Inverse-transformation of 4-dimensional Rindler spacetim

In special relativity theory, we discovered 4-dimensional transformation of general Rindler spacetimefrom 4-dimensional Lorentz transformation in inertial frames.We try to discover 4-dimensional inverse-transformation of general Rindler space-time.

Jordan and Einstein Frames Hamiltonian Analysis for FLRW Brans-Dicke Theory

We analyze the Hamiltonian equivalence between Jordan and Einstein frames considering a mini-superspace model of the flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe in the Brans–Dicke theory. Hamiltonian equations of motion are derived in the Jordan, Einstein, and anti-gravity (or anti-Newtonian) frames. We show that, when applying the Weyl (conformal) transformations to the equations of motion in the Einstein frame, we did not obtain the equations of motion in the Jordan frame. Vice-versa, we re-obtain the equations of motion in the Jordan frame by applying the anti-gravity inverse transformation to the equations of motion in the anti-gravity frame.

MATHEMATICAL MODEL OF AUTOMATION OF THE DIAGNOSIS OF INTERNAL COMBUSTION ENGINES OF THE YAMZ-238 FAMILY

Constructive improvement of mobile energy means, in particular their main unit - the internal combustion engine, is directed on: maintenance of differentiation of size of parameters of functioning of mechanisms of systems depending on variability of conditions and modes of operation of cars; increase of technical resource at use of cars on purpose in the set operating conditions. The existing methods and tools for diagnosing vehicle engines do not fully determine their current technical condition, which requires the development of mathematical models to automate the process of diagnosing their components and parts was found іn the analysis of literature sources. The object of diagnosis is a diesel internal combustion engine of the YaMZ-238 family, which is part of the power unit of most vehicles. Mathematical model of automation of the process of diagnosing internal combustion engines of the YaMZ-238 family is presents in the article. Replacing real technical devices with their idealized models allows the widespread use of various mathematical methods. In this case, the internal combustion engine of the YaMZ-238 family, as the object of diagnosis, is presented in the form of a «black box», the input and output parameters of which have a finite set of values. In general, the mathematical model is a system of functional relationships between each diagnostic signal and structural parameters. For internal combustion engines of the YaMZ-238 family, a diagnostic matrix has been compiled, which includes a list of faults and signs of faults. It is determined that the process of diagnosis based on the model of the diagnostic object is possible if the inverse transformation of the number of signs of malfunctions into the number of structural parameters (malfunctions) of the object was unambiguous. The proposed mathematical model of automation of the process of diagnosing internal combustion engines of the family YaMZ-238 will detect faults of components and parts depending on their characteristics.

Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma

Hyperthermia therapy is now being used to treat cancer. However, understanding the pattern of temperature increase in biological tissues during hyperthermia treatment is essential. In recent years, many physicians and engineers have studied the use of computational and mathematical models of heat transfer in biological systems. The rapid progress in computing technology has intrigued many researchers. Many medical procedures also use engineering techniques and mathematical modeling to ensure their safety and assess the risks involved. One such model is the modified Pennes bioheat conduction equation. This paper provides an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time by incorporating in it the (MGT) equation. The suggested model examines heat transport in biological tissues as forming an infinite concentric spherical region during magnetic fluid hyperthermia. To investigate thermal reactions caused by temperature shock, specifically the influence of heat generation through heat treatment on a skin tumor [AEGP9], the Laplace transformation, and numerical inverse transformation methods are used. This model was able to explain the effects of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences, transfer, metabolism support, and blood perfusion. Comparison of the numerical results of the suggested model with those in the literature confirmed the validity of the model’s numerical results.

Complexity Assessment of Chronic Pain in Elderly Knee Osteoarthritis Based on Neuroimaging Recognition Techniques

The chronic pain of knee osteoarthritis in the elderly is investigated in detail in this paper, as well as the complexity of chronic pain utilising neuroimaging recognition techniques. Chronic pain in knee osteoarthritis (KOA) has a major effect on patients’ quality of life and functional activities; therefore, understanding the causes of KOA pain and the analgesic advantages of different therapies is important. In recent years, neuroimaging techniques have become increasingly important in basic and clinical pain research. Thanks to the application and development of neuroimaging techniques in the study of chronic pain in KOA, researchers have found that chronic pain in KOA contains both injury-receptive and neuropathic pain components. The neuropathic pain mechanism that causes KOA pain is complicated, and it may be produced by peripheral or central sensitization, but it has not gotten enough attention in clinical practice, and there is no agreement on how to treat combination neuropathic pain KOA. As a result, using neuroimaging techniques such as magnetic resonance imaging (MRI), electroencephalography (EEG), magnetoencephalography (MEG), and near-infrared spectroscopy (NIRS), this review examines the changes in brain pathophysiology-related regions caused by KOA pain, compares the latest results in pain assessment and prediction, and clarifies the central brain analgesic mechanistic. The capsule network model is introduced in this paper from the perspective of deep learning network structure to construct an information-complete and reversible image low-level feature bridge using isotropic representation, predict the corresponding capsule features from MRI voxel responses, and then, complete the accurate reconstruction of simple images using inverse transformation. The proposed model improves the structural similarity index by about 10%, improves the reconstruction performance of low-level feature content in simple images by about 10%, and achieves feature interpretation and analysis of low-level visual cortical fMRI voxels by visualising capsule features, according to the experimental results.

A novel Image Security Protection Method Based on DCT Compression Theory and Hyper-chaotic Mapping

This paper studies the current situation of image compression encryption and analyzes the influence of low frequency (DC coefficient) and high frequency (AC coefficient) on image structure in DCT transformation. Based on this, a novel image security protection method based on DCT compression theory and hyper-chaotic mapping is proposed. First, the position of the pixel of the original image is disturbed, and converts the image from spatial domain into frequency domain by the two-dimensional DCT transformation and quantization. Second, change the pixel values by modifying the values of the sign bit of AC coefficient and DC coefficient. At last, the encrypted image is obtained by carrying out inverse quantization, inverse transformation and reverse operation by bit.

Inverse Transformation in Eddy Current Tomography with Continuous Optimization of Reference Defect Parameters

This paper presents a methodology of inverse tomography transformation in eddy current tomography with the use of continuous optimization of reference defect parameters. Ferromagnetic steel samples with rectangular air inclusion defects of known dimensions were prepared and measured using an eddy current tomography setup. FEM-based (Finite Element Method based) forward tomography transformation was developed and utilized in inverse tomography transformation. The presented method of inverse tomography transformation is based on the continuous optimization of parameters that can describe the sample, such as the diameter and dimensions of the reference defect. The obtained results of inverse tomography transformation were in high accordance with the real parameters of the samples. Additionally, the presented method had acceptable repeatability. The obtained values of the sample parameters fit within the range of expanded uncertainty when compared to the real parameters of the sample.

Psychological Stress Detection and Early Warning System Based on Wireless Network Transmission

To improve the accuracy of stress detection and stress warning errors, this paper designed a new psychological stress detection and warning system based on wireless network transmission. To achieve this objective, we established a real-time setup. The hardware of the system is composed of pulse acquisition module, signal low-pass filtering and amplification module, real-time clock module, wireless network transmission module, and power supply module, respectively. Based on the aforementioned hardware platform, the system software is designed, mainly through the construction of pulse signal noise and the use of wavelet denoising threshold for sensing wavelet packet inverse transformation, to get the reconstructed signal. The peak point of the reconstructed signal is determined, and the value of pulse signal is extracted. According to the characteristic value’s extraction results, the degree of psychological stress is quantified using the psychological stress index (PSI). When the PSI exceeds a predefined threshold, it indicates an early warning of psychological stress. The experimental results show that the psychological stress detection of our system is consistent with the expert evaluation results, the warning time is short, and the practical application effect is good.

Progress in Analytical Modeling of Water Hammer

In this paper analytical formulas of water hammer known from the literature are simplified to the shortest possible mathematical form based on dimensionless parameters: dimensionless time, water hammer number, etc. Novel formulas are determined, for example for the flow velocity and wall shear stress in the Muto and Takahashi solution. A complete solution in the Laplace domain is presented and the problem of its inverse transformation is discussed. A series of comparative studies of analytical solutions with numerical solutions and the results of experimental research were carried out. The compared analytical solutions, taking into account the frequency-dependent nature of the hydraulic resistances, show very good agreement with the experimental results in a wide range of water hammer numbers, in particular when Wh ≤ 0.1. On the other hand, it turned out that the analytical model based on the quasi-steady friction in great detail simulates dynamic pressure response in systems characterized by a high value of the water hammer number Wh ≥ 0.5.

MODEL OF THEMATIC INTERPRETOTION OF THE VIEW IMAGES

The subject matter of the article is thematic interpretation of species images. The goal of the work is to develop a model for thematic interpretation of species images, which will be based on the model for the formation of species images and additionally take into account geographic zoning. The following task was solved in the article: development of a model of thematic interpretation of view images, which takes into account the shortcomings of existing models and is based on the model of formation of view images, carries out the reverse transformation of the image coordinates into geospatial coordinates and clustering the image into separate classes according to their color and texture, additionally taking into account geographic zoning, which provides the possibility of advanced analysis and forecasting the temporal dynamics of data in geospatial information processing systems. The following methods used are – mathematical apparatus of the theory of matrices, methods of mathematical modelling, methods of data clustering, methods of differential calculus, methods of digital image processing. The following results were obtained – groups of existing models for interpreting the results of remote sensing of the Earth, their advantages and disadvantages have been analyzed; a mathematical model of the formation of a species image for a section of the earth's surface has been formulated in general form; a mathematical model of thematic interpretation of species images was formulated in general form; the operator of transformation of coordinates, operators of clustering, operators of zoning and their explicit form are considered; a model of thematic interpretation of species images in operator form is obtained. Conclusions: for the first time, a model of thematic interpretation of view images was developed, which, based on the model of formation of view images, carries out the inverse transformation of coordinates into geospatial coordinates and clustering by their color and texture, additionally taking into account geographical zoning, which provides the possibility of advanced analysis and forecasting of the temporal dynamics of data in processing systems geospatial information.