Recently, the relevation transformation has received further attention from researchers, and some interesting results have been developed. It is well known that the active redundancy at component level results in a more reliable coherent system than that at system level. However, the lack of study of this problem with relevation redundancy prevents us from fully understanding such a generalization of the active redundancy. In this note we deal with relevation redundancy to coherent systems of homogeneous components. Typically, for a series system of independent components, we have proved that the lifetime of a system with relevation redundancy at component level is larger than that with relevation redundancy at system level in the sense of the usual stochastic order and the likelihood ratio order, respectively. For a coherent system with dependent components, we have developed a sufficient condition in terms of the domination function to the usual stochastic order between the system lifetime with redundancy at component level and that at system level.

In the literature on active redundancy allocation, the redundancy lifetimes are usually postulated to be independent of the component lifetimes for the sake of technical convenience. However, this unrealistic assumption leads to a risk of inaccurately evaluating system reliability, because it overlooks the statistical dependence of lifetimes due to common stresses. In this study, for k-out-of-n:F systems with component and redundancy lifetimes linked by the Archimedean copula, we show that (i) allocating more homogeneous redundancies to the less reliable components tends to produce a redundant system with stochastically larger lifetime, (ii) the reliability of the redundant system can be uniformly maximized through balancing the allocation of homogeneous redundancies in the context of homogeneous components, and (iii) allocating a more reliable matched redundancy to a less reliable component produces a more reliable system. These novel results on k-out-of-n:F systems in which component and redundancy lifetimes are statistically dependent are more applicable to the complicated engineering systems that arise in real practice. Some numerical examples are also presented to illustrate these findings.

The optimization of laser pulse shapes is of great importance and a major challenge for laser direct-drive implosions. In this paper, we propose an efficient intelligent method to perform laser pulse optimization via hydrodynamic simulations guided by the genetic algorithm and random forest algorithm. Compared to manual optimizations, the machine-learning guided method is able to efficiently improve the areal density by a factor of 63% and reduce the in-flight-aspect ratio by a factor of 30% at the same time. A relationship between the maximum areal density and ion temperature is also achieved by the analysis of the big simulation dataset. This design method has been successfully demonstrated by the 2021 summer double-cone ignition experiments conducted at the SG-II upgrade laser facility and has great prospects for the design of other inertial fusion experiments.

This paper investigates the shock-induced instability of the interfaces between gases and dense granular media with finite length via the coarse-grained compressible computational fluid dynamics–discrete parcel method. Despite generating a typical spike-bubble structure reminiscent of the Richtmyer–Meshkov instability (RMI), the shock-driven granular instability (SDGI) is governed by fundamentally different mechanisms. Unlike the RMI arising from baroclinic vorticity deposition on the interface, the SDGI is closely associated with the interfacial and bulk granular dynamics, which evolve with the transient coupling between particles and gases. Consequently, the SDGI follows a growth law distinctly different from that of the RMI, namely a semilinear slow regime followed by an exponentially expedited regime and a quadratic asymptotic regime. We further establish the instability criteria of the SDGI for granular media with infinite and finite lengths, which do not exist in the RMI. A scaling growth law of the SDGI for dense granular media with finite length is derived by normalizing the time with the rarefaction propagation time, which successfully collapses the data from cases with varying shock strength, particle column length and particle volume fraction and ought to hold for granular media with varying particle parameters. The effect of the initial perturbation magnitude can be properly considered in the scaling growth law by incorporating it into the length normalization.

We characterized the proteome profile of mid-lactation small-tailed Han (STH) and DairyMeade (DM) ovine milk in order to explore physiological variation and differences in milk traits between the two breeds. Methodology combined a tandem mass tag (TMT) proteomic approach with LC-MS/MS technology. A total of 656 proteins were identified in STH and DM ovine milk, of which 17and 29 proteins were significantly upregulated (P < 0.05) in STH and DM, respectively. Immune-related proteins and disease-related proteins were highly expressed in STH milk, whereas S100A2 and AEBP1 were highly expressed in DM milk, which had beneficial effects on mammary gland development and milk yield. Our results provide a theoretical basis for future breeding of dairy sheep.

We have previously bred Chinese local dairy sheep through grading up with local Small-Tailed Han (STH) sheep as female parent and DairyMeade (DM) sheep as male parent. In this research communication we characterize the whey protein profile of STH sheep and their offspring (F1, F2) to reveal physiological differences and variation in milk traits. A total of 1032 whey proteins were identified through tandem mass tag labeling (TMT) proteome profiling. Three proteins were significantly differentially abundant between F1 and STH milk, six between F2 and STH milk and five between F1 and F2 milk. In terms of differential changes between generations, WASHC4 and CUTA of F1 and Ig-like domain-containing protein of F2 milk were dominant whey proteins. Overall, the results showed that the whey protein profiles of different generations varied little. The crossbreeds of STH and DM sheep would be suitable for the development of the Chinese local sheep milk industry, and the F2 may be a better population for sheep milk production.

As the remnant of the South Qilian Ocean, the South Qilian suture zone recorded abundant information on the Cambrian–Ordovician subduction history of the southern branch of the Proto-Tethyan Ocean. However, the closure timing of the South Qilian Ocean and subsequent collision are poorly constrained. In this study, we report early Silurian (433–435 Ma) U–Pb ages of felsic subvolcanic rocks from Lianhuashan, Ayishan and Shihuiyao of the Lajishan district within the South Qilian suture zone. They intruded the Late Ordovician – Silurian sedimentary or Late Ordovician volcanic rocks and have high SiO2 (61.43–73.06 wt%), Sr/Y ratios with significant different rare earth elements (REEs) and trace-element spider diagrams, and Sr–Nd isotopic compositions, probably implying that they were formed through distinctly different generation mechanisms. Geochemistry of the Lianhuashan dacites reveals compositions typical of adakitic rocks derived from partial melting of lower crust in a thickened setting. The Ayishan dacites were derived from partial melting of crustal materials with the involvement of minor peridotite mantle, and the Shihuiyao rhyolites were derived from partial melting of felsic crust. The similar geochemical characteristics of coeval post-collisional igneous rocks in the Central Qilian and South Qilian blocks indicates that the lower Silurian subvolcanic rocks were generated in a thickened crust of post-collisional setting. Considering their intrusive contacts with Late Ordovician – Silurian retro-foreland basin and Late Ordovician collisional volcanic rocks, we propose that the South Qilian suture zone was at a transitional stage from collisional to post-collisional during the early Silurian Period.

This paper studies the allocation of active redundancies to coherent systems on the context that the base and redundancy components have mutual independent lifetimes. For systems with two symmetric components and systems with one component's minimal cut sets (minimal path sets) covering those of another, we derive sufficient conditions to compare the resultant system lifetimes. Some numerical examples are also presented to illustrate the theoretical results.

Sulphur isotopes can be used as a powerful tool to trace fluid evolution and explore the formation of chimneys. To clarify the in situ S isotopic variations of sulphides at the micro-scale, we analyzed a sulphide chimney collected from the hydrothermal field in the East Pacific Rise 1–2° S using a sensitive high-mass-resolution ion micro-probe for stable isotopes (SHRIMP SI). Three mineral zones can be identified in the chimney: an external outer wall of porous anhydrite and colloform pyrite, an internal middle zone of sub-euhedral pyrite and massive chalcopyrite, and an inner zone of massive pyrite. The δ34SV-CDT values of the sulphides fall within the range 1.83–7.51 ‰ (avg. 4.05 ‰, n = 16), and S isotopic values increase from the core (3.09 ‰, n = 3) to the middle (3.78 ‰, n = 11) to the edge (6.99 ‰, n = 2). These results illustrate mineral crystallization processes and the mixing between seawater-derived S and magmatic–hydrothermal fluids during the growth of the chimney. The zones from the edge to the core are characterized by crystal morphologies of colloform/anhedral pyrite to massive pyrite with decreasing δ34S values, revealing multi-stage mineral deposition and sulphur isotopic fractionation. In contrast to the increase in δ34S values from the core to the edge in one profile (profile A), anomalously low δ34S values in fine-grained pyrite relative to chalcopyrite in another profile (profile B) in the middle zone result from S isotopic exchange between seawater SO42− and fluid H2S due to different fluid–seawater mixing, possibly caused by variations in permeability and porosity across the chimney.

It is a common belief for actuaries that the heterogeneity of claim severities in a given insurance portfolio tends to increase its dangerousness, which results in requiring more capital for covering claims. This paper aims to investigate the effects of orderings and heterogeneity among scale parameters on the aggregate claim amount when both claim occurrence probabilities and claim severities are dependent. Under the assumption that the claim occurrence probabilities are left tail weakly stochastic arrangement increasing, the actuaries' belief is examined from two directions, i.e., claim severities are comonotonic or right tail weakly stochastic arrangement increasing. Numerical examples are provided to validate these theoretical findings. An application in assets allocation is addressed as well.

In this paper we study general aggregation of stochastic arrangement increasing random variables, including both the generalized linear combination and the standard aggregation as special cases. In terms of monotonicity, supermodularity, and convexity of the kernel function, we develop several sufficient conditions for the increasing convex order on the generalized aggregations. Some applications in reliability and risks are also presented.

For the weighted k-out-of-n system with statistically dependent component lifetimes, we have a discussion on the system performance through investigating the ordering properties of the total system weight with respect to component weight vector. Applications of the present ordering results to signature of coherent systems are presented as well.

In this paper we build the increasing convex (concave) order for the scalar product of random vectors with an upper (lower) tail permutation decreasing joint density. As applications, we revisit allocations of portfolio risks in financial engineering and of coverage limits and deductibles in insurance. Some related results in the literature are substantially updated.

In this paper we develop two permutation theorems on argument increasing functions of a multivariate random vector and a real parameter vector. We use the unified approach of our two theorems to provide some important theoretical results on the capital allocation in actuarial science, the deductible and upper limit allocations in insurance policy, and portfolio allocation in financial engineering. Our results successfully improve or extend the corresponding works in the literature.

This paper carries out stochastic comparisons of series and parallel systems with independent and heterogeneous components in the sense of the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. The main results extend and strengthen the corresponding ones by Misra and Misra [18] and by Ding, Zhang, and Zhao [8]. Meanwhile, the results on the hazard rate order of parallel systems and the reversed hazard order of series systems serve as nice supplements to Theorem 16.B.1 of Boland and Proschan [4] and Theorem 3.2 of Nanda and Shaked [20], respectively.

Balakrishnan and Zhao does an excellent job in this issue at reviewing the recent advances on stochastic comparison between order statistics from independent and heterogeneous observations with proportional hazard rates, gamma distribution, geometric distribution, and negative binomial distributions, the relation between various stochastic order and majorization order of concerned heterogeneous parameters is highlighted. Some examples are presented to illustrate main results while pointing out the potential direction for further discussion.

This paper builds a mixture representation of the reliability function of the conditional residual lifetime of a coherent system in terms of the reliability functions of conditional residual lifetimes of order statistics. Some stochastic ordering properties for the conditional residual lifetime of a coherent system with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors.

This note introduces bivariate dual generalized Marshall–Olkin distribution and builds a comparison result on the copula of this distribution. Several applications in survival analysis and actuarial science are presented as well.

Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16].