An Arithmetic-Trigonometric Optimization Algorithm with Application for Control of Real-Time Pressure Process Plant

This paper proposes a novel hybrid arithmetic–trigonometric optimization algorithm (ATOA) using different trigonometric functions for complex and continuously evolving real-time problems. The proposed algorithm adopts different trigonometric functions, namely sin, cos, and tan, with the conventional sine cosine algorithm (SCA) and arithmetic optimization algorithm (AOA) to improve the convergence rate and optimal search area in the exploration and exploitation phases. The proposed algorithm is simulated with 33 distinct optimization test problems consisting of multiple dimensions to showcase the effectiveness of ATOA. Furthermore, the different variants of the ATOA optimization technique are used to obtain the controller parameters for the real-time pressure process plant to investigate its performance. The obtained results have shown a remarkable performance improvement compared with the existing algorithms.

Distortion Coefficients of the $$\alpha $$-Grushin Plane

We compute the distortion coefficients of the $$\alpha $$ α -Grushin plane. They are expressed in terms of generalised trigonometric functions. Estimates for the distortion coefficients are then obtained and a conjecture of a measure contraction property condition for the generalised Grushin planes is suggested.

Pengembangan Lembar Kegiatan Siswa Berbasis Online Berbantuan Geogebra Book untuk Siswa SMA Kelas X pada Materi Trigonometri

The implementation of distance learning can not be separated from various problems, including students who are lack of motivation, teachers who find difficulties to work together with parents, and teachers who find difficulties to develop ideas on technology-based learning. To overcome these problems, the student activity sheet which equipped with practice questions and assessments with Geogebra Book aid is already developed as a learning innovation. The material developed in this research is trigonometry with the sub material of graph of trigonometric functions. The research model which used is ADDIE (Analysis, Design, Development, Implement, Evaluate). The research was conducted in SMA Negeri 1 Kepanjen by involving 10 students of social class grade X as test subjects, consisting of 3 students with low ability, 4 students with moderate ability, and 3 students with high ability. Data analysis was measured based on aspects of validity and practicality. Calculation of research data shows that the research product is valid based on an average validity score of 93% and practical based on an average practicality score of 84%. Based on the results of this data analysis, it can be concluded that the product development of student activity sheet along with practice questions and assessments meets the valid and practical criteria to facilitate students and teachers in the process of learning activities.

Exponentials of general multivector in 3D Clifford algebras

Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Clp;q are presented for n = p + q = 3. The obtained exponential formulas were applied to find exact GA trigonometric and hyperbolic functions of MV argument. We have verified that the presented exact formulas are in accord with series expansion of MV hyperbolic and trigonometric functions. The exponentials may be applied to solve GA differential equations, in signal and image processing, automatic control and robotics.

Two Trigonometric Intuitionistic Fuzzy Similarity Measures

Intuitionistic Fuzzy Sets(1986) invented by Atanassov(Atanassov, 1986) has gained the wide popularity among various researchers because of its applications in various fields such as image processing, edge detection, medical diagnosis, pattern recognition etc. One of the significant tool by which the decision can be made is Intuitionistic Fuzzy Similarity Measure. In this communication, the authors have introduced two new Intuitionistic fuzzy similarity measures based on the trigonometric functions and its validity is proved. The proposed similarity measure is applied to medical diagnosis and pattern recognition.

To the question of restoring symbol sequences encoding noisy periodic functions

In business informatics, one of the research subjects is the analysis of data on processes in applied subject areas; here problems of qualitative analysis arise. Such problems arise, for example, in the qualitative study of log files of business processes, in the analysis and prediction of time series and other processes of a different nature. Quite often, to represent information about the processes under study, the methods of qualitative analysis use symbolic coding, which makes it possible to remove unnecessary detailing of numerical descriptions. The relevance of this study is due to the fact that when working with the raw data, researchers often face the presence of noise and distortions of the data, which significantly complicates the solution of the problems of qualitative analysis. When working with symbolic representations of the processes under study, which quite often have a periodic nature, we observe noise of deletion, insertion and replacement of symbols, which complicate the solution of the problem of revealing and analyzing the periodicity. This article deals with the problem of recovering periodic symbolic sequences obtained by coding from samples of continuous periodic functions and distorted by noise of insertion, replacement and deletion of symbols. Trigonometric functions are considered as a specific example of synthetic time series data. To encode trigonometric functions, alphabets of various cardinalities are used. The article presents an experimental study of the dependence of the quality characteristics of the method of period and a periodically repeating fragment recovery, previously proposed by the authors and improved in this study. For alphabets of different cardinalities at fixed sampling intervals, the fraction of sequences with a satisfactorily reconstructed period and the relative error in determining the period are given. The quality of reconstruction of a periodically repeating fragment is estimated by the edit distance from the reconstructed periodic sequence to the original sequence distorted by noise.

Automatic Object Detection, Labelling, and Localization by Camera’s Drone System

This work explores the designing a system of an automated unmanned aerial vehicles (UAV( for objects detection, labelling, and localization using deep learning. This system takes pictures with a low-cost camera and uses a GPS unit to specify the positions. The data is sent to the base station via Wi-Fi connection. The proposed system consists of four main parts. First, the drone, which was assembled and installed, while a Raspberry Pi4 was added and the flight path was controlled. Second, various programs that were installed and downloaded to define the parts of the drone and its preparation for flight. In addition, this part included programs for both Raspberry Pi4 and servo, along with protocols for communication, video transmission, and sending and receiving signals between the drone and the computer. Third, a real-time, modified, one dimensional convolutional neural network (1D-CNN) algorithm, which was applied to detect and determine the type of the discovered objects (labelling). Fourth, GPS devices, which were used to determine the location of the drone starting and ending points . Trigonometric functions were then used for adjusting the camera angle and the drone altitude to calculate the direction of the detected object automatically. According to the performance evaluation conducted, the implemented system is capable of meeting the targeted requirements.

The Evaluation of Electric Power by Separate Analysis of Fourier Transform Components

This paper presents a substantiation of an approach for the evaluation of components of apparent power and intended to simplify the computational procedures which usually should be implemented in order to process the preliminary sampled waveform of instantaneous power. The results of carried out studies have shown that both active and reactive power can be calculated by the analysis of calculated components of sine and cosine Fourier transforms. This paper also presents the discussion of restrictions, which should be imposed on the duration of the analyzed signal and on frequencies of the auxiliary trigonometric functions, which are applied in order to calculate components of Fourier transform which are used for the evaluation of active and reactive power. The compliance with these restrictions allows us to eliminate the undesirable bias of active and reactive power estimation caused by the refusal from the decomposition of the analyzed waveform of the instantaneous power by applying the complete system of orthogonal trigonometric functions, as the evaluation of components of the apparent power is attained based on separate analysis of sine and cosine Fourier transforms calculated for the analyzed signal. The results of carried out simulations illustrate the frequency dependencies of sine Fourier transform calculated for the case of compliance with the restrictions, which allow to attain the highest accuracy of estimation and for the case when the duration of analyzed signal does not fit these restrictions.

Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.