposed models.

This paper shows that the so-called q-exponential function deformed by the amount is the model which better explains the individuals' preferences on both delayed gains and losses. To the extent of the authors' knowledge, this is the first time that a function different from the general hyperbola fits better to the individuals' preferences.

This paper contributes to the search of an alternative model able to explain the individual behavior in a more realistic way.