In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

In this paper we present a new method for solving fully fuzzy multi-objective linear programming problems and find the fuzzy optimal solution of it. Numerical examples are provided to illustrate the method.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

This paper delves into some significant performance measures (PMs) of a bulk arrival queueing system with constant batch size b, according to arrival rates and service rates being fuzzy parameters. The bulk arrival queuing system deals with observation arrival into the queuing system as a constant group size before allowing individual customers entering to the service. This leads to obtaining a new tool with the aid of generating function methods. The corresponding traditional bulk queueing system model is more convenient under an uncertain environment. The α-cut approach is applied with the conventional Zadeh's extension principle (ZEP) to transform the triangular membership functions (Mem. Fs) fuzzy queues into a family of conventional b

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

     The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated.  The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters,  and , with the int

The main objective of e-learning platforms is to offer a high quality instructing, training and educational services. This purpose would never be achieved without taking the students' motivation into consideration. Examining the voice, we can decide the emotional states of the learners after we apply the famous theory of psychologist SDT (Self Determination Theory). This article will investigate certain difficulties and challenges which face e-learner: the problem of leaving their courses and the student's isolation.
Utilizing Gussian blending model (GMM) so as to tackle and to solve the problems of classification, we can determine the learning abnormal status for e-learner. Our framework is going to increase the students’ moti

Infectious diseases pose a global challenge, necessitating an exploration of novel methodologies for diagnostics and treatments. Since the onset of the most recent pandemic, COVID-19, which was initially identified as a worldwide health crisis, numerous countries experienced profound disruptions in their healthcare systems. To combat the spread of the COVID-19 pandemic, governments across the globe have mobilized significant efforts and resources to develop treatments and vaccines. Researchers have put forth a multitude of approaches for COVID-19 detection, treatment protocols, and vaccine development, including groundbreaking mRNA technology, among others.

This matter represents not only a scientific endeavor but also an essenti

The growth of developments in machine learning, the image processing methods along with availability of the medical imaging data are taking a big increase in the utilization of machine learning strategies in the medical area. The utilization of neural networks, mainly, in recent days, the convolutional neural networks (CNN), have powerful descriptors for computer added diagnosis systems. Even so, there are several issues when work with medical images in which many of medical images possess a low-quality noise-to-signal (NSR) ratio compared to scenes obtained with a digital camera, that generally qualified a confusingly low spatial resolution and tends to make the contrast between different tissues of body are very low and it difficult to co

Semantic segmentation is an exciting research topic in medical image analysis because it aims to detect objects in medical images. In recent years, approaches based on deep learning have shown a more reliable performance than traditional approaches in medical image segmentation. The U-Net network is one of the most successful end-to-end convolutional neural networks (CNNs) presented for medical image segmentation. This paper proposes a multiscale Residual Dilated convolution neural network (MSRD-UNet) based on U-Net. MSRD-UNet replaced the traditional convolution block with a novel deeper block that fuses multi-layer features using dilated and residual convolution. In addition, the squeeze and execution attention mechanism (SE) and the s