An optimal perturbation bound

Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.     

Censored lifetime learning: Optimal Bayesian age-replacement policies

We consider a sequence of age-replacement problems with a general lifetime distribution parametrized by an a-priori unknown parameter. There is a trade-off: Preventive replacements are censored but cheap, whereas corrective replacements are uncensored but costly observations of the lifetime distribution. We first analyze the optimal policy for a finite sequence and establish some properties. We then propose a myopic Bayesian policy that almost surely learns the unknown parameter and converges to the optimal policy with full knowledge of the parameter.     

基于拟相对内部集值优化问题弱有效元的最优性条件

本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.     

An approach for solving a fuzzy multiobjective programming problem

In this paper we present a new approach, based on the Nearest Interval Approximation Operator, for dealing with a multiobjective programming problem with fuzzy-valued objective functions.     

Pareto-optimal reinsurance arrangements under general model settings

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts.     

A self‐adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application

The self‐adaptive intelligence gray predictive model (SAIGM) has an alterable‐flexible model structure, and it can build a dynamic structure to fit different external environments by adjusting the parameter values of SAIGM. However, the order number of the raw SAIGM model is not optimal, which is an integer. For this, a new SAIGM model with the fractional order accumulating operator (SAIGM_FO) was proposed in this paper. Specifically, the final restored expression of SAIGM_FO was deduced in detail, and the parameter estimation method of SAIGM_FO was studied. After that, the Particle Swarm Optimization algorithm was used to optimize the order number of SAIGM_FO, and some steps were provided. Finally, the SAIGM_FO model was applied to simulate China's electricity consumption from 2001 to 2008 and forecast it during 2009 to 2015, and the mean relative simulation and prediction percentage errors of the new model were only 0.860% and 2.661%, in comparison with the ones obtained from the raw SAIGM model, the GM(1, 1) model with the optimal fractional order accumulating operator and the GM(1, 1) model, which were (1.201%, 5.321%), (1.356%, 3.324%), and (2.013%, 23.944%), respectively. The findings showed both the simulation and the prediction performance of the proposed SAIGM_FO model were the best among the 4 models.     

Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex.     

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In this paper, the empirical Bayes (EB) two-sided test for parameter of Cox models is investigated under square loss functions. At first by using recursive kernel estimation of probability function the empirical Bayes two-sided test rule is constructed. It proves that the proposed empirical Bayes test rule is asymptotic optimal and convergence rates are obtained under suitable conditions. Finally an example of satisfying theorem conditions is given.     

基于改进的GM(1,1)-Markov链组合模型广东省单位GDP能耗预测

本文以灰色系统理论的GM(1,1)模型和随机过程理论的Markov链模型为基础构建了一个动态GM(1,1)-Markov链组合预测模型。该模型同时利用了GM(1,1)模型对序列趋势因素良好的拟合能力和Markov链模型对残差序列信息的提取能力。为进一步提高该模型的预测精度,用泰勒(Taylor)近似方法和新信息优先的思想对该模型进行了改进。最后,以1991-2014年广东省单位GDP能耗数据实证了该模型的预测效果。     

Effect of Filtrated Osmotic Solution Based on Concentrated Chokeberry Juice and Mint Extract on the Drying Kinetics,Energy Consumption and Physicochemical Properties of Dried Apples

Background: Filtration of osmotic solution affects selective penetration during osmotic dehydration (OD), and after drying is finished, this can influence the chemical composition of the material, which is also modified by OD. Methods: Osmotic dehydration was carried out in filtrated and non-filtrated concentrated chokeberry juice with the addition of mint infusion. Then, this underwent convective drying, vacuum-microwave drying and combined convective pre-drying, followed by vacuum-microwave finishing drying. Drying kinetics were presented and mathematical models were selected. The specific energy consumption for each drying method was calculated and the energy efficiency was determined. Results and Discussion: The study revealed that filtration of osmotic solution did not have significant effect on drying kinetics; however, it affected selective penetration during OD. The highest specific energy consumption was obtained for the samples treated by convective drying (CD) (around 170 kJ·g⁻¹ fresh weight (fw)) and the lowest for the samples treated by vacuum-microwave drying (VMD) (around 30 kJ·g⁻¹ fw), which is due to the differences in the time of drying and when these methods are applied. Conclusions: Filtration of the osmotic solution can be used to obtain the desired material after drying and the VMD method is the most appropriate considering both phenolic acid content and the energy aspect of drying.