Some techniques are available to solve numerically higher order boundary value problems. The aim of this paper is to apply Galerkin weighted residual method (GWRM) for solving eleventh order linear and nonlinear boundary value problems. Using GWRM, approximate solutions of eleventh-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results are depicted both graphically and numerically. All results are compared with the analytical solutions to show the convergence of the proposed algorithm. It is observed that the present method is a more effective tool and yields better results. All problems are computed using the software MATLAB R2017a.

A water plant is one out of numerous examples of critical infrastructure which include electric power systems, traffic control systems, manufacturing systems. Humans, domestic animals, industries, and to mention a few, rely so much on these critical infrastructures as they depend solely on water plants services. However, the present situation is such that water plant falls short of its use due to breakthdown, underperformance and lack of proper management in place, especially in Nigeria. This situation has hindered effective process control of water plants, thereby making it impossible to account correctly for its production process and to prevent break down of machinery. In this paper, we formulated, designed and evaluated a model that offers effective process control during production by a water plant. By means of a quantitative research approach, the study provided a full description of the flow paths and compartments connected in a process plant. We extracted information about the tanks sizes, piped diameter, number of pumps and number of tanks from the operational manual booklet of the water plants as the source of the dataset. A prototype model for the process plant was specified to establish the system's flow parts and storage compartments of mass. Based on the extracted data, we formulated mathematical models to describe the system’s behaviour. The model was simulated in Simulink MatLab and used to investigate the effects of varying the parameters of the plant, especially the restriction (R) against water flow in the connecting pipes, as it affects the capacity of the tanks. The results of the simulation show that varying any of the values of the model parameters affects the water levels in the various tanks. Also, the results suggest a safe process parameter during processing. Notably, the result reveals that reducing the diameter of a pipe 1 from 300mm to 25mm or below will lead to water overflow in tanks, which will result in water wastage, machine and environmental damages. Thus, the research provided an effortless way of determining the various pipes sizes, sizes of tanks to be used and the expected output of the production process of the plant, before going into its physical production.

In this study, we propose an effective numerical algorithm to study the Covid-19 epidemic model that is in the form of a system of the coupled ordinary differential equation. This algorithm includes the collocation method and truncated Laguerre wavelet. Here, we reduce the system of a differential equation into a set of algebraic equations which are having unknown Laguerre wavelet coefficients. Moreover, the modeling of the spreading of a Covid-19 disease in a population is numerically solved by the present method.

With the increasing knowledge integration and task complexity, individual ability demands a highly cohesive interdisciplinary team to amplify. To study the elements of successful team cooperation and explore valuable team strategies, this paper present a network pattern recognition model based on PageRank algorithm and principal component analysis method. Further, a team cooperation performance model based on group dynamic theory is built to capture the individual contribution and teamwork characteristic as a supplementary evaluation. By applying the model into football competition, we found our model has 73.68% accuracy, proving its outstanding adaptability. Based on the model, we can get the information of the inner network structure of a team, know the most significant contributors pertinent with team success, and make further justification plans and suggestions to achieve teamwork improvement.

This article puts forward the double pulse delay investor sentiment spread model, using the stroboscopic map of discrete system, prove the existence of periodic solution, by impulsive differential inequalities proved the global asymptotic stability of the emotional balance, use comparison principle prove persistent rumors of impulsive differential equation, analyses the threshold delay affect mood, finally, the numerical simulation results, the result confirms my analysis very well.

In this paper, we briefly introduce four methods for functional classification. To compare the effects of the four models, we generate the data from Gaussian process based on a functional mixed-effects model, square exponential kernel is used in random-effect term to describe the nonlinear structure of the data. The outcomes show that the two functional classification models have a better prediction correct rate than the two machine learning classification models.

This research starts from the lack of reliable and effective disease identification biomarkers for attention deficit hyperactivity disorder (ADHD). Based on the functional classification methods, including functional generalized linear model (FGLM), functional linear discriminant analysis (FLDA) method and functional principal component analysis (FPCA), we establish models of corpus callosum (CC) shape and give some analyses. The purpose is to verify whether the corpus callosum shape data can be used as an effective classification basis for disease discrimination and classification, and to provide a new auxiliary discriminant diagnosis idea for ADHD disease discrimination.

In this paper, we studied the application of two-dimensional convolutional neural networks to the classification of multivariate time series. Time series sample data is usually a set of measurement values of a single attribute or multiple attributes at continuous time points separated by uniform time intervals. It is a set of structured data, usually non-discrete, time-related between data Features such as sex, feature space, and large dimension. At present, most methods for time series classification problems need to go through an extremely complex data preprocessing process and related feature engineering and do not consider the long pattern information hidden in different time dimensions of time series data, and the different characteristics of multivariate time series data Relevant information in the space dimension between. By converting multivariate time series data into matrix form, this paper proposes an end-to-end deep learning model Pyramid-CNN based on two-dimensional convolutional neural networks, which uses two-dimensional convolution kernels to extract the spatial dimensions of multivariate time series data and the relevant information in the time dimension, and applied it to the user behavior recognition time series data set. The experimental results show that for this data set, compared with the existing methods, the model proposed in this paper has higher performance Accuracy and robustness, with a good classification effect.

This paper proposes a new class of nonlinear systems called generalized Lorenz-like systems which can be used to describe many usual three-dimensional chaotic systems such as Lorenz system, Lü system, Chen system, Liu system, etc. Then the control and synchronization problems for generalized Lorenz-like system via a single input are studied and two control laws are proposed based on partial feedback linearization with asymptotically stable zero dynamics. Finally, the numerical simulations demonstrate the correctness and effectiveness of the proposed control strategies.