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Activation functions play a crucial role in enabling neural networks to carry out tasks with increased flexibility by introducing non-linearity. The selection of appropriate activation functions becomes even more crucial, especially in the context of deeper networks where the objective is to learn more intricate patterns. Among various deep learning tools, Convolutional Neural Networks (CNNs) stand out for their exceptional ability to learn complex visual patterns. In practice, ReLu is commonly employed in convolutional layers of CNNs, yet other activation functions like Swish can demonstrate superior training performance while maintaining good testing accuracy on different datasets. This paper presents an optimally refined strategy for deep learning-based image classification tasks by incorporating CNNs with advanced activation functions and an adjustable setting of layers. A thorough analysis has been conducted to support the effectiveness of various activation functions when coupled with the favorable softmax loss, rendering them suitable for ensuring a stable training process. The results obtained on the CIFAR-10 dataset demonstrate the favorability and stability of the adopted strategy throughout the training process. [ABSTRACT FROM AUTHOR]

The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to understand the intricate correlations between the oscillator's variables and to precisely capture their dynamics by being trained on a dataset of known oscillator behaviors. In this work, we discuss the main challenge of predicting the behavior of oscillators without depending on complex strategies or time-consuming simulations. The present work proposes a favorable modified form of neural structure to improve the strategy for simulating linear and nonlinear harmonic oscillators from mechanical systems by formulating an ANN as a DNN via an appropriate oscillating activation function. The proposed methodology provides the solutions of linear and nonlinear differential equations (DEs) in differentiable form and is a more accurate approximation as compared to the traditional numerical method. The Van der Pol equation with parametric damping and the Mathieu equation are adopted as illustrations. Experimental analysis shows that our proposed scheme outperforms other numerical methods in terms of accuracy and computational cost. We provide a comparative analysis of the outcomes obtained through our proposed approach and those derived from the LSODA algorithm, utilizing numerical techniques, Adams–Bashforth, and the Backward Differentiation Formula (BDF). The results of this research provide insightful information for engineering applications, facilitating improvements in energy efficiency, and scientific innovation. [ABSTRACT FROM AUTHOR]

This paper accords with the theoretical study of lifting and drainage of Sisko fluid film on a vertically upward moving cylinder with surface tension. The flow on cylinder is induced by the upward motion of the cylinder, gravity and surface tension gradient. The resulting nonlinear ordinary differential equation is solved for a series form solution by making use of the Adomian decomposition method (ADM). Expressions for the flow variables like velocity, volume flow rate, shear stress and surface tension are derived. Positions of stationary points and thickness of uniform film are computed numerically in MATHEMATICA. The inverse capillary number C, Stokes number S t , Sisko fluid parameter β and fluid behavior index n emerged as flow control parameters. The study showed that the positions of stationary points relocate towards the surface of the cylinder by the increase of C and S t while their positions relocate towards the fluid–air interface with increasing β and n. Thickness of uniform film decreases when the values of C and S t are increased whilst it increases with the increase of β and n. Analogy between the Newtonian fluid and the Sisko fluid's shear thinning and shear thickening behaviors for positions of stationary points, thickness of uniform film and surface tension is also made. [ABSTRACT FROM AUTHOR]

In this study, we look at the solutions of nonlinear partial differential equations and ordinary differential equations. Scientists and engineers have had a hard time coming up with a way to solve nonlinear differential equations. Almost all of the nature's puzzles have equations that aren't linear. There aren't any well-known ways to solve nonlinear equations, and people have tried to improve methods for a certain type of problems. This doesn't mean, however, that all nonlinear equations can be solved. With this in mind, we'll look at how well the variation approach works for solving nonlinear DEs. Different problems can be solved well by using different methods. We agree that a nonlinear problem might have more than one answer. Factorization, homotropy analysis, homotropy perturbation, tangent hyperbolic function and trial function are all examples of ways to do this. On the other hand, some of these strategies don't cover all of the nonlinear problem-solving methods. In this paper, a new method called the variation iterative method with Laplace transformation is used to find a solution to the highly nonlinear evolution of a simple pendulum whose rotation revolves around its fixed position. When the Laplace operator is used to change the Maximum Minimum Approach, Amplitude Frequency Formulation and Variation Iteration Method (VIM) nonlinear oscillators, the results of the analysis are all the same. The method for solving nonlinear oscillators, as well as their time and boundary conditions, can be shown to be correct by comparing analytical results of VIM obtained through the Laplace transformation. [ABSTRACT FROM AUTHOR]

Optimizers in Convolutional Neural Networks play an important role in many advanced deep learning models. Studies on advanced optimizers and modifications of existing optimizers continue to hold significant importance in the study of machine tools and algorithms. There are a number of studies to defend and the selection of these optimizers illustrate some of the challenges on the effectiveness of these optimizers. Comprehensive analysis on the optimizers and alteration with famous activation function Rectified Linear Unit (ReLU) offered to protect effectiveness. Significance is determined based on the adjustment with the original Softmax and ReLU. Experiments were performed with Adam, Root Mean Squared Propagation (RMSprop), Adaptive Learning Rate Method (Adadelta), Adaptive Gradient Algorithm (Adagrad) and Stochastic Gradient Descent (SGD) to examine the performance of Convolutional Neural Networks for image classification using the Canadian Institute for Advanced Research dataset (CIFAR-10). [ABSTRACT FROM AUTHOR]

Securing data in this era of technology is the most challenging task. Cryptography is a practice of different techniques and methodologies for data confidentiality, data integrity, authentication, and non-repudiation. Many mathematical techniques are being used in cryptography from ancient times. The Laplace integral transforms and its inverse forms gain significant importance to design cryptographic methods. In this work, we propose cryptography methodology based on Natural and Elzaki transform and this study comprises a unique structure that provides Laplace-Elzaki and Sumudu-Elzaki methodologies. A generalized version of Laplace and Sumudu transform is also presented. [ABSTRACT FROM AUTHOR]

Let Tn be the set of trees with n vertices and having diameter 4. We show that four classes in Tn satisfy a conjecture posed by Radenkovi and Gutman [Total π-electron energy and Laplacian energy: how far the analogy goes? J. Serb. Chem. Soc., 72:12:1343–1350, 2007]. The conjecture relates the Laplacian energy of path Pn, tree Tn, and star Sn. [ABSTRACT FROM AUTHOR]

A mathematical model comprising Darcy Forchheimer effects on the 3D nanofluid flow with engine oil as a base fluid containing suspended carbon nanotubes (CNTs) is envisioned. The CNTs are of both types i.e., multi-wall carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs). The flow is initiated by an exponentially stretched surface. The impacts of Cattaneo–Christov heat flux along with velocity and thermal slip conditions are key factors in the novelty of the defined model. The boundary layer notion is designed to convert the compact form of equations into the component shape. Appropriate transformations lead to differential equations with high nonlinearity. The final non-dimensional system is solved numerically by a "MATLAB" function known as bvp4c. For both CNTs, different graphical sketches are drawn to present the influence of arising parameters versus related profiles. The outcomes show that higher slip parameter boosts the axial velocity, whereas fluid temperature lowers for a sturdier relaxation parameter. [ABSTRACT FROM AUTHOR]