In the spirit of a publication by Cheung in 2013 we study generalized Gerber-Shiu functions in the compound Poisson risk model perturbed by diffusion. These generalized Gerber-Shiu functions can be used to analyze the moments of the total discounted claim costs until ruin. Integral equations for the generalized Gerber-Shiu functions are derived and a solution procedure is also provided. Some explicit results are given when the claim size density is a combination of exponentials, and some numerical results are also given.

Hexagonal boron nitride (h‐BN) exhibits great potential for tribological applications due to its attractive 2D layered structure. In this work, functionalised hexagonal boron nitride (f‐BN) was prepared by ultrasonic exfoliation of pristine h‐BN in water and subsequent hydrothermal modification with sodium oleat. Fourier infrared spectra and X‐ray photoelectron spectra analyses showed that long alkyl‐chains were successfully grafted on the surface of f‐BN by modification process. The tribological properties of the as‐prepared f‐BN as lubricant additive in poly‐alpha‐olefin 10 (PAO10) for lubricating MoN coating sliding against Si3N4 ball were evaluated by a ball‐on‐disc friction tester. The friction coefficient and wear rate of the oil dispersed with 2 mg/mL f‐BN was respectively reduced by 42% and 29% in comparison with the pure PAO10 oil, suggesting that f‐BN was an effective lubricating additive for reducing friction and wear. Finally, the lubricating mechanism of f‐BN dispersed in PAO10 was discussed and proposed.

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We introduce the weighted mixed almost unbiased ridge estimator (WMAURE) based on the weighted mixed estimator (WME) (Trenkler and Toutenburg 1990) and the almost unbiased ridge estimator (AURE) (Akdeniz and Erol 2003) in linear regression model. We discuss superiorities of the new estimator under the quadratic bias (QB) and the mean square error matrix (MSEM) criteria. Additionally, we give a method about how to obtain the optimal values of parameterskandw. Finally, theoretical results are illustrated by a real data example and a Monte Carlo study.

In this paper, we consider a perturbed compound Poisson model with varying premium rates. The surplus process is observed at a sequence of review times. The effective premium rate is adjusted according to the surplus increment between the inter-review times. We study the Gerber-Shiu functions by Laplace transform method. When the claim size density is a combination of exponentials, the explicit expressions for the Laplace transforms of ruin time are derived.