Computational Sciences and Engineering
Volume:2 Issue: 1, Spring 2022

Fractional differential equations (FDEs) have recently attracted much attention. ‎‎‎‎‎‎Fractional Mathieu equation is a well-known FDE.‎ ‎‎‎Here, a method based on operational matrix of triangular functions for fractional order integration is introduced for the numerical solution of fractional Mathieu equation.‎‎‎‎This technique is a successful method because of reducing the problem to a system of linear equations. By solving this system, an approximate solution is obtained. ‎‎‎‎Illustrative examples demonstrate accuracy and efficiency of the method.

Electromechanical and regular contractions of the smooth muscles of the gastric wall are responsible for grinding, mixing, and propulsion food into the intestines. Lack of proper functioning in contracting the smooth muscle causes digestive disorders. This study aimed to present an electromechanical model for the contraction of smooth muscles of the human gastric wall in the physiological state. In this model, the electromechanical contraction of the smooth muscles is due to the distribution of the electrophysiological slow wave (Due to ionic interaction of cells with extracellular environment and adjacent cells) over 240 cells and 548 links. The results showed that the contraction started at the beginning of the gastric wall and gradually transferred to the end of the wall (pylorus). Also, it was found that the maximum contraction of about 34.7% occurs at the end of the model and near the pyloric sphincter. Finally, the behavior of tissues can be simulated non-invasively using the modeling and their function can be examined under physiological and pathological conditions.

The brain’s free energy principle (FEP), and active inference, proposed by Karl Friston is a model that, based on the Bayesian inference, shows uncertainly how the concepts are generated based on the stimuli perceived by the human. In this model, it is assumed that the concepts exist in a hidden and real form in the environment, and the agent should identify and encode the concepts in his brain through the indirect perception of the stimuli of these concepts. This process takes place based on the Bayesian inference in the declarative or procedural real concepts (concepts in the environment) generation requiring the agent’s actions and perceptions by the active inference process. Declarative concepts are concepts that do not require any action on the environment to learn and are learned directly through the transfer of knowledge. But procedural concepts are concepts that require the selection of different actions on the environment to learn (such as driving). In the current study, objectification or construction of abstract concepts (concepts that do not exist in the environment but are formulated by the agent through the reception of environmental stimuli in his brain) is based on active inference. In the proposed model, which is an extension to the active inference model, the policies must be identified or generated by the agent because these policies do not already exist. The identification or construction of these policies to generate or objectify the abstract concepts would mean knowledge generation and learning how the concepts are generated.

In this paper, we study the number of solutions of commutator equation [x^{n},y]=g in two classes of finite groups. For $g in G$ we consider $ rho^{n}_g(G)={(x,y)| x,yin G, [x^{n},y]=g}$ . Then the probability that the commutator equation [x^{n},y]=g has a solution in a finite group $G$, written , $P^{n}_g(G)$ is equal to $frac{|rho^{n}_{g}(G)|}{|G|^2}$ . By using the numerical solutions of the equation $xy - zu equiv t(bmod~n)$ we derive formulas for calculating the probability of $P^{n}_g(G)$, for some finite groups $G$ .

*The formulas are not displayed correctly.

One of the most important and essential requirements for Internet of things is security of its limited resources. The simple nature of many devices on the internet of things makes them the main purpose of a variety of attacks .To deal with these attacks, there are many protocols for authentication for internet of things .In fact, an appropriate authentication protocol plays an important role in ensuring secure communications for internet of things. In this paper, we propose an authentication scheme with key agreement on elliptic curve cryptography (ECC).the simulation results using SCYTHER show that our protocol is secure against active and passive attacks.

Today, countries' sovereignty and national security strongly rely on the reliable operation and continuous monitoring of information technology infrastructure against security threats. As a result, the importance of comprehensive command and control and consistent oversight of IT security has become increasingly apparent in recent years. Modern command and control systems are dynamically and continuously monitoring and analyzing their mission space. This scope of operations increases the need to create a coherent and integrated structure in developing a system based on a well-defined architecture. Best of over knowledge has been little discussion on how to design command and control systems better. In this paper, we proposed architecture using data analysis solutions in cyber command and control missions. The proposed architecture is based on service-oriented and layered architecture to activate the quality features of interoperability, distributability, heterogeneous development, and scalability. Also, a prototype has been implemented to demonstrate its applicability through solution architecture. The online survey questionnaire validates the proposed architecture and its implementation.

Efficiency of convolutional neural networks (CNNs) with different dimensions is assessed for polarimetric synthetic aperture radar (PolSAR) image classification in this work. This article is the extended version of the paper presented in “4 International Conference on Soft Computing (CSC2021)”. A PolSAR image contains polarimetric and spatial information of materials present in the scene. So, processing of these information in one, two or three dimensions results in different outputs. Three simple architectures of CNNs with different dimensions are proposed for PolSAR image classification in this paper. A one dimensional CNN (1D CNN) is suggested for polarimetric feature extraction. A 2D CNN is presented for spatial feature extraction and a 3D CNN is introduced for polarimetric-spatial feature extraction. The performance of CNNs are compared with morphological profile of PolSAR cube when fed to the support vector machine (SVM) and random forest (RF) classifiers. The experiments are done in two cases of using 1% and 5% training samples. Superiority of 3D CNN compared to other methods is shown using different quantitative classification measures.

The present study focuses on the developments of analytical solutions for vehicle dynamic behaviour under the influence of magnetorheological fluid damper. Dynamic models of a quarter vehicle are considered. Also, the damping force of the magnetorheological fluid damper is modelled using Bouc-Wen and modified Bouc-Wen models. The developed vibration models for the study of the dynamic behaviour of the vehicle are solved using Laplace transform method. The parametric studies reveal that the oscillation of the displacement of the axle is more fluctuating compared to the displacement of the body due to the installation of the damper between the body and the axle in which the damper acts as a shock-absorber. Moreover, the variation between the two models of Bouc-Wen and modified Bouc-Wen models is established. It is analytically validated that the Bouc-Wen model cannot produce the experimentally observed roll-off in the yield region for velocities with a small absolute value and operational sign opposite to the sign of the acceleration. Therefore, the use of the modified Bouc-Wen model is recommended. It is hoped that the developed exact analytical models will serve as the basis for comparisons of any other method of analysis of the problem.

In this paper a third-order rectangular nanoplate model is developed for the bending and vibration analysis of a graphene nanoplate based on a modified couple stress theory. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, and the frequencies of the nanoplate are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The governing equations are numerically solved. The effect of material length scale, length, width and thickness of the nanoplate on the bending and vibration ratios are investigated and the results are presented and discussed in details.

In the current study, the influences of adding graphene nanosheets (GNSs) on the elastic characteristics of concrete are examined using the Mori-Tanaka micromechanical model. By the use of the base concrete hydration equation, the role of hydration time in the Young’s modulus and Poisson ratio of GNS-filled concrete is analyzed. Also, the formation of GNS agglomeration as one of the most major microstructural features of composite materials containing nano-sized particles is considered in the micromechanical simulation. Significant contribution of the hydration time to the elastic properties of GNS-reinforced concrete is confirmed. Generally, the addition of GNSs can help to enhance the concrete elastic modulus and decrease the Poisson’s ratio. The results show that well-dispersed GNSs lead to the enhancement of mechanical performance of the concrete, whereas GNS agglomeration causes significant reduction of elastic modulus.

With the advent of the Web today, users' opinions can be incorporated into a variety of applications. Automated methods have been developed to derive users' general sense from these textual comments, often known as sentiment analysis, and aim to determine the polarity of a text relative to a subject. One of the challenges is the inability to use one domain of data to analysis sentiment in another domain and the lack of sufficient labelled data in a particular domain. To address these challenges, multi-domain sentiment analysis systems have been developed. This paper propose Bi-GRU Capsule ensemble approaches for multi-domain sentiment classification to address the mentioned issues. Using a weighted score of Term-Frequency and Inverse Document Frequency degree and the initial polarity of the sample test data on each domain, a new aggregated score of final polarity is obtained. The DRANZIERA protocol is used for evaluation of the proposed model. The outcomes demonstrate the effectiveness of the proposed approach and also set a plausible starting point for future work

The purpose of this paper is to present a wavelet method for numerical solutions Fokker-Planck-Kolmogorov time-fractional differential equations with initial and boundary conditions. The authors was employed the Bernoulli wavelets for the solution of Fokker-Planck-Kolmogorov time-fractional differential equation. We calculated the Bernoulli wavelet fractional integral operation matrix of the fractional order and the upper error boundary for the Riemann‐Levilleville fractional integral operation matrix and the Bernoulli wavelet fractional integral operation matrix. The Fokker-Planck-Kolmogorov time-fractional differential equation is converted to the linear equation using the Bernoulli wavelet operation matrix in this technique. This method has the advantage of being simple to solve. The simulation was carried out using MATLAB software. Finally, the proposed strategy was used to solve certain problems. the Bernoulli wavelet and Bernoulli fraction of the fractional order, the Bernoulli polynomial, and the Bernoulli fractional functions were introduced. Explaining how functions are approximated by fractional-order Bernoulli wavelets as well as fractional-order Bernoulli functions. The Bernoulli wavelet fractional integral operational matrix was used to solve the Fokker-Planck-Kolmogorov fractional differential equations. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. The results revealed that the suggested numerical method is highly accurate and effective when used to Fokker-Planck-Kolmogorov time fraction differential equations