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Nitrogen isotope ratios of amino acids (δ15NAA) have widely been employed as a powerful tool for estimating the trophic position of organisms in food webs. This estimation is based on an elevation pattern in the δ15NAA value, a large elevation for the trophic amino acids (e.g., 8.0‰ for glutamic acid) while a little elevation for the source amino acids (e.g., 0.4‰ for phenylalanine), associated with the deamination of amino acids in consumers. However, several elevation patterns can be found in natural environments, one of which may be caused by the hydrolysis of specific protein under nutritional stress. In the present study, we identified 'protein-specific elevation pattern' for collagen, which connected to muscle tissues of fish and gastropods under nutritional stress. Time-series starvation for 45 days results in that collagen is consumed by 86% for the fish Girella punctata and by 50% for the gastropod Turbo sazae. Moreover, during the starvation, although a little change in the δ15NAA value is found in muscle fibers, a gradual elevation in the δ15NAA value is found in collagen for both trophic and source amino acids (e.g., by up to 11‰ for glutamic acid and up to 3‰ for phenylalanine, respectively, which can be explained by the Rayleigh fractionation model). We thus demonstrate that the consumption of collagen in organisms under starvation shows a unique elevation pattern in the δ15NAA value, which is consistent with the observation that collagen is degraded non-quantitatively by the collagenase reaction, whereas muscle is degraded quantitatively by the chaperone-mediated autophagy. The effect of δ15N elevation in all amino acids of collagen is negligible for G. punctata and diluted for T. sazae to the elevation in whole muscle tissue (i.e., = muscle fibers + collagen) even under long-term starvation, because the collagen proportion in the whole muscle is relatively small and is considerably decreased under the nutritional stress. Based on these results, we predict that the difference in the δ15NAA value between collagen and muscle fibers can be useful for evaluating the nutritional stress of fishes. However, great care will be required if studying food webs where collagen-rich organisms (i.e., gelatinous zooplankton) are abundant or if using collagen-rich materials in our studies. [ABSTRACT FROM AUTHOR]

In this study, the pressure-cast-in-situ pile with spray-expanded frustum (PPSF) was proposed to increase pile bearing capacity, reduce pile settlement, and improve construction speed. The construction process of the PPSF composed of pile body, ribbed plate, and expanded body with double frustum was introduced. To capture the PPSF response, field static load tests on three PPSFs installed with string wire stress gauges were carried out. The ultimate bearing capacity (UBC) of a single PPSF was obtained, and the distribution of axial force, skin friction, and end force were analyzed using the measured results. Following the assumption that the strength of pile–soil interface elements was statistically described by the probability density function of the Rayleigh distribution, the load transfer models of PPSF were established based on the disturbed state concept (DSC) theory. The research results showed that there is a compression effect between the expanded body of the PPSF and the surrounding soil, which can effectively improve the bearing capacity of the PPSF. Considering the concrete consumption per unit volume, the UBC of PPSF is 66% more than that of the cast-in-situ bored pile. According to the results of measured and fitted relationships, the load transfer models of PPSF can be well described using the DSC theory and the Rayleigh distribution. [ABSTRACT FROM AUTHOR]

Over the last decades, the chromium (Cr) stable isotope system (referred to as δ53Cr) has emerged as a proxy to reconstruct past oxygenation changes in Earth's atmosphere and oceans. Although Cr is a promising paleoproxy, uncertainties remain as to the modern marine Cr cycle, and limited data are yet available in large swaths of the ocean, including the Atlantic Ocean. Here we present dissolved seawater Cr concentrations ([Cr]) and δ53Cr along a meridional transect from the North to the South Atlantic (AMT 29). Chromium concentrations range from of 2.51 to 3.96 nmol kg−1 (n = 68) and δ53Cr values range from +0.86 ± 0.04 ‰ (2SEM) to +1.20 ± 0.02 ‰ (2SEM) (n = 68). In contrast to data from other ocean basins [Cr] and δ53Cr show only a weak correlation (δ53Cr vs. Ln([Cr]) R2 = 0.17), inconsistent with a closed-system Rayleigh distillation model. These results can mainly be explained by horizontal advection and water mass mixing, which our data demonstrate are the dominant processes controlling [Cr] and δ53Cr distributions throughout much of the Atlantic, while the impact of in situ biogeochemical cycling is comparatively minor. There is, indeed no clear impact of biological productivity nor of dysoxic environments in the (sub)tropical Atlantic on the cycling of Cr along the transect. This is likely explained by insufficiently depleted oxygen concentrations and relatively low biological productivity, resulting in these processes being of secondary importance relative to water mass mixing in shaping the distribution of Cr in the low- to mid-latitude Atlantic Ocean. [ABSTRACT FROM AUTHOR]

An image watermarking scheme is typically evaluated using three main conflicting characteristics: imperceptibility, robustness, and capacity. Developing a good image watermarking method is challenging because it requires a trade-off between these three basic characteristics. In this paper, we propose a statistical image watermark decoder in undecimated discrete wavelet transform-polar complex exponentiated transform magnitude domain, wherein a probability density function based on the exponentiated Cauchy–Rayleigh distribution is used, in view of the fact that this probability density function provides a better statistical match to the empirical probability density function of the robust undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes of the image. In watermark embedding, we first perform the undecimated discrete wavelet transform on the carrier image. We then select the maximum energy subband and divide it into blocks, and compute the polar complex exponentiated transform for each block. Finally, we embed watermark in undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes using nonlinear multiplicative approach. In the decoding process, we first analyze the robustness and statistical characteristics of undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes. We then observe that, with a small number of parameters, the new exponentiated Cauchy–Rayleigh model can capture accurately the statistical distributions of the robust undecimated discrete wavelet transform-polar complex exponentiated transform magnitudes of the image. Meanwhile, statistical model parameters can be estimated effectively by using genetic simulated annealing based maximum likelihood approach. Motivated by our modeling results, we finally design a new statistical image watermark decoder using the exponentiated Cauchy–Rayleigh distribution and maximum likelihood decision rule. Experimental results on extensive test images demonstrate that the proposed watermark decoder provides a performance better than that of most of the state-of-the-art methods recently proposed in the literature. [ABSTRACT FROM AUTHOR]

This study aims to explore the issues of evaluating the parameters and the accelerating factor based on constant stress for partially accelerating life tests when the potential failure times have an exponentiated Rayleigh distribution. Within the framework of progressive Type-II censoring schemes, we employ the Newton-Raphson algorithm as an iterative methodology to gain the maximum likelihood estimates, accompanied by proof of the existence of these point estimators. We also construct asymptotic confidence intervals for interested parameters and acceleration factors by utilizing the asymptotical characteristics of the maximum likelihood estimators. The Bayesian estimations of unknown parameters are derived by using the independent gamma priors and dependent Gamma-Dirichlet prior on the basis of square error and relatively smooth LINEX loss functions, respectively. Furthermore, we adopt the importance sampling method to compute Bayesian point estimates and the credible intervals with the highest posterior density. To validate the effectiveness of the suggested approaches, a series of simulated experiments are carried out. Lastly, we conduct analyzes on two actual datasets to show the applicability of the suggested techniques. [ABSTRACT FROM AUTHOR]

In the examination of real-life situations, the application of probability distributions is often crucial for statistical analysis of the real-life scenarios. Many models based on probability have been utilized in disciplines such as music education, music engineering, and other music-related areas. Hence, acknowledging the significance of probability-based approaches, this article introduces an innovative probability model known as a new generalized Rayleigh distribution. The suggested model is established on merging the generalized Rayleigh distribution with a prominent weighted probabilistic method. The mathematical properties, specifically the quartile-based features of the novel generalized Rayleigh distribution, are investigated. Moreover, we outline the derivation of the point estimators for the unknown parameters of the new model. A thorough simulation study is also conducted to examine the performances of these point estimators. Within the music industry, specifically in music education and music engineering, we examine the practical implications of the new generalized Rayleigh distribution. We observe that it offers a superior fit when contrasted with other distributions. Our findings demonstrate that the new distribution is a inclusion to the group of probability distributions that can be applied in music engineering and other closely connected engineering fields for the statistical analysis of real-life events. [ABSTRACT FROM AUTHOR]

In this work, bridge network model with Rayleigh distribution lifetimes is used. Two main techniques are calculated to upgrade this model: reduction and redundancy techniques. In order to compare the effectiveness of the various approaches, the survival function, the mean time to failure and gamma-fractiles for the original and upgraded model are calculated. Finally, we analyze comprehensively a computer simulation example to distingue between the methods. The numerical simulations were done in Mathematica which indicated that the upgraded system performs better than the original one and the best technique is by cold duplication. [ABSTRACT FROM AUTHOR]

This paper presents a novel extension of the exponentiated inverse Rayleigh distribution called the half-logistic exponentiated inverse Rayleigh distribution. This extension improves the flexibility of the distribution for modeling lifetime data for both monotonic and non-monotonic hazard rates. The statistical properties of the half-logistic exponentiated inverse Rayleigh distribution, such as the quantiles, moments, reliability, and hazard function, are examined. In particular, we provide several techniques to estimate the half-logistic exponentiated inverse Rayleigh distribution parameters: weighted least squares, Cramér-Von Mises, maximum likelihood, maximum product spacings and ordinary least squares methods. Moreover, numerical simulations were performed to evaluate these estimation methods for both small and large samples through Monte Carlo simulations, and the finding reveals that the maximum likelihood estimation was the best among all estimation methods since it comprises small mean square error compared to other estimation methods. We employ real-world lifetime data to demonstrate the performance of the newly generated distribution compared to other distributions through practical application. The results show that the half-logistic exponentiated inverse Rayleigh distribution performs better than alternative versions of the Rayleigh distributions. [ABSTRACT FROM AUTHOR]

This study examines Rayleigh wave propagation dynamics in a nonlocal orthotropic medium with thermoelastic diffusion, utilizing Eringen's nonlocal elasticity theory and the Lord–Shulman hyperbolic thermoelasticity model. Normal mode analysis is used to solve the problem, deriving the frequency equation for Rayleigh waves and analyzing specific cases. The elliptical path of surface particles and its eccentricity are calculated. Graphs illustrate the relationships of propagation speed, attenuation coefficient, penetration depth, and specific loss of Rayleigh waves concerning wave number for both thermally insulated and isothermal surfaces. The results reveal that the presence of nonlocal parameters and diffusion significantly increases the values of physical variables, especially with higher wave numbers, highlighting their considerable impact on the system's dynamics. [ABSTRACT FROM AUTHOR]

Published Sn isotope data along with 150 new analyses of cassiterite and four granite analyses constrain two major tin isotope fractionation steps associated with (1) separation of tin from the magma/orthomagmatic transitional environment and (2) hydrothermal activity. A distinct Sn isotope difference across deposit type, geological host rocks, and time of ore deposit formation demonstrates that the difference in the mean δ124Sn value represents the operation of a unified process. The lower Sn isotope values present in both residual igneous rocks and pegmatite suggest that heavier Sn isotopes were extracted from the system during orthomagmatic fluid separation, likely by F ligands with Sn. Rayleigh distillation models this first F ligand-induced fractionation. The subsequent development of the hydrothermal system is characterized by heavier Sn isotope composition proximal to the intrusion, which persists in spite of Sn isotope fractionating towards isotopically lighter Sn during hydrothermal evolution. [ABSTRACT FROM AUTHOR]

In a different area of life testing, designing experiments needs higher stress level than normal stress one. Also, the time to failure of experimental units is resulted by one of a fetal risk factors, only. In this paper, we consider the simple step-stress model with competing risks under Type-I censoring. The cumulative exposure model is assumed when the lifetime of test units follows Rayleigh distribution. Under this setup, we obtain the maximum likelihood estimates and the Bayes Estimators of the unknown parameters using Markov chain Monte Carlo (MCMC) method under various loss functions. Furthermore, to demonstrate the proposed methods, dataset is analyzed. Also, the confidence intervals are derived by using the asymptotic distributions of the maximum likelihood estimates. For comparison, we obtain the highest posterior density (HPD) credible intervals based on different prior distributions. Their performance is assessed through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In this study, the best parameter estimator for the scale parameter (θ) of the inverse Rayleigh distribution was determined based on a comparison of the maximum likelihood estimator (MLE) method, the Bayesian generalized squared error loss function (SELF), the Bayesian linear exponential loss function (LINEX LF), and the Bayesian entropy loss function (ELF). The prior distribution chosen was the non-informative prior, namely the Jeffrey prior, and the informative prior using the exponential distribution. The estimator evaluation method used was based on the smallest value of the Akaike information criterion (AIC), corrected Akaike information criterion (AICc), and Bayesian information criterion (BIC). Based on simulation studies and real data, it was found that the best parameter estimator on the data for the scale parameter (θ) of the inverse Rayleigh distribution is the Bayes ELF prior exponential (̂θEE) [ABSTRACT FROM AUTHOR]

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This paper introduces a new non-homogeneous stochastic diffusion process related the generalized Rayleigh distribution called the stochastic generalized Rayleigh diffusion process, thanks to the idea of extending the Rayleigh distribution families by introducing a positive shape parameter. The explicit forms of some important probabilistic characteristics of the process such as the analytical form of the process, the probability density function, and the conditional and non-conditional mean functions are obtained analytically. Then, we provide a computational statistical approach to estimate the process parameters via the maximum likelihood method through the discrete sampling. In order to obtain the estimators of the parameters, we find a nonlinear equation. To achieve this, we propose the simulated annealing algorithm to maximize the log-likelihood function once the parameter space has been bounded by a proposed stepwise procedure. We will end up by exploring the possibility of using this new GSRDP to fit and predict simulated data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a maximum likelihood estimation (MLE) of user velocity based on Rayleigh distributed handover counts in heterogeneous networks (HetNets). The high density of base stations (BSs) in HetNets leads to mobile users experiencing unnecessary handovers and service outages, emphasizing the importance of mobility management in HetNets. Since user velocity plays an important role in the handover process, its knowledge is necessary for efficient mobility management. Our proposed velocity estimation strategy involves tracking of both vertical and horizontal handovers over a defined period. We utilized mathematical modeling to estimate that the probability mass function (PMF) of the handover counts in the HetNets scenario follows a Rayleigh distribution. We determined the scale parameter by analyzing the close deployment of small cells and macro-cell BSs using stochastic geometry. Our approach assumes a random distribution of BSs based on a homogeneous Poisson point process and investigates the handover-count PMF considering factors such as user velocity, BS density, and the duration of handover-count measurements. Using these statistics, we derived the Cramer–Rao lower bound (CRLB) and applied a MLE technique to estimate user velocity. The MATLAB simulation method is used to validate our approach for the velocity estimation, and the results show the tight closeness of MLE asymptotic variance with CRLB. The numerical analysis indicates that as user velocity increases, the variance of the estimation also increases. Conversely, the simulation results demonstrate that as BS density and the time span for handover-count measurements increase, the velocity estimation error decreases. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the enhancement of global navigation satellite system (GNSS) adaptive acquisition using metaheuristic optimization techniques is proposed. The principal goal of this work is to optimize the cell averaging constant false alarm rate (CA‐CFAR) thresholding in Rayleigh fading channels. In GNSS acquisition, pilot and data blocks may have different thresholds. Thus, the optimization will focus on two scaling factors (T1 and T2). Two fusion rules have been used here ("AND" and "OR"). Due to their performances in different optimization problems, metaheuristics have been chosen to be our tool for solving this kind of problem. Simulation results show that the optimized thresholds have an important influence on the performance of the acquisition system. [ABSTRACT FROM AUTHOR]

Probability-oriented methodologies have been firmly established and recognized as essential tools for illustrating and describing applied phenomena. Given this background, this paper delves into the development of a new probability distribution. Consequently, the main accomplishment of this paper is the development of a new probability distribution by merging the generalized Rayleigh model with a tangent-based technique. The proposed innovative model is known as the tangent generalized Rayleigh (TG-Rayleigh) distribution. The TG-Rayleigh distribution stands out for its lack of additional parameters, effectively preventing re-parameterization issues. Through mathematical derivations, certain properties and estimators for the model parameters of the TG-Rayleigh distribution are determined. The assessment of these estimators is done through a simulation study. In addition, the TG-Rayleigh distribution's applicability and proficiency are illustrated using two specific data sets. These data sets are obtained from reliability engineering (referred to as Data 1) and music engineering (referred to as Data 2). When taking into account specific assessment criteria utilized as diagnostic tools, it becomes apparent that the TG-Rayleigh model stands out as the most effective and optimal model for analyzing Data 1 and Data 2 in comparison to other candidate probability distributions. [ABSTRACT FROM AUTHOR]

The submergence depth directly affects the safety of semi-submersible marine structures due to that the submergence depth significantly impacts on the hydrodynamic characteristics and wave loads of structures excited by extreme wave. This paper studies the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures by establishing a numerical model of the interaction between solitary waves and semi-submersible structures based on the SPH model and Rayleigh theory. Furthermore, equations for transmission coefficient, reflection coefficient, and wave load are fitted. The calculated wave heights of solitary wave propagation test case are in good agreement with the theoretical values. The maximum relative error of the wave peak is 8.4%. The calculated wave loads of submerged horizontal plates test case has a consistent trend with the experimental data. The maximum relative error of wave load peak and valley is 54% (absolute error 0.37 N). Furthermore, the interaction between solitary waves and structures with different submergence depths is investigated by using the meshless numerical model. It is found that the reflection coefficient first increases and then decreases with increasing submergence depth, and reaching a maximum value of 0.39 at the submergence depth equal to 0.0 m. On the contrary, the transmission coefficient decreases first and then increases with the increase of submergence depth. The minimum value of transmission coefficient is 0.36 with the submergence depth of 0.3 m. As the submergence depth increased, the horizontal wave load peak of the structure gradually increases, and the maximum value of 0.13 is obtained at the submergence depth of 0.7 m. The peak of vertical wave load rapidly increases with the increase of submergence depth and then gradually decreases while the trough gradually decreases with increasing submergence depth. [ABSTRACT FROM AUTHOR]

In this paper, we have derived and studied new probability distributions by extending the 2‐dimensional Rayleigh distribution (RD). First, we extend the RD to 3 dimensions and then generalize it to k dimensions for any positive integer k ≥ 3. The distributions are named the 3‐dimensional Rayleigh distribution (3‐DRD) and k‐dimensional Rayleigh distribution (k‐DRD), respectively. For both 3‐DRD and k‐DRD, detailed mathematical and statistical properties including derivations of the corresponding cumulative distribution, probability density, survival, and hazard functions, moments, moment generating functions, mode, skewness, kurtosis, and differential entropy are obtained in closed forms. Parameter estimation is done for both models using the maximum likelihood estimation method and some statistical properties of the estimator are discussed for each case. Interestingly, the commonly known Normal, Rayleigh, Maxwell–Boltzmann, chi‐square, gamma, and Erlang distributions are related to the newly developed extended RDs as special cases. For the 3‐DRD, plots of cumulative distribution, probability density, survival, and hazard functions are exhibited, a simulation study is carried out, and random samples are generated using the standard accept–reject (AR) algorithm to check the efficiency of the maximum likelihood estimates of the parameter. Moreover, the new 3‐DRD model is fitted to one simulated and three real datasets, revealing good performance compared to four existing Rayleigh‐based distributions. This study will contribute new knowledge to the field of applied statistics and probability, and the findings will be used as a basis for future research in the field. [ABSTRACT FROM AUTHOR]

The dispersion and attenuation characteristics of Rayleigh waves in a non-uniform viscoelastic half-space with a covering layer are studied in this paper. The half-space and the covering layer are modeled by the fractional-order Zener viscoelastic solid. Compared with the traditional integer-order viscoelastic model, the viscoelastic model with fractional-order derivative is more flexible in describing the complicated history-dependent mechanical behavior. Legendre and Laguerre orthogonal polynomials are used to approximate the displacement field of surface waves. The rectangular window function is used to merge the surface boundary conditions. The complicated problem of solving the complex wave number in the complex region is ultimately transformed into an eigenvalue problem. The correctness of the method is verified by comparing our outcomes with those in the literature. It is found that the present spectrum method avoids the complicated iterative process of root-finding and the pseudo-root and root-missing problem compared to the traditional root-finding method. Moreover, the uneven gradient distribution of the cover layer and half-space has opposite effects on the propagation of Rayleigh waves at low and high frequencies, and the same influence applies to fractional-order effects. The present study has important theoretical significance and application potential in the geophysical exploration and earthquake engineering. [ABSTRACT FROM AUTHOR]

In our research paper, we introduce an innovative statistical distribution known as the New Transmuted Rayleigh Distribution. This distribution serves as a versatile expansion of the traditional Rayleigh distribution and has been developed using a novel transmutation technique. We provide an in-depth analysis of several statistical properties of this new distribution. The resulting model has the ability to represent complex shapes, making it suitable for a wide range of applications. Our manuscript thoroughly examines the fundamental characteristics of the new model, outlining the methodology for estimating its unknown parameters through maximum likelihood estimation. Additionally, we demonstrate the practical significance of the model by applying it to an empirical dataset and conclusively establishing its superiority over some existing prominent models. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing an acceptance sampling plan for a truncated life test where the lifetime of the product follows a generalized Rayleigh distribution. The study identifies the minimum sample sizes needed to ensure the specified mean life for various acceptance numbers, confidence levels, and ratios of the fixed experiment time to the specified mean life. The operating characteristic values of the sampling plans, along with the producer's risk, are discussed. Additionally, tables are provided to facilitate the application of these sampling plans, and a numerical example is included to illustrate the use of these tables. [ABSTRACT FROM AUTHOR]

This paper focuses on the designing of the Repetitive Deferred sampling plan for truncated life test for percentiles using Kumaraswamy Exponentiated Rayleigh distribution. A truncated life test may be conducted to evaluate the smallest sample size to insure certain percentile life time of products. The main objective of the proposed sampling plan is to minimize the sample size because the analogous inspection time and inspection cost will be reduced. The operating characteristic function values are calculated according to various quality levels and the minimum ratios of the true average life to the specified average life at the specified producer’s risk are derived. Certain real life examples are provided. [ABSTRACT FROM AUTHOR]

Surface angled cracks on critical components in high-speed machinery can lead to fractures under stress and pressure, posing a significant threat to the operational safety of equipment. To detect surface angled cracks on critical components, this paper proposes a "Quantitative Detection Method for Surface Angled Cracks Based on Full-field Scanning Data". By analyzing different ultrasonic signals in the full-field scanning data from laser ultrasonics, the width, angle, and length of surface angled cracks can be determined. This study investigates the propagation behavior of ultrasonic waves and their interaction with surface angled cracks through theoretical calculations. The crack width is solved by analyzing the distribution of Rayleigh waves in the full-field scanning data. This paper also discusses the differences in ultrasonic wave propagation between near-field and far-field detection and identifies the critical point between these regions. Different computational methods are employed to calculate the inclination angle and the crack endpoint at various scan positions. Four sets of experiments were conducted to validate the proposed method, with results showing that the errors in determining the width, angle, and length of the surface angled cracks were all within 5%. This confirms the feasibility of the method for detecting surface angled cracks. The quantitative detection of surface angled cracks on critical components using this method allows for a comprehensive assessment of the component's condition, aiding in the prediction of service life and the mitigation of operational risks. This method shows promising application potential in areas such as aircraft engine blade inspection and gear inspection. [ABSTRACT FROM AUTHOR]

It is shown here that if the PDF (Probability Distribution Function) of wind speed is a Rayleigh distribution with parameter $s$ s , then the PDF of wind power is a Weibull distribution with parameters $a = \sqrt 2 \rho s^3\comma \; \; b = \displaystyle{2 \over {3\; }}$ a = 2 ρ s 3 , b = 2 3 , where $\rho$ ρ is the air density; if the wind speed PDF is a Weibull distribution with parameters $a\comma \; b$ a , b , then the wind power PDF is also a Weibull distribution with parameters $\; \displaystyle{{a^3\rho } \over 2}\comma \; \displaystyle{b \over 3}$ a 3 ρ 2 , b 3 ; if the PDF of wind speed is a log-normal distribution with parameters $\mu \comma \; \sigma$ μ , σ , then the PDF of wind power is also a log-normal distribution with parameters $\ln \displaystyle{\rho \over 2} + 3\mu \comma \; 3\sigma$ ln ρ 2 + 3 μ , 3 σ . The derived relationships allow us to quickly estimate parameters that indicate the wind power potential of the considered site, and the amount of wind energy generated by the turbine. [ABSTRACT FROM AUTHOR]

This study presents an innovative fractional order Rayleigh fading model that can be used for channel capacity estimation in the presence of additive white generalized Gaussian noise. The proposed model assumes that the real and imaginary parts of channel gains are generalized Gaussian random variables, which makes it possible to consider the traditional Rayleigh fading model as a special case of fractional order Rayleigh fading. Compared to the Rayleigh model, the fractional order Rayleigh fading model offers a more precise representation of new real‐world communication, such as integrating terrestrial and underwater networks in sixth‐generation communications channels. The probability density function of the channel gain with additive white generalized Gaussian noise is analyzed here. Furthermore, the ergodic and outage capacities of the channel are determined, taking into account the assumption that the channel state information is only available at the receiver. The ergodic capacity is calculated using Meijer's G‐functions, resulting in a closed‐form expression. Numerical simulations demonstrate the superiority of the fractional order Rayleigh fading model over the Rayleigh channel. Moreover, the impact of ergodic and outage capacities under diverse channel characteristics is assessed. [ABSTRACT FROM AUTHOR]

By utilizing chirp-BOK (binary orthogonal keying) modulation into a troposphere scattering communication system, a lower demodulation threshold can be achieved with excellent linear frequency modulation properties in a strong noise and weak signal environment. Firstly, the bit error rate (BER) formula of chirp-BOK modulation over a Rayleigh fading channel was derived theoretically. Then, the BER performance with different chirp-BOK parameters were numerically calculated. In order to investigate the performance of chirp-BOK over deeping fading troposphere scattering link, a seven-path equal-delay Rayleigh fading model was employed. Finally, the system BER performance was simulated under different tap delay and time–bandwidth product parameters. The results demonstrate that when BER reaches 10 − 4 , the optimal configuration of the system achieves a gains approximately from 1.7 dB to 10 dB compared to non-optimized configuration under different Path-Gain-Vector with varying tap delays. [ABSTRACT FROM AUTHOR]

We consider a sequence (n = 1, 2, ⋯) of finite Markov chains {ωn,t}t≥1 with discrete time describing the percolation process in a band of width n of a multilayered random medium in which a flow (breakdown) already exists, and random variable ωn,t equals to the width of the percolation cluster at time t. For each value of n and given random percolation mechanism the Markov chain {ωn,t}t≥1 has a limit stationary distribution, corresponding to the random variable ωn. In the case when the width n of the layers of the medium under consideration tends to infinity, the limit distribution of the random variables Ωn b / n (b is some constant) is found, which is the Rayleigh distribution. [ABSTRACT FROM AUTHOR]

This paper investigates how atmospheric vertical profiles of pressure, temperature, and concentration affect molecular absorption calculation. This sensitivity analysis is performed in preparation to the upcoming TRUTHS mission, anticipated to provide hyperspectral TOA BRF records with a radiometric accuracy better than 1%. Two methods for characterizing the atmospheric vertical profile are compared: rescaling the H2O and O3 concentrations of an AFGL U.S. Standard vertical profile, and using customized profiles based on CAMS data. The study investigates the effects of those methods on multi-spectral observations in key spectral regions affected, respectively, by water vapour, ozone and methane, as well as on hyperspectral observations covering the visible to SWIR region. Results show that when molecular transmittance exceeds 97%, the choice of method has minimal impact, with less than 1% uncertainty. When the molecular transmittance decreases from 97% to 75%, the corresponding uncertainty on the TOA BRF simulation increases from 1% up to 5%. For transmittance below 75%, using CAMS data for vertical profile characterization is recommended. The study also highlights how pressure and temperature profiles influence Rayleigh optical thickness estimation, particularly affecting TOA BRF in the blue spectral region. [ABSTRACT FROM AUTHOR]

In this study, the focus is on the reduction of channel attenuation through diversity techniques. The effectiveness of the diversity system was evaluated based on its ability to lower the carrier noise ratio (CNR) and carrier-to-interference ratio (CIR) at a specific probability of error (Pe). The analysis concentrated on statistically reducing the fading dynamic range of the average CNR and CIR. The aim was to examine two branches (N=2) of diversity systems that employed pre-detection combining, a highly advantageous and effective method in radio mobile communications. The initial phase of the research involved investigating the statistical properties of CNR and CIR without diversity using a Rayleigh fading model. Diversity was then introduced into the experiment. Maximal ratio (MRC) combining, Equal gain (EGC) combining and Selection (SC) combining were simulated and compared. The results showed that the use of diversity techniques significantly reduced the fading dynamic range of the instantaneous CNR γ compared to the instantaneous CIR λ of about 10-3dB Furthermore, maximal-ratio combining (MRC) demonstrated the highest level of performance improvement compared to other methods. [ABSTRACT FROM AUTHOR]

In this paper, we present the evaluation of network parameters for the unmanned aerial vehicle (UAV)-enabled triple-hop mixed RF/FSO-based wireless communication system, where one relay is a fixed relay and the second relay is a UAV which acts as decode-and-forward relay for communication from the base station (B) to the multiple mobile users (M i) ,   i ∈ { 1 , 2 ⋯ N } . The first hop from B to fixed relay (R1) is the radio frequency (RF) link modeled using α − κ − μ fading distribution, the second hop from the relay R1 to the UAV relay (R2) is a free space optics (FSO) link modeled using Gamma-Gamma fading, and the third hop from R2 to the M i is, again, an RF link modeled using the Rayleigh fading model. The direct communication between the B and the M i is not feasible due to the very large distance. We derive the closed form analytical expression for the outage probability of the proposed system and find the effect of the base system parameters on the performance of the system. We also analyze the outage probability of the system at high SNR values to get further insights of the system performance. In addition, altitude optimization of UAV is carried out to know the optimal elevation angle in correspondence with UAV's optimal altitude in order to maximize performance of the system. [ABSTRACT FROM AUTHOR]

In this study, the properties of Rayleigh wave fields scattered at a surface from open vertical cracks with different shapes are investigated. The scattered Rayleigh wave is determined by both the incident Rayleigh wave and its interaction with the crack, and the wave fields are modeled using the Green's function method based on the reciprocity theorem. The reflection coefficient of the Rayleigh wave in two-dimensional coordinates is employed to simplify the area integration over the crack surface for the scattered Rayleigh wave to a line integration over the length of the crack. Numerical simulations are carried out, and the effects of the crack length and depth on the scattered Rayleigh wave fields are discussed. The results indicate that the distribution of a scattered Rayleigh wave field is mainly determined by the crack length, while the amplitude is closely related to the crack depth. Since the reflection coefficient becomes almost stable when the ratio of the crack depth to the Rayleigh wavelength is larger than 1, the variation in the scattered Rayleigh wave field is insignificant for cracks with the same length but varying depths. This work will be helpful for solving the inverse problem of evaluating crack geometry using ultrasonic Rayleigh waves and for further work on Rayleigh waves scattered by cracks with different directions of extension and angles with the surface. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, an outdated channel state information‐based heterogeneous wireless communication system is analyzed, which involves an underwater multiuser acoustic sensor network, decode‐and‐forward relay, and terrestrial radio frequency destination with multiple antennas. The outdated channel state information is an utmost parameter to deal with practical conditions of underwater environment as well as of the terrestrial environment. Due to this fact, each channel is constrained to this factor in our investigation. The underwater acoustic network takes advantage of multiuser diversity based on generalized selection user scheduling, where the Lth$$ {L}_{th} $$ best user is chosen out of several active acoustic sources to continue transmitting data via relay to the destination. To boost system performance, the destination makes the use of the maximal ratio combining strategy. Moreover, each channel follows Rayleigh fading model. The closed form expressions of outage probability and average bit error rate are obtained along with their asymptotic results under the practical scenarios. The ergodic capacity and its upper bound expressions are also derived. Further, analytical results are verified with Monte‐Carlo simulation. [ABSTRACT FROM AUTHOR]

It has been widely acknowledged that probability-based methodologies play a crucial role in guiding decision-making processes when faced with uncertain or vague circumstances. To ensure that decisions made under such conditions are both meaningful and productive, a variety of methodologies centered around probability have been developed, endorsed, and put into practice. This study also aims to contribute to the existing body of knowledge by introducing a new probability model known as the weighted sine generalized Rayleigh distribution. For the proposed model, certain properties are derived. Furthermore, the parameter estimation technique and simulation studies based on the proposed model are also presented. Finally, the proposed model is successfully implemented on three distinct data sets sourced from sports and different engineering disciplines. By evaluating the statistical significance through the p -value and other various tests, it is evident that the proposed model consistently outperforms its competitor distributions. The practical illustration, emphasizes the efficacy and potential of the proposed model for widespread applications in sports and engineering research and practice. [ABSTRACT FROM AUTHOR]

Autochthonous dissolved organic matter (Auto-DOM) produced by a biological carbon pump using dissolved inorganic carbon (DIC) from carbonate weathering plays an important role in carbon cycling within inland waters. However, little is known regarding how environmental conditions impact the composition and fate of organic matter, especially in surface waters of the semi-arid Loess Plateau, which is enriched in DIC by significant carbonate weathering. To obtain novel insight, we combined hydrochemistry, isotopic composition (δ2H, δ18O, and δ13C DIC), Rayleigh fractionation model, optical spectroscopy (absorbance and fluorescence), and Fourier transform ion cyclotron resonance mass spectrometry measurements to elucidate how primary production and hydrology impact the composition of DOM and the stability of the resulting Auto-DOM throughout the river–reservoir–wetland aquatic continuum of the Bahe River in the carbonate-mineral-rich semi-arid Loess Plateau where carbonate weathering is significant. The Rayleigh fractionation model results indicated that watershed DIC is primarily consumed through aquatic primary production rather than CO 2 degassing. Further investigation revealed that primary production and evaporation co-occurred in this watershed. With the enrichment of the stable water isotope δ2H, the relative abundances of the allochthonous compounds decreased and the relative abundances of the autochthonous substances increased, suggesting that the terrestrial signal of riverine DOM decreased while autochthonous production increased along the flow pathway. In addition, associations between optical and molecular characteristics among DOM samples from different water bodies revealed that the stability ratio (Fmax(C2/(C2 + C4))) of Auto-DOM to the ratio of carboxylic-rich alicyclic molecules showed a consistent trend, suggesting that phytoplankton-derived and biomineralized C2 compounds are potentially recalcitrant DOM in inland waters. We conclude that hydrology and primary production affect the source, composition, and, potentially, the stability of DOM in DIC-enriched surface waters of the semi-arid Loess Plateau, which may lead to a more humic-like DOM composition in inland water and export this lower bioavailability DOC to the ocean in the long term. [ABSTRACT FROM AUTHOR]

Primary multiphase inclusions trapped in host minerals such as garnet may provide important information about the nature of fluids and melts and their crystallization products. The occurrence of melt and fluid inclusions in the same cluster suggests primary fluid-melt immiscibility during partial melting. Here we report the coexistence of diamond-bearing fluid inclusions with melt inclusions in metasedimentary UHP rocks of the Nordmannvik Nappe at Heia, in the Arctic Caledonides of Norway. Multiphase fluid inclusions (Type I) and primary melt inclusions (Type II) have been identified in garnet and studied in detail. Microscopic observations, Raman spectroscopy, FIB-SEM, and EDS analysis show that microdiamonds occur in situ, in multiphase fluid inclusions (Type I) distributed in clusters in the garnet mantle. The Raman spectra suggest partial transformation of diamond to disordered sp2-bonded carbon structure. Along with diamond, Type I inclusions contain (i) rutile and apatite as trapped solid phases, (ii) carbonates (magnesite-siderite) and Al-phyllosilicates (white mica, phlogopite, pyrophyllite) as daughter or step-daughter minerals, and (iii) CO2 as a residual fluid phase. Former melt inclusions (Type II) occur in the same microstructural position in the host garnet. They contain muscovite, paragonite, phlogopite, K-feldspar, plagioclase, albite and quartz as solid phases crystallized from a melt, and kyanite as accidentally trapped mineral. The occurrence of melt inclusions in the inner part of garnets thus suggests that garnet was growing in the presence of melt. Garnet is nearly homogeneous with respect to major elements Mg, Fe, Ca and Mn, expressed by pyrope (0.18–0.22 X Prp), grossular (0.09–0.12 X Grs), almandine (0.67–0.70 X Alm) and spessartine (0.01–0.03 X Sps) except local Ca enrichment in the rim. Trace elements show decreasing HREE and Y patterns from the core to the mantle suggesting garnet growth according to the Rayleigh fractionation model. Phosphorus shows an elevated content in the core and mantle. A positive correlation between P and Na indicates a coupled NaPM2+−1Si−1 substitution in garnet. Minimum P–T conditions of 3.7 to 3.8 GPa and 840°C to 870°C for the peak metamorphic stage were estimated from garnet composition (X Prp = 0.22), zirconium-in rutile thermometry of rutile inclusions in garnet (747–977 ppm of Zr) and diamond/graphite stability boundary. Partial melting on a prograde P–T path was controlled by the decomposition of phengite in the presence of C–O–H fluid, producing peritectic garnet ± kyanite along with melt, in the diamond stability field. The coexistence of diamond-bearing multiphase fluid inclusions with melt inclusions suggests primary fluid-melt immiscibility at UHP conditions. During exhumation, the rock underwent decompression and second partial melting, leading to enrichment in Ca, Y, Cr and Sc of garnet rims. Microdiamonds found in metasedimentary crustal rocks at Heia provide new evidence of UHP metamorphism in the Nordmannvik Nappe of the Arctic Caledonides. The results favour a correlation with the pre-Scandian subduction and arc–continent collision events of the Caledonian Orogeny. [ABSTRACT FROM AUTHOR]

Software is used in diverse settings and depends on development and testing environments. Software development should improve the reliability, quality, cost, and stability of software, making the software testing period crucial. We proposed a software reliability model (SRM) that considers the uncertainty of software environments and the fault detection rate function as a Rayleigh distribution, with an explicit mean value function solution in the model. The goodness-of-fit of the proposed model relative to several existing nonhomogeneous Poisson process (NHPP) SRMs is presented based on three software application failure datasets. Further, a cost model is also presented that addresses the error-removal risk level and required time. The optimal testing release policy for minimizing the expected total cost (ETC) is also determined for NHPP SRMs. The impact of the software environment is studied by varying it, and the optimal release times and minimum ETCs are compared. The goodness-of-fit comparison confirmed that the proposed model has more accurate prediction values than other models. Further, whereas the existing models applied to the cost model do not change after a certain operation period, the proposed model yields changes in release time even for long operating periods. [ABSTRACT FROM AUTHOR]

In this paper we have for the first time proposed a novel transformed Gaussian process method for the estimation of rogue wave occurrence in a short crested mixed sea. The saddle point approximation of a specific joint density is utilised to further improve the computational efficiency of the proposed method. The proposed method has been applied to forecast the rogue wave occurrence in four short-crested mixed sea states, two with directional wave spectra based on measured surface elevation data at the coast of Yura, and another two with typical directional bimodal wave spectra. It is shown in these four cases that the proposed method can offer more accurate forecasting results than those obtained from the linear simulation method, from the transformation based on Hermite polynomials and from using the Rayleigh distribution model. It is also demonstrated that the proposed method is more efficient than the nonlinear simulation method. [ABSTRACT FROM AUTHOR]

In "An Improved Approximation Algorithm for TSP," Karlin, Klein, and Oveis Gharan design the first improvement over the classical 1.5 approximation algorithm of Christofides-Serdyukov after more than 40 years. Their algorithm first chooses a random spanning tree from the maximum entropy distribution of spanning trees with marginals equal to the optimum LP solution of TSP, and then, similar to Christofides' algorithm, it adds the minimum cost matching on the odd degree vertices of the tree. To analyze their simple algorithms, they prove and exploit new tools from the theory of strongly Rayleigh distributions. For some ϵ>10−36 , we give a randomized 3/2−ϵ approximation algorithm for metric TSP. Funding: This work was supported by the Air Force Office of Scientific Research [Grant FA9550-20-1-0212], the Alfred P. Sloan Foundation [Grant FG-2019-12196], and the Division of Computing and Communication Foundations [Grants CCF-1552097, CCF-1813135, and CCF-1907845]. [ABSTRACT FROM AUTHOR]

In recent years, the use of "near-net forming" to manufacture key components of aeroengines has become a mainstream development direction. In this paper, "near-net forming" of rotating parts such as disks and shafts is realized by using axial closed die rolling (ACDR) deformation technology. Numerical simulation and experimentation research were utilized to compare the plastic deformation characteristics and microstructure evolution of TC11 disc component forming by upsetting and ACDR forming, including strain distribution, temperature distribution, and microstructure evolution mechanisms. The FEM results revealed that during the ACDR process, the equivalent strain exhibits a radial distribution pattern with the center of contact area between the billet and upper die. The top surface of the billet was located in the severe plastic deformation zone and had better microstructure uniformity as a whole. In addition, ACDR forming enables continuous "near-net forming" at relatively low loads. The experimental results illustrated that ACDR formation is characterized by three types of deformation: radial tension, circumferential torsion, and axial compression, and at the same time, the overall strain is higher. As a result, the initial α size in the core was finer and exhibited an equiaxial shape, and the remaining areas of the grain were relatively fine and more uniformly distributed. The ACDR forming process can obtain a uniform and refined TC11 microstructure more efficiently. The TEM morphology observation of the ACDR specimens revealed that the lamella α-phase was bent, twisted, and fractured under the combined action of axial and shear stresses. The spheroidization models are primarily the globularization model of shearing lamellar structure the grain boundary splitting model, the termination migration globularization model, and the globularization model of Rayleigh instability. [ABSTRACT FROM AUTHOR]

Structural damping, which has been widely used to quantify the energy dissipation of engineering structures, plays an important role in dynamic analysis during the design phase and the assessment of existing structures. However, the development of an accurate damping model remains an open question due to the unclear mechanism. In this study, structural damping was identified based on loss factors for beam structures, which were used for presenting the damping behavior during vibrations. The equation of motion for the bending deformation of a Timoshenko beam was derived, accounting for the material damping. To identify the loss factor of the beam from the response signals at a limited number of measurement points, an inverse algorithm based on wave coefficient estimation was developed, considering the numerical stability for data interpretation. Based on the proposed loss factor identification method, several beam models with different shapes of cross-sections were investigated, focusing on the feasibility of the method of varying cross-section cases. Comparing the spectral element model with the loss factor and the finite element model with Rayleigh damping, it was confirmed that the loss factor can better describe the actual energy dissipation behavior of the structure. It provides a more accurate theoretical model for estimating structural damping in practical engineering. [ABSTRACT FROM AUTHOR]

Nitrous oxide (N2O) is a potent greenhouse gas and the most significant anthropogenic ozone-depleting substance currently being emitted. A major source of anthropogenic N2O emissions is the microbial conversion of fixed nitrogen species from fertilizers in agricultural soils. Thus, understanding the enzymatic mechanisms by which microbes produce N2O has environmental significance. Measurement of the 15N / 14N isotope ratios of N2O produced by purified enzymes or axenic microbial cultures is a promising technique for studying N2O biosynthesis. Typically, N2O-producing enzymes combine nitrogen atoms from two identical substrate molecules (NO or NH2OH). Position-specific isotope analysis of the central (Nα) and outer (Nβ) nitrogen atoms in N2O enables the determination of the individual kinetic isotope effects (KIEs) for Nα and Nβ, providing mechanistic insight into the incorporation of each nitrogen atom. Previously, position-specific KIEs (and fractionation factors) were quantified using the Rayleigh distillation equation, i.e., via linear regression of δ15 Nα or δ15 Nβ against [ -fln⁡f/(1-f) ], where f is the fraction of substrate remaining in a closed system. This approach, however, is inaccurate for Nα and Nβ because it does not account for fractionation at Nα affecting the isotopic composition of substrate available for incorporation into the β position (and vice versa). Therefore, we developed a new expansion of the Rayleigh model that includes specific terms for fractionation at the individual N2O nitrogen atoms. By applying this Expanded Rayleigh model to a variety of simulated N2O synthesis reactions with different combinations of normal, inverse, and/or no KIEs at Nα and Nβ, we demonstrate that our new model is both accurate and robust. We also applied this new model to two previously published datasets describing N2O production from NH2OH oxidation in a methanotroph culture (Methylosinus trichosporium) and N2O production from NO by a purified Histoplasma capsulatum (fungal) P450 NOR, demonstrating that the Expanded Rayleigh model is a useful tool in calculating position-specific fractionation for N2O synthesis. [ABSTRACT FROM AUTHOR]

Wood and steel have different physical properties. By combining the two kinds of materials as bonded parallel beams, wood-steel frame structures can be prepared. This work considers the seismic performance of such engineering structures. Based on the Rayleigh damping model of substructures, the non-proportional damping coefficient is used to quantify the structural non-proportional damping characteristic of wood-steel frame structures. A complex mode superposition method is used to calculate seismic responses. Numerical cases showed that compared with the frame structure with upper steel and lower wood, the overall lateral performance is lower and the local lateral performance is higher for the frame structure with upper wood and lower steel. The overall lateral seismic design needs to be improved for the wood-steel frame structure with upper wood and lower steel. The local lateral seismic design needs be improved for the wood-steel frame structure with upper steel and lower wood. [ABSTRACT FROM AUTHOR]

Modelling in lifetime phenomena is a significant issue in many scientific areas. Sometimes many standard models lack superiority in modelling data set. Designing a new form of probability distribution by using different techniques has received a widely attention in statistical theory in the recent years. In this paper, we formulated exponentiated exponential Rayleigh (EER) distribution. We discussed the reliability and hazard rate functions of the EER distribution and computed the quantile, median, skewness and kurtosis. Moreover, the correlations between the parameters and the median, skewness, and kurtosis are investigated. Bayesian and non-Bayesian approaches are adopted to estimate the unknown parameters of EER distribution. In Bayesian approach, we are used Markov Chen Monte Carlo (MCMC) method to obtain the approximate Bayes point estimate. The proposed distribution is used to analyze, light-emitting diodes data, strength of glass fibers data and Wheaton River data. The estimation results of the EER distribution are compared with exponential Rayleigh, Rayleigh, and exponential distributions. [ABSTRACT FROM AUTHOR]

In this article, we investigated the problem of estimating the parameters of power Rayleigh distribution using a range of classical and Bayesian estimate strategies. For applied statisticians and reliability engineers, parameter estimation provides a guide for choosing the best method of estimating the model parameters. Six frequentist estimation methods, including maximum likelihood estimation, Cramer-von Mises estimation, Anderson-Darling estimation, least square estimation, weighted least square estimation, and maximum product of spacing estimation, were taken into consideration when estimating the parameters of the power Rayleigh model. The expressions for Bayes estimators of the scale parameter are derived under squared error and precautionary loss functions and utilizing extensions of Jeffrey's prior and natural conjugate priors. To investigate the finite sample properties of the parameter estimations, Monte Carlo simulations are also performed. Finally, two applications to real data are used to highlight the versatility of the suggested model and the comparison is made with the Rayleigh and some of its well-known extensions such as exponentiated Rayleigh and weighted Rayleigh distributions. [ABSTRACT FROM AUTHOR]

This paper present methods for estimating a scale parameters and modified reliability for the Inverse Exponential Rayleigh Distribution include Maximum Likelihood, rank set sampling and Cramér-von-Mises Estimations. In all the mentioned estimation methods, the Newton-Raphson iterative numerical method was used. Then a simulation was conducted to compare the three methods with six cases and different sample sizes. The comparisons between scale parameter estimates were based on values from Mean Square Error while it was based on values from Integrated Mean Square Error for the estimates of the modified reliability function. The results show that Cramér-von-Mises (MCV) estimators is the best among the other two methods for estimating the modified reliability function. [ABSTRACT FROM AUTHOR]

The paper deals with a new model based on Eringen's nonlocal thermoelasticity. The propagation of Rayleigh waves in a nonlocal thermoelastic layer which is lying over a nonlocal thermoelastic half-space is considered in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach.The frequency equation of Rayleigh surface wave is derived. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss and penetration depth of Rayleigh surface waves is presented graphically. [ABSTRACT FROM AUTHOR]

The switching dynamics of antiferroelectric lead zirconate (PbZrO3) freestanding capacitors compared to their epitaxial counterparts is reported. Frequency dependence of hysteresis indicates that freestanding capacitors exhibit a lower dispersion of switching fields, lower residual polarization, and faster switching response as compared to epitaxially‐clamped capacitors. As a consequence, freestanding capacitor membranes exhibit better energy storage density and efficiency. [ABSTRACT FROM AUTHOR]