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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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Rotating machinery faults generally result in the generation of impulse components, accompanied by multi-order harmonics. However, the impulse phenomena may inherently be submerged within noisy stationary components, which introduces challenges to identify machinery faults. Existing methods for impulse extraction are mainly divided into two categories: signal decomposition and deconvolution-based methods. The former fundamentally rely on single band-pass filtering, making them incapable of extracting impulse components distributed across multiple frequency bands. The latter functions as frequency-shaping filters, which are prone to cause waveform damage to impulse components. To overcome these limitations, this paper proposes an adaptively impulse extraction methodology for rotating machinery, defined as spectrum discrepancy impulse reconstruction (SDIR). Its innovation lies in the accurate differentiation of each frequency corresponding to impulses, stationary components or noise based on spectrum discrepancies for subsequent signal reconstruction. The spectrum of impulses is determined by comparing the original spectrum with the spectrum after highlighting impulses using optimal weight impulse extraction (OWIE). Additionally, noise is split out through a threshold determined according to the Rayleigh distribution of noise spectrum amplitude. The effectiveness of the proposed SDIR is validated through simulation case studies and experimental fault signals. Results demonstrate that the SDIR is able to decompose the raw signal into three intrinsic sub-signals adaptively for impulses extraction with considerable accuracy. [ABSTRACT FROM AUTHOR]

• The equation for converting S-N curves with different stress ratios to S-N curve with a stress ratio of −1 was developed. • The effect of the mean stress on Rayleigh distribution was studied. • A probability density function of the vibration signal considering the mean stress was proposed. For vibration response signals with mean stress, a Rayleigh function with a multiplier was used to fit the probability distribution of stress amplitude corrected to vibration response signals with zero mean stress. An equation was developed by the obtained S-N curves for welded 1Cr18Ni9Ti stainless steel connections with stress ratios of −1, 0.1, and 0.5, respectively, to convert the stress amplitudes of cyclic loadings with different mean stress to stress amplitudes with zero mean stress for the same fatigue life. Based on the S-N curve of material with a stress ratio of −1 and the Miner linear damage accumulation theory, a vibration fatigue life prediction method was proposed. The results of the random vibration fatigue test with non-zero mean stress on the pipeline of the launch vehicle have verified the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Mitigation of channel impairments and detection of transmitted symbols remain challenging for both wireless and optical environments. Multi input multi output orthogonal frequency division multiplexing (MIMO OFDM) modeling can be used for both wireless and free space optical channels to analyze the receiver performance. But the receiver performance degrades due to fading effects in wireless channels and scintillation effects in free space optical channels. As equalizer role is crucial to compensate the channel effects, development of adaptive equalization models help to enhance the receiver throughput. Low complexity neural network architecture can be effectively used to develop equalization models that can minimize bit errors even in the practical channel conditions. Single layer neural network based equalization models are proposed in the paper to reconstruct data stream with minimum bit error. Gamma-gamma model is used to analyze free space optical (FSO) medium. Similarly the fading statistics of wireless channel can be realized using Rayleigh and Nakagami-m models which characterize outdoor wireless environment. Hyperbolic secant cost Least Mean Square (LMS) algorithm is used to train the models and the performance is verified as well as evaluated in terms of BER, MSE and eye diagram. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) offer a potential alternative for providing voice services in areas where communication is disrupted due to natural disasters. These UAVs can be configured as aerial base stations (ABSs), enabling the deployment of a temporary communications network. However, communication networks based on ABSs pose several significant challenges. One of these challenges involves addressing interruptions or limitations in network coverage caused by natural disasters. In such situations, there is a high likelihood that users within the affected area may be unable to communicate due to a lack of coverage. This is a complex problem because it depends on factors, such as the mobile user locations, the characteristics of the air-to-ground channel, and geographical details of the area. In this work, we propose an optimization model to determine the placement of a set of ABSs within a limited disaster area that maximizes the probability of successful voice services (PSVSs). This optimization model integrates a network evaluation model that analyzes the wireless environment at a specific time. The network evaluation model utilizes two-ray and Rayleigh channel models, enabling the simulation of a worst-case scenario for wireless communication systems. We evaluate the proposed optimization model using the (1+1)-evolution strategy with a one-fifth success rule. We explore various parameter configurations to understand their impact on algorithm performance. This analysis helps identify the configuration of the optimization model that yields the maximum PSVSs. Simulation results indicate that by appropriately configuring the evolution strategy algorithm and comparing random ABS locations with those determined ABS locations by the evolution strategy algorithm, the PSVS can be enhanced by an average of 60%. • We propose an optimization model for aerial base station placement. • We create an instance that contains real geographic coordinates. • The proposed optimization model incorporates a network communication model. [ABSTRACT FROM AUTHOR]

[Display omitted] • Scheelite-bearing veinlet was found in deep-seated biotite monzogranite. • Ore-forming fluid originated from magma and Neoproterozoic metasedimentary rocks. • Fluid underwent apatite fractionation before scheelite precipitation. • Scheelites in Zhuxi share a similar source but are various in fluid process. The coexistence of multiple types of tungsten (W) mineralization is a hallmark of giant W deposits. The Zhuxi deposit in South China, the largest W deposit globally, contains 4.22 Mt of WO 3. Here, we investigate newly identified scheelite-bearing biotite monzogranite from the Zhuxi deposit, analyzing the elemental compositions and Sr isotopic signatures of scheelite and apatite coexisting within veinlets hosted in the biotite monzogranite. Micropetrographic relationships and rare earth element (REE) compositions in minerals indicate that apatite crystallized earlier than scheelite. Using the Rayleigh distillation model, our simulations indicate that the ore-forming fluids underwent approximately 10 % apatite-dominated fractional crystallization prior to scheelite crystallization. The apatites exhibit homogeneous 87Sr/86Sr ratios ranging from 0.71743 to 0.71921, suggesting that the ore-forming fluids inherited their Sr isotopic signatures from both the parental magma and Neoproterozoic metasedimentary rocks. The 87Sr/86Sr ratios of scheelite, ranging from 0.71689 to 0.71820, are consistent with those of scheelite from other occurrences within the Zhuxi deposit. This similarity indicates that ore-forming fluids across the Zhuxi deposit were derived from common sources. This study also compiled compositional data for scheelite from various occurrences in the Zhuxi deposit reported in the literature, dividing them into four types: (type-I) scheelite overprinting massive prograde skarn, (type-II) scheelite overprinting prograde skarn veinlets, (type-III) scheelite hosted in quartz–muscovite veins within marble, and (type-IV, analyzed in this study) scheelite in veinlets within biotite monzogranite. The type-IV scheelite exhibits REE contents (mean: 83 ppm) and Y/Ho ratios (mean: 33) comparable to those of the ore-forming granites in the Zhuxi deposit. In contrast, the other three types display significantly lower REE contents and higher Y/Ho ratios, suggesting that the fluids responsible for type-I, −II, and −III scheelite crystallization underwent varying degrees of fluid evolution and interaction. Our systematic investigation of various occurrences of scheelite within the Zhuxi deposit reveals that the significant variations in composition of scheelites may be influenced by factors such as the assemblage of coexisting minerals, the host rock properties, and the intensity of fluid-rock interactions. [ABSTRACT FROM AUTHOR]

• Probability distributions of the generalized envelopes of normal machine vibration signals are established. • Typical sparsity measures of the generalized envelopes of normal machine vibration signals are theoretically calculated. • Sparsity measures of the generalized envelope of Gaussian noise are used as machine state baselines. • Sparsity measures of the generalized envelope are applied to machine condition monitoring. The establishment of probability distributions of machine vibration signals is crucial for calculating theoretical baselines of machine health indicators. Health indicators based on the envelope and squared envelope are an important family for condition monitoring. Under the assumption that the vibration signals of a good machine are Gaussian distributed, the envelope of a normal machine signal with zero mean is proven to follow a Rayleigh distribution with one parameter that depends on the noise variance, and its squared envelope follows an exponential distribution with one parameter, while the exact distribution parameter is undefined. The recently introduced log-envelope (i.e. the logarithm of the envelope) and generalized envelope (GE) exhibit attractive properties against interfering noise, however, their probability distributions have not yet been established. In this paper, the probability distributions of the squared envelope, log-squared envelope (i.e. the logarithm of the squared envelope), log-envelope and GE with parameter greater than 0 of Gaussian noise and corresponding distribution parameters are derived and established theoretically, and the important characteristic that their distribution parameters vary with the noise variance is clarified. On this basis, typical sparsity measures of GE of Gaussian noise are theoretically calculated, including kurtosis, skewness, Li / Lj norm, Hoyer measure, modified smoothness index, negentropy, Gini index, Gini index Ⅱ and Gini index Ⅲ. These typical sparsity measures of GE with parameter greater than 0 of Gaussian noise and the skewness and kurtosis of the log-envelope of Gaussian noise are proven to be independent of the noise variance, which enables them to serve as baselines for machine condition monitoring. Numerical simulations verify the correctness of the probability distributions and theoretical values of typical sparsity measures of GE with different parameters of Gaussian noise. The analysis results of four bearing run-to-failure experiments verify the feasibility and effectiveness of the sparsity measure of Gaussian noise as a condition monitoring baseline and demonstrate the efficacy and performance of GE-based sparsity measures for machine condition monitoring. [ABSTRACT FROM AUTHOR]

Granites and rare metal pegmatites of the Mufushan granitic batholith form a continuous magmatic sequence linked by fractional crystallization. Tourmaline is present in muscovite leucogranites and all types of pegmatites, including highly evolved Li-rich pegmatites. We utilized major element, trace element and in-situ B isotope analyses of tourmaline to investigate the effects of magmatic fractional crystallization and magmatic volatile phase (MVP) exsolution on Li migration and exceptional Li enrichment. Eight types of tourmaline are identified across three rock units: (i) Isolated (Tur Ia) and nodular (Tur Ib) tourmaline within muscovite leucogranites; (ii) black tourmaline in veins and/or clusters (Tur IIa), as isolated crystals (Tur IIb) and in tourmaline-quartz segregations (Tur IIc) within Li-poor pegmatites; and (iii) tourmaline as isolated pink crystals with zoning patterns (Tur IIIa), as isolated pink crystals and/or radiating clusters (Tur IIIb), and as isolated crystals enclosed in quartz block (Tur IIIc) within Li-rich pegmatites. Tourmaline in Mufushan muscovite leucogranites and Li-poor pegmatites belongs to the alkali-group and schorl series with Mg/(Mg + Fe) ratios of 0.10–0.31 and 0.12–0.48, respectively, containing almost no Li* and F (apfu, based on X + Y + Z = 15). In contrast, tourmaline in Li-rich pegmatites exhibits schorl-elbaite and elbaite-rossmanite compositions with low Mg/(Mg + Fe) ratio (avg. = 0.01), and evolved Li* (0.01–0.90 apfu, avg. = 0.41 apfu) and F (0.00–0.91 apfu, avg. = 0.36 apfu) contents. A pronounced increase in YAl, (Li* + Mn) contents, and Y[Al/(Al + Fe)] ratio is observed across the transition from Li-poor to Li-rich pegmatites, consistent with the anticipated pattern of fractional crystallization. The concentration of Li exhibits a sharp increase in Li-rich pegmatites (avg. Li = 6786 ppm) compared to Li-poor pegmatites (avg. Li = 114 ppm) and leucogranites (avg. Li = 469 ppm). Lithium contents increase and reach a peak during the crystallization of Tur IIIb (6686–11,667 ppm), and have lower peak contents during the precipitation of Tur IIIc (8261–9160 ppm), indicating that the incorporation of Li is influenced by MVP accumulation and exsolution. MVP exsolution significantly reduces the solubility of Nb, Ta, and Be in the residual melt, promoting the precipitation of beryl and columbite group minerals and facilitating the migration of fluid-mobile elements such as Li, Rb, Cs, and Ga to form lepidolite. The B isotope compositions of tourmaline range from −14.8 ‰ ∼ −12.6 ‰ in Li-poor pegmatites to −17.1 ‰ ∼ −14.0 ‰ in Li-rich pegmatites. Rayleigh fractionation modeling reveals that MVP saturation occurs after approximately 60 % B was removed from the pegmatite melt. The compositional variation of tourmaline demonstrates that Li enrichment is not only governed by continuous fractional crystallization, but also by MVP-related accumulation and exsolution mechanism. • Tourmaline chemistry traces magma development in leucogranites and pegmatites. • Magma volatile phases (MVP) control Li exceptional enrichment. • Tourmaline can be used as a tracer for Li mineralization in rare metal pegmatites. [ABSTRACT FROM AUTHOR]

[Display omitted] • The δ66Zn values of sphalerite at Caixiashan increase from south to north. • The increase in δ66Zn values may indicate the pathway of fluid flow outward. • The remobilization of Zn from Precambrian basement rocks generates the Caixiashan deposit. The ore-forming fluids responsible for the formation of distal carbonate replacement Pb–Zn deposits have the capacity to migrate over considerable distances. Pinpointing the source of metals and tracing fluid flow pathways for such distal mineralization can, therefore, be challenging. Zinc isotopes can serve as a tool to assess these ambiguities since different fluid reservoirs are characterized by distinct Zn isotopic compositions and metal precipitation processes cause systematic changes to Zn isotope ratios. In this contribution, we utilize newly acquired Zn isotopic data of the large Caixiashan distal carbonate replacement Pb–Zn deposit (131 million tons of ore at 3.95 wt% Pb + Zn) in the Eastern Tianshan to investigate the source of metals and fluid flow pathways. The δ66Zn values of sphalerite from the four ore zones (i.e., ore zones Ⅰ, Ⅱ, Ⅲ, and Ⅳ) range from −0.04 to 0.18 ‰, −0.04 to 0.07 ‰, −0.42 to −0.32 ‰ and −0.39 to 0.07 ‰, respectively. The average δ66Zn values of the sphalerite samples from the four ore zones increase systematically from south to north, specifically from the zones III to II and IV to I. The felsic intrusions and barren country rocks have δ66Zn values ranging from –0.11 to –0.06 ‰ and –0.32 to –0.02 ‰, respectively. The Zn isotopic ratios of sphalerite are positively correlated with Zn/Cd ratios, demonstrating that the δ66Zn values of sphalerite shift towards heavier values as the hydrothermal fluid from which they precipitated evolved. This systematic increase in δ66Zn values with fluid evolution resulted from continued precipitation of sphalerite, which is typically isotopically light. Based on Rayleigh distillation modeling, sphalerite with δ66Zn values as light as –0.48 ‰ would have required that the initial ore-forming fluid had δ66Zn values of about –0.2 ‰. A fluid with this isotopic composition could not have exsolved from the Carboniferous felsic intrusions, and is more likely to have been derived from remobilization of earlier Zn-rich Precambrian basement. This contribution highlights that the formation of large Pb–Zn deposits, such as Caixiashan, may depend on the remobilization of previously precipitated Zn. [ABSTRACT FROM AUTHOR]