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In this paper, we consider some finite-time dividend and ruin problems in a class of risk models under the constant dividend barrier strategy. This class of risk models includes Brownian motion risk model and the compound Poisson model with and without diffusion. By using Laguerre series expansion, we derive infinite series expansion formulas for the time T-deferred Laplace transform of the ruin time and time T-deferred expected present valued of dividend payments until ruin. [ABSTRACT FROM AUTHOR]

Palm leaf manuscripts (PLMs) are of great importance in recording Buddhist Scriptures, medicine, history, philosophy, etc. Some damages occur during the use, spread, and preservation procedure. The comprehensive investigation of Sanskrit PLMs is a prerequisite for further conservation and restoration. However, current damage identification and investigation are carried out manually. They require strong professional skills and are extraordinarily time-consuming. In this study, PLM-SegFormer is developed to provide an automated damage segmentation for Sanskrit PLMs based on the SegFormer architecture. Firstly, a digital image dataset of Sanskrit PLMs (the PLM dataset) was obtained from the Potala Palace in Tibet. Then, the hyperparameters for pre-processing, model training, prediction, and post-processing phases were fully optimized to make the SegFormer model more suitable for the PLM damage segmentation task. The optimized segmentation model reaches 70.1% mHit and 51.2% mIoU. The proposed framework automates the damage segmentation of 10,064 folios of PLMs within 12 h. The PLM-SegFormer framework will facilitate the preservation state survey and record of the Palm-leaf manuscript and be of great value to the subsequent preservation and restoration. The source code is available at https://github.com/Ryan21wy/PLM_SegFormer. [ABSTRACT FROM AUTHOR]

In this paper, the microstructure evolution of as-cast and homogenized Mg-9Gd-4Y-2Zn-0.5Zr alloys during hot compression was studied by electron backscattered diffraction analysis. Specimens were compressed at 420 °C with reductions of 20, 40, and 70%. The results indicated that more recrystallized grains were obtained in the as-cast alloy, which was attributed to many block-shaped phase grains. Under the same conditions, the as-cast alloy had a finer microstructure and weaker texture. In the initial stage, dynamic recrystallization in the form of discontinuous dynamic recrystallization participated in deformation. Further deformation contributed to fine grains in the interior of deformed grains in the form of continuous dynamic recrystallization. Basal slip played an active part in the deformed grains, and the recrystallized grains activated pyramidal slip. [ABSTRACT FROM AUTHOR]

A fully discrete finite element method with a Gauss collocation in time is proposed for solving the nonlinear Schrödinger equation with a wave operator in the d-dimensional torus, d ∈ { 1 , 2 , 3 } . Based on Gauss collocation method in time and the scalar auxiliary variable technique, the proposed method preserves both mass and energy conservations at the discrete level. Existence and uniqueness of the numerical solutions to the nonlinear algebraic system, as well as convergence to the exact solution with order O (h p + τ k + 1) in the L ∞ (0 , T ; H 1) norm, are proved by using Schaefer’s fixed point theorem without requiring any grid-ratio conditions, where (p, k) is the degree of the space-time finite elements. The Newton iterative method is applied for solving the nonlinear algebraic system. The numerical results show that the proposed method preserves discrete mass and energy conservations up to machine precision, and requires only a few Newton iterations to achieve the desired accuracy, with optimal-order convergence in the L ∞ (0 , T ; H 1) norm. [ABSTRACT FROM AUTHOR]

To date, there has been ample work dedicated to understanding how framing typologies impact audiences. However, there has been rather little empirical evidence pertaining to the relationship between framing typologies and subsequent user engagement, specifically in regards to how frames impact how users engage with online content. The goal of the present study seeks to expand upon the existing literature, with a specific focus on some of the most prolific typologies used within the communication discipline. In an analysis of Facebook content produced by 239 Down syndrome nonprofits over the course of one year, we offer several findings regarding the relationship between the frames used within Facebook content and the subsequent user engagement that they received. Most notably, results indicate that Facebook posts that utilized elements of the human-interest frame were associated with higher user engagement. Further, despite existing literature indicating the contrary, there does not appear to be a statistically significant difference in user engagement between posts that utilized episodic as opposed to thematic framing. The results presented here offer recommendations for practitioners, marketing professionals, as well as individuals looking to grow their social media presence. [ABSTRACT FROM AUTHOR]

Microstructure evolution, phase development and mechanical property of AZ80 alloy cup with various processing temperatures (573 K, 613 K, 653 K) and rotating revolutions (N = 0, 5, 50, 100) during rotating backward extrusion (RBE) were explored. The study founded that reducing deformation temperature or increasing revolution could promote the grain refinement and DRX proportion. And the sample deformed at the condition of 573 K and N = 100 exhibited the best grain refinement effect (grain size was 2.5 μm, DRX ratio was up to 99.01%). The bulk eutectic phase existed at all deformation temperatures, while the dynamic precipitation was only precipitated at temperature of 573 K and 613 K. Increasing the deformation temperature or revolution could reduce the proportion of the second phase. And an increase in revolution or a reduction of temperature would reduce the average size of second phase, due to the phase could be broken by large strain and resolved with elevated temperature. Moreover, increasing the revolution and deformation temperature could promote the texture weakening, which would be contributed to the occurrence of new recrystallization grains with random orientation and the activation of non-basal slip system. The mechanical property of microhardness was significantly improved with rotating revolution increasing and deformation temperature decreasing. Supported by the grain refinement and dispersion strengthening, the sample deformed at condition of 573 K and N = 100 achieved maximum hardness values of 96.3 HV. [ABSTRACT FROM AUTHOR]