Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator

Ercan ÇELİK

In this study, the modification of the concept of exponentially convex function, which is a general version of convex functions, given on the coordinates, is recalled. With the help of an integral identity which includes the Riemann-Liouville (RL) fractional integral operator, new Hadamard-type inequalities are proved for exponentially convex functions on the coordinates. Many special cases of the results are discussed. Keywords: hadamard-type inequalities; rectangle

The Consecutive Substitution Method for Boundary Value Problems (BVPs) with Retarded Argument

Ercan ÇELİK

In this study, we applied an approximate solution method for solving the boundary value problems (BVPs) with retarded argument. The method is the consecutive substitution method. The consecutive substitution method was applied and an approximate solution was obtained. The numerical solution and the analytical solution are compared in the table. The solutions were found to be compatible. Keywords: approximate solution; boundary-value problem; numerical solution; retarded argument; solution methods; substitution method; boundary value problems

Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation

Ercan ÇELİK

In this study, the Lie symmetry analysis is given for the time-fractional telegraph equation with the Riemann-Liouville derivative. This equation is useable to describe the physical processes of models possessing memory. By applying classical and nonclassical Lie symmetry analysis for the telegraph equation with & alpha;,& beta; time-fractional derivatives and some technical computations, new infinitesimal generators are obtained. The actual methods give some classical symmetries while the nonclassical approach will bring back other symmetries to these equations. The similarity reduction and c ...More

Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Ercan ÇELİK

In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo-Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p & sdot; and q & sdot;. Finally, we prove a finite-time blow-up result for negative initial energy. Keyword: global existence; wave-equation

Existence, Decay, and Blow-up of Solutions for a Weighted m -Biharmonic Equation with Nonlinear Damping and Source Terms

Ercan ÇELİK

In this paper, we consider the weighted m-biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao's inequality. Finally, we proved the blow-up of solutions in finite time.

Approximate Solution of Volterra-Stieltjes Linear Integral Equations of the Second Kind with the Generalized Trapezoid Rule

Avıt ASANOV | Elman HAZAR | Kalıskan MATANOVA

The numerical solution of linear Volterra-Stieltjes integral equations of the second kind by using the generalized trapezoid rule is established and investigated. Also, the conditions on estimation of the error are determined and proved. A selected example is solved employing the proposed method.

Computational Intelligence and Things Technology-Based Collection and Design of Inheritance Characteristics of Tea Product Packaging Art Form

In view of the core process data such as temperature and humidity of the tea product packaging process and the automatic control operation parameters of the production line, this paper designs a smart tea product packaging 5G Internet of Things gateway system, which realizes the 5G Internet of Things onsite monitoring and remote monitoring of the tea product packaging production line equipment. The design and implementation of the 5G Internet of Things gateway system are divided into three aspects, namely, 5G Internet of Things gateway configuration design, data communication protocol conversi ...More

Internet of Things Application of Intelligent and Innovative Learning Strategies in the Higher English Education System

In order to improve the effect of higher English teaching, this paper builds a higher English education system based on Internet of Things technology. The optimization aim of this study is to provide an online DRX parameter optimization technique that is compatible with the RRC protocol architecture. This work employs algorithms based on reinforcement learning to accomplish parameter optimization and dynamic control by selecting optimal DRX parameters and dynamically configuring them via decision-making processes. Furthermore, this article enhances the Internet of Things algorithm and applies ...More

Harr-NMF Feature Extraction for Multilevel Educational Technology Teaching Big Data System

An essential role in improving educational informatization and encouraging new approaches to education is played by educational technology, a specialist field that supports both theorising and doing in this area. When it comes to learning educational technology, students must have excellent professional knowledge and abilities, as well as a thorough understanding of data. Harr-NMF feature extraction for educational technology teaching large data systems is the focus of this project. With the help of big data technology, the construction of a teaching resource sharing system provides useful sol ...More

Application of Virtual Reality Technology in Visual Optimization of Product Appearance Design

Virtual reality technology is used in this research to perform an in-depth investigation and the analysis of visual optimization of product appearance design, as well as to adapt evolving technology to practical design. The breadth of virtual display technology may be further investigated, and software abilities can be enhanced by studying the virtual display of intelligent goods. The performance indicators of the product may be exhibited in an all-around manner via the virtual display, giving customers an intuitive experience and thereby stimulating consumers' desire to purchase. To achieve t ...More

Image Recognition about Stability of Soft Surrounding Rock in Tunnel Based on ILBP Algorithm

With China's fast expansion of urban traffic and railway engineering, a great number of subway and railway lines have been erected in subterranean tunnels in recent years. When the tunnel is in the process of construction, it will encounter the weak fracture zone, and the surrounding rock of this part of the tunnel is often poor stability and deformation is difficult to control, which will lead to the smooth progress of the project, delay and other problems. Therefore, to facilitate the timely treatment of tunnel soft surrounding rock, the study of image recognition of its stability is particu ...More

Intelligent Action Recognition and Dance Motion Optimization Based on Multi-Threshold Image Segmentation

In order to improve the recognition and optimization effect of dance movements, this paper combines multi-threshold image segmentation technology to perform intelligent recognition of dance movements. Moreover, this paper analyzes the window focus calibration process in the cascade multi-threshold expansion method and focuses the window on the object body to expand from small to large. Then, due to the local optimum problem of single-layer expansion, this paper proposes a cascade expansion method, and comparative experiments analyze the effect of this method on window optimization. In addition ...More