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Keywords = transcendental probability

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23 pages, 4015 KiB  
Article
Performance Analysis of FSO-UWOC Mixed Dual-Hop Relay System with Decode-and-Forward Protocol
by Yu Zhou, Yueheng Li, Meiyan Ju and Yong Lv
Electronics 2025, 14(11), 2227; https://doi.org/10.3390/electronics14112227 - 30 May 2025
Viewed by 355
Abstract
This study investigates the performance of a mixed dual-hop free-space optical/underwater wireless optical communication (FSO-UWOC) system employing a decode-and-forward (DF) relay protocol, particularly under a comprehensive hybrid channel fading model. The FSO link is assumed to experience Gamma–Gamma atmospheric turbulence fading, combined with [...] Read more.
This study investigates the performance of a mixed dual-hop free-space optical/underwater wireless optical communication (FSO-UWOC) system employing a decode-and-forward (DF) relay protocol, particularly under a comprehensive hybrid channel fading model. The FSO link is assumed to experience Gamma–Gamma atmospheric turbulence fading, combined with air path loss and pointing errors. Meanwhile, the UWOC link is modeled with generalized Gamma distribution (GGD) oceanic turbulence fading, along with underwater path loss and pointing errors. Based on the proposed hybrid channel fading model, closed-form expressions for the average outage probability (OP) and average bit error rate (BER) of the mixed dual-hop system are derived using the higher transcendental Meijer-G function. Similarly, the closed-form expression for the average ergodic capacity of the mixed relay system is obtained via the bivariate Fox-H function. Additionally, asymptotic performance analyses for the average outage probability and BER under high signal-to-noise ratio (SNR) conditions are provided. Finally, Monte Carlo simulations are conducted to validate the accuracy of the derived theoretical expressions and to illustrate the effects of key system parameters on the performance of the mixed relay FSO-UWOC system. Full article
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16 pages, 312 KiB  
Article
Joint Approximation by the Riemann and Hurwitz Zeta-Functions in Short Intervals
by Antanas Laurinčikas
Symmetry 2024, 16(12), 1707; https://doi.org/10.3390/sym16121707 - 23 Dec 2024
Cited by 1 | Viewed by 779
Abstract
In this study, the approximation of a pair of analytic functions defined on the strip {s=σ+itC:1/2<σ<1} by shifts [...] Read more.
In this study, the approximation of a pair of analytic functions defined on the strip {s=σ+itC:1/2<σ<1} by shifts (ζ(s+iτ),ζ(s+iτ,α)), τR, of the Riemann and Hurwitz zeta-functions with transcendental α in the interval [T,T+H] with T27/82HT1/2 was considered. It was proven that the set of such shifts has a positive density. The main result was an extension of the Mishou theorem proved for the interval [0,T], and the first theorem on the joint mixed universality in short intervals. For proof, the probability approach was applied. Full article
(This article belongs to the Section Mathematics)
25 pages, 4338 KiB  
Article
Mathematical Analysis of the Reliability of Modern Trolleybuses and Electric Buses
by Boris V. Malozyomov, Nikita V. Martyushev, Vladimir Yu. Konyukhov, Tatiana A. Oparina, Nikolay A. Zagorodnii, Egor A. Efremenkov and Mengxu Qi
Mathematics 2023, 11(15), 3260; https://doi.org/10.3390/math11153260 - 25 Jul 2023
Cited by 29 | Viewed by 1655
Abstract
The rhythmic and stable operation of trolleybuses and autonomous trolleybuses or urban electric buses, depends to a large extent on the reliability of the equipment installed on the trolleybus. The actual operational reliability of trolleybus electrical equipment (EE) depends on its technical condition. [...] Read more.
The rhythmic and stable operation of trolleybuses and autonomous trolleybuses or urban electric buses, depends to a large extent on the reliability of the equipment installed on the trolleybus. The actual operational reliability of trolleybus electrical equipment (EE) depends on its technical condition. Under the influence of external factors and specific operating modes, the technical condition of the equipment is continuously deteriorating, reliability indicators are decreasing, and the number of failures is increasing. Using the mathematical theory of reliability, probability theory and mathematical statistics, numerical methods of solving nonlinear and transcendental equations, this article defines the conditions of diagnostics depending on the intensity of failures and the given probability of failure-free operation of the equipment. Additionally, the inverse problem of determining the current reliability of electrical engineering systems depends on the terms of diagnostics and the intensity of failures being solved. As a result of the processing of statistical information on failures it is established that for the electrical equipment of a trolleybus, after a number of repair measures, the maximum density of failures occurs at a lower mileage, and the probability of failure-free operation can vary depending on the degree of wear of the equipment, i.e., on the number of previous failures. It is theoretically substantiated and experimentally confirmed that the reliability of trolleybus electrical equipment changes according to the exponential law of distribution of a random variable. It has been established that the real averaged diagnostic terms regulated by instructions are not optimal in most cases and differ several times from those defined in this paper. The dependence of switching equipment run-in on time has been clarified, which served as a prerequisite for specifying the inter-repair period for various types of trolleybus electrical equipment. A method of adjustment of the inter-repair time for the electrical equipment of trolleybuses is proposed. Full article
(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)
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16 pages, 357 KiB  
Article
An Extension of the Poisson Distribution: Features and Application for Medical Data Modeling
by Mohamed El-Dawoody, Mohamed S. Eliwa and Mahmoud El-Morshedy
Processes 2023, 11(4), 1195; https://doi.org/10.3390/pr11041195 - 13 Apr 2023
Cited by 4 | Viewed by 4017
Abstract
This paper introduces and studies a new discrete distribution with one parameter that expands the Poisson model, discrete weighted Poisson Lerch transcendental (DWPLT) distribution. Its mathematical and statistical structure showed that some of the basic characteristics and features of the DWPLT model include [...] Read more.
This paper introduces and studies a new discrete distribution with one parameter that expands the Poisson model, discrete weighted Poisson Lerch transcendental (DWPLT) distribution. Its mathematical and statistical structure showed that some of the basic characteristics and features of the DWPLT model include probability mass function, the hazard rate function for single and double components, moments with auxiliary statistical measures (expectation, variance, index of dispersion, skewness, kurtosis, negative moments), conditional expectation, Lorenz function, and order statistics, which were derived as closed forms. DWPLT distribution can be used as a flexible statistical approach to analyze and discuss real asymmetric leptokurtic data. Moreover, it could be applied to a hyperdispersive data model. Two different estimation methods were derived, i.e., maximal likelihood and the moments technique for the DWPLT parameter, and some advanced numerical methods were utilized for the estimation process. A simulation was performed to examine and analyze the performance of the DWPLT estimator on the basis of the criteria of the bias and mean squared errors. The flexibility and fit ability of the proposed distribution is demonstrated via the clinical application of a real dataset. The DWPLT model was more flexible and worked well for modeling real age data when compared to other competitive age distributions in the statistical literature. Full article
(This article belongs to the Section AI-Enabled Process Engineering)
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15 pages, 1158 KiB  
Article
Optoelectronic Properties of a Cylindrical Core/Shell Nanowire: Effect of Quantum Confinement and Magnetic Field
by Mohamed El-Yadri, Jawad El Hamdaoui, Noreddine Aghoutane, Laura M. Pérez, Sotirios Baskoutas, David Laroze, Pablo Díaz and El Mustapha Feddi
Nanomaterials 2023, 13(8), 1334; https://doi.org/10.3390/nano13081334 - 11 Apr 2023
Cited by 13 | Viewed by 2533
Abstract
This study investigates the effect of quantum size and an external magnetic field on the optoelectronic properties of a cylindrical AlxGa1xAs/GaAs-based core/shell nanowire. We used the one-band effective mass model to describe the Hamiltonian of an interacting [...] Read more.
This study investigates the effect of quantum size and an external magnetic field on the optoelectronic properties of a cylindrical AlxGa1xAs/GaAs-based core/shell nanowire. We used the one-band effective mass model to describe the Hamiltonian of an interacting electron-donor impurity system and employed two numerical methods to calculate the ground state energies: the variational and finite element methods. With the finite confinement barrier at the interface between the core and the shell, the cylindrical symmetry of the system revealed proper transcendental equations, leading to the concept of the threshold core radius. Our results show that the optoelectronic properties of the structure strongly depend on core/shell sizes and the strength of the external magnetic field. We found that the maximum probability of finding the electron occurs in either the core or the shell region, depending on the value of the threshold core radius. This threshold radius separates two regions where physical behaviors undergo changes and the applied magnetic field acts as an additional confinement. Full article
(This article belongs to the Topic Electronic and Optical Properties of Nanostructures)
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22 pages, 6958 KiB  
Article
Susceptibility Mapping of Typical Geological Hazards in Helong City Affected by Volcanic Activity of Changbai Mountain, Northeastern China
by Xiaohui Sun, Chenglong Yu, Yanrong Li and Ngambua N. Rene
ISPRS Int. J. Geo-Inf. 2022, 11(6), 344; https://doi.org/10.3390/ijgi11060344 - 10 Jun 2022
Cited by 13 | Viewed by 2879
Abstract
The purpose of this paper was to produce the geological hazard-susceptibility map for the Changbai Mountain area affected by volcanic activity. First, 159 landslides and 72 debris flows were mapped in the Helong city are based on the geological disaster investigation and regionalization [...] Read more.
The purpose of this paper was to produce the geological hazard-susceptibility map for the Changbai Mountain area affected by volcanic activity. First, 159 landslides and 72 debris flows were mapped in the Helong city are based on the geological disaster investigation and regionalization (1:50,000) project of Helong City. Then, twelve landslide conditioning factors and eleven debris flow conditioning factors were selected as the modeling variables. Among them, the transcendental probability of Changbai Mountain volcanic earthquake greater than VI degrees was used to indicate the relationship between the geological hazard-susceptibility and Changbai Mountain volcanic earthquake occurrence. Furthermore, two machine learning models (SVM and ANN) were introduced to geological hazard-susceptibility modeling. Receiver operating characteristic curve, statistical analysis method, and five-fold cross-validation were used to compare the two models. Based on the modeling results, the SVM model is the better model for both the landslide and debris flow susceptibility mapping. The results show that the areas with low, moderate, high, and very high landslide susceptibility are 31.58%, 33.15%, 17.07%, and 18.19%, respectively; and the areas with low, moderate, high, and very high debris flow susceptibility are 25.63%, 38.19%, 23.47%, and 12.71%, respectively. The high and very high landslide and debris flow susceptibility classes make up 85.54% and 80.55% of the known landslides and debris flow, respectively. Moreover, the very high and high landslide and debris flow susceptibility are mainly distributed in the lower elevation area, and mainly distributed around the cities and towns in Helong City. Consequently, this paper will be a useful guide for the deployment of disaster prevention and mitigation in Helong city, and can also provide some reference for evaluation of landslide susceptibility in other volcanically active areas. Full article
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21 pages, 10304 KiB  
Article
Three-Phase Multilevel Inverter Using Selective Harmonic Elimination with Marine Predator Algorithm
by Nancy Riad, Wagdy Anis, Ahmed Elkassas and Abd El-Wahab Hassan
Electronics 2021, 10(4), 374; https://doi.org/10.3390/electronics10040374 - 3 Feb 2021
Cited by 25 | Viewed by 3290
Abstract
In this paper, the marine predator algorithm (MPA) is proposed for solving transcendental nonlinear equations in a selective harmonic elimination technique using a multilevel inverter (MLI). It proved its suitability and supremacy over the other selective harmonic (SHE) techniques used in recent research [...] Read more.
In this paper, the marine predator algorithm (MPA) is proposed for solving transcendental nonlinear equations in a selective harmonic elimination technique using a multilevel inverter (MLI). It proved its suitability and supremacy over the other selective harmonic (SHE) techniques used in recent research as it has good precision, high probability of convergence, and improving quality of output voltage. The optimum values of switching angles from MPA are applied to control a three-phase 11-level MLI using cascaded H-bridge (CHB) topology to control the fundamental component and cancel the low order harmonics for all values of modulation index from 0 to 1. Analytical and simulation results demonstrate the robustness and consistency of the technique through the MATLAB simulation platform. The results obtained from simulation show that the MPA algorithm is more efficient and accurate than other algorithms such as teaching-learning-based optimization (TLBO), flower pollination algorithm (FPA), and hybrid particle swarm optimization with gray wolf optimization (PSOGWO). A prototype for a three-phase seven-level cascaded H-bridge inverter (7L-MLI-CHB) experimental setup is carried out. The output of this experimental test validated and supported the results obtained from the simulation analysis. The model of power loss of three-phase 7L-MLI-CHB using the silicon metal-oxide-semiconductor field-effect transistor (MOSFET) is obtained according to the modulation technique. Conduction and switching losses are calculated based on the experimental manufacturer data from the Si-MOSFET using the thermal model of Piecewise Linear Electrical Circuit Simulation (PLECS). Losses and output power are measured at different modulation index values based on the MPA algorithm. Finally, a design of heatsink volume is presented for this design at different temperatures. Full article
(This article belongs to the Section Power Electronics)
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9 pages, 777 KiB  
Review
What is Known Regarding the Participation of Factor Nrf-2 in Liver Regeneration?
by José A. Morales-González, Eduardo Madrigal-Santillán, Ángel Morales-González, Mirandeli Bautista, Evila Gayosso-Islas and Cecilia Sánchez-Moreno
Cells 2015, 4(2), 169-177; https://doi.org/10.3390/cells4020169 - 20 May 2015
Cited by 27 | Viewed by 6623
Abstract
It has been known for years that, after chemical damage or surgical removal of its tissue, the liver initiates a series of changes that, taken together, are known as regeneration, which are focused on the recovery of lost or affected tissue in terms [...] Read more.
It has been known for years that, after chemical damage or surgical removal of its tissue, the liver initiates a series of changes that, taken together, are known as regeneration, which are focused on the recovery of lost or affected tissue in terms of the anatomical or functional aspect. The Nuclear factor-erythroid 2-related factor (Nrf-2) is a reduction-oxidation reaction (redox)-sensitive transcriptional factor, with the basic leucine Zipper domain (bZIP) motif, encoding the NFE2L2 gene. The Keap1-Nrf2-ARE pathway is transcendental in the regulation of various cellular processes, such as antioxidant defenses, redox equilibrium, the inflammatory process, the apoptotic processes, intermediate metabolism, detoxification, and cellular proliferation. Some reports have demonstrated the regulator role of Nrf-2 in the cellular cycle of the hepatocyte, as well as in the modulation of the antioxidant response and of apoptotic processes during liver regeneration. It has been reported that there is a delay in liver regeneration after Partial hepatectomy (PH) in the absence of Nrf-2, and similarly as a regulator of hepatic cytoprotection due to diverse chemical or biological agents, and in diseases such as hepatitis, fibrosis, cirrhosis, and liver cancer. This regulator/protector capacity is due to the modulation of the Antioxidant response elements (ARE). It is postulated that oxidative stress (OS) can participate in the initial stages of liver regeneration and that Nrf-2 can probably participate. Studies are lacking on the different initiation stages, maintenance, and the termination of liver regeneration alone or with ethanol. Full article
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