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The purpose of this study is to introduce the reproducing kernel algorithm for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.

The method provides appropriate representation of the solutions in convergent series formula with accurately computable components. This representation is given in the W(Ω) and H(Ω) inner product spaces, while the computation of the required grid points relies on the R_(y,s) (x, t) and r_(y,s) (x, t) reproducing kernel functions.

Numerical simulation with different order derivatives degree is done including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found and is very valid for solving such time-fractional models.

Future work includes the application of the reproducing kernel algorithm to highly nonlinear time-fractional partial differential equations such as those arising in single and multiphase flows. The results will be published in forthcoming papers.

The study included a description of fundamental reproducing kernel algorithm and the concepts of convergence, and error behavior for the reproducing kernel algorithm solvers. Results obtained by the proposed algorithm are found to outperform in terms of accuracy, generality and applicability.

Developing analytical and numerical methods for the solutions of time-fractional partial differential equations is a very important task owing to their practical interest.

This study, for the first time, presents reproducing kernel algorithm for obtaining the numerical solutions of some certain classes of Robin time-fractional partial differential equations. An efficient construction is provided to obtain the numerical solutions for the equations, along with an existence proof of the exact solutions based upon the reproducing kernel theory.

The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.

Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed.

The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations.

In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.

The purpose of this paper is to introduce a local Newton basis functions collocation method for solving the 2D nonlinear coupled Burgers’ equations. It needs less computer storage and flops than the usual global radial basis functions collocation method and also stabilizes the numerical solutions of the convection-dominated equations by using the Newton basis functions.

A meshless method based on spatial trial space spanned by the local Newton basis functions in the “native” Hilbert space of the reproducing kernel is presented. With the selected local sub-clusters of domain nodes, an approximation function is introduced as a sum of weighted local Newton basis functions. Then the collocation approach is used to determine weights. The method leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs).

The method is successfully used for solving the 2D nonlinear coupled Burgers’ equations for reasonably high values of Reynolds number (Re). It is a well-known issue in the analysis of the convection-diffusion problems that the solution becomes oscillatory when the problem becomes convection-dominated if the standard methods are followed without special treatments. In the proposed method, the authors do not detect any instability near the front, hence no technique is needed. The numerical results show that the proposed method is efficient, accurate and stable for flow with reasonably high values of Re.

The authors used more stable basis functions than the standard basis of translated kernels for representing of kernel-based approximants for the numerical solution of partial differential equations (PDEs). The local character of the method, having a well-structured implementation including enforcing the Dirichlet and Neuman boundary conditions, and producing accurate and stable results for flow with reasonably high values of Re for the numerical solution of the 2D nonlinear coupled Burgers’ equations without any special technique are the main values of the paper.

Higher order statistics (HOS)-based blind source separation (BSS) technique has been applied to separate data to obtain a better performance than second order statistics-based method. The cost function constructed from the HOS-based separation criterion is a complicated nonlinear function that is difficult to optimize. The purpose of this paper is to effectively solve this nonlinear optimization problem to obtain an estimation of the source signals with a higher accuracy than classic BSS methods.

In this paper, a new technique based on HOS in kernel space is proposed. The proposed approach first maps the mixture data into a high-dimensional kernel space through a nonlinear mapping and then constructs a cost function based on a higher order separation criterion in the kernel space. The cost function is constructed by using the kernel function which is defined as inner products between the images of all pairs of data in the kernel space. The estimations of the source signals is obtained through the minimizing the cost function.

The results of a number of experiments on generic synthetic and real data show that HOS separation criterion in kernel space exhibits good performance for different kinds of distributions. The proposed method provided higher signal-to-interference ratio and less sensitive to the source distribution compared to FastICA and JADE algorithms.

The proposed method combines the advantage of kernel method and the HOS properties to achieve a better performance than using a single one. It does not require to compute the coordinates of the data in the kernel space explicitly, but computes the kernel function which is simple to optimize. The use of nonlinear function space allows the algorithm more accurate and more robust to different kinds of distributions.

Multiple-input multiple-output (MIMO) combined with multi-user massive MIMO has been a well-known approach for high spectral efficiency in wideband systems, and it was targeted to detect the MIMO signals. The increasing data rates with multiple antennas and multiple users that share the communication channel simultaneously lead to higher capacity requirements and increased complexity. Thus, different detection algorithms were developed for the Massive MIMO.

This paper focuses on the various literature analyzes on various detection algorithms and techniques for MIMO detectors. Here, it reviews several research papers and exhibits the significance of each detection method.

This paper provides the details of the performance analysis of the MIMO detectors and reveals the best value in the case of each performance measure. Finally, it widens the research issues that can be useful for future researchers to be accomplished in MIMO massive detectors

This paper has presented a detailed review of the detection of massive MIMO on different algorithms and techniques. The survey mainly focuses on different types of channels used in MIMO detections, the number of antennas used in transmitting signals from the source to destination, and vice-versa. The performance measures and the best performance of each of the detectors are described.

Compared with the low-fidelity model, the high-fidelity model has both the advantage of high accuracy, and the disadvantage of low efficiency and high cost. A series of multi-fidelity surrogate modelling method were developed to give full play to the respective advantages of both low-fidelity and high-fidelity models. However, most multi-fidelity surrogate modelling methods are sensitive to the amount of high-fidelity data. The purpose of this paper is to propose a multi fidelity surrogate modelling method whose accuracy is less dependent on the amount of high-fidelity data.

A multi-fidelity surrogate modelling method based on neural networks was proposed in this paper, which utilizes transfer learning ideas to explore the correlation between different fidelity datasets. A low-fidelity neural network was built by using a sufficient amount of low-fidelity data, which was then finetuned by a very small amount of HF data to obtain a multi-fidelity neural network based on this correlation.

Numerical examples were used in this paper, which proved the validity of the proposed method, and the influence of neural network hyper-parameters on the prediction accuracy of the multi-fidelity model was discussed.

Through the comparison with existing methods, case study shows that when the number of high-fidelity sample points is very small, the R-square of the proposed model exceeds the existing model by more than 0.3, which shows that the proposed method can be applied to reducing the cost of complex engineering design problems.

Research and development (R&D) is increasingly considered to be a key driver of economic growth. The relationship between these variables is commonly examined using linear models and thus relies only on single-point estimates. Against this background, this paper provides new evidence on the impact of R&D on economic growth using a machine learning approach that makes it possible to go beyond single-point estimation.

The authors use the kernel regularized least squares (KRLS) approach, a machine learning method designed for tackling econometric models without imposing arbitrary functional forms on the relationship between the outcome variable and the covariates. The KRLS approach learns the functional form from the data and thus yields consistent estimates that are robust to functional form misspecification. It also provides pointwise marginal effects and captures non-linear relationships. The empirical analyses are conducted using a sample of 101 countries over the period 2000–2020.

The estimates indicate that R&D expenditure and high-tech exports positively and significantly influence economic growth in a non-linear manner. The authors also find a positive and statistically significant relationship between economic growth and greenhouse gas emissions. In both cases, the effects are higher for upper-middle-income and high-income countries. These results suggest that a substantial effort is needed to green economic growth. Internet access is found to be an important factor in supporting economic growth, especially in high-income and middle-income countries.

This paper contributes to underlining the importance of investing in R&D to support growth and shows that the disparity between countries is driven by the determinants of economic growth (human capital in R&D, high-tech exports, Internet access, economic freedom, unemployment rate and greenhouse gas emissions). Moreover, since the authors find that R&D expenditure and greenhouse gas emissions are positively associated with economic growth, technological progress with green characteristics may be an important pathway for green economic growth.

This paper uses an innovative machine learning method to provide new evidence that innovation supports economic growth.

The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation.

In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives.

The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy.

The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

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.

This paper aims to propose a robust method for non-rigid point set registration, using the Gaussian mixture model and accommodating non-rigid transformations. The posterior probabilities of the mixture model are determined through the proposed integrated feature divergence.

The method involves an alternating two-step framework, comprising correspondence estimation and subsequent transformation updating. For correspondence estimation, integrated feature divergences including both global and local features, are coupled with deterministic annealing to address the non-convexity problem of registration. For transformation updating, the expectation-maximization iteration scheme is introduced to iteratively refine correspondence and transformation estimation until convergence.

The experiments confirm that the proposed registration approach exhibits remarkable robustness on deformation, noise, outliers and occlusion for both 2D and 3D point clouds. Furthermore, the proposed method outperforms existing analogous algorithms in terms of time complexity. Application of stabilizing and securing intermodal containers loaded on ships is performed. The results demonstrate that the proposed registration framework exhibits excellent adaptability for real-scan point clouds, and achieves comparatively superior alignments in a shorter time.

The integrated feature divergence, involving both global and local information of points, is proven to be an effective indicator for measuring the reliability of point correspondences. This inclusion prevents premature convergence, resulting in more robust registration results for our proposed method. Simultaneously, the total operating time is reduced due to a lower number of iterations.