Construction of Dependence Structure for Rainfall Stations by Joining Time Series Models with Copula Method

Copula model has applied in various hydrologic studies, however, most analyses conducted does not considering the non-stationary conditions that may exist in the time series. To investigate the dependence structure between two rainfall stations at Johor Bahru, two methods have been applied. The first method considers the non-stationary condition that exists in the data, while the second method assumes stationarity in the time series data. Through goodness-off-fit (GOF) and simulation tests, performance of both methods are compared in this study. The results obtained in this study highlight the importance of considering non-stationarity conditions in the hydrological data.

On implicit variables in optimization theory

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming, evaluated multiobjective optimization, or nonlinear optimization problems with slack variables. In order to deal with implicit variables, they are often interpreted as explicit ones. Here, we first point out that this is a light-headed approach which induces artificial locally optimal solutions. Afterwards, we derive various Mordukhovich-stationarity-type necessary optimality conditions which correspond to treating the implicit variables as explicit ones on the one hand, or using them only implicitly to model the constraints on the other. A detailed comparison of the obtained stationarity conditions as well as the associated underlying constraint qualifications will be provided. Overall, we proceed in a fairly general setting relying on modern tools of variational analysis. Finally, we apply our findings to different well-known problem classes of mathematical optimization in order to visualize the obtained theory. Comment: 34 pages

Identification without assuming mean stationarity: Quasi ML estimation of dynamic panel models with endogenous regressors

Linear GMM estimators for dynamic panel models with predetermined or endogenous regressors suffer from a weak instruments problem when the data are highly persistent. In this paper we propose new random and fixed effects Limited Information Quasi ML estimators (LIQMLEs) for such models. We also discuss LIQMLEs for models that contain time-varying individual effects. Unlike System GMM estimators, the LIQMLEs do not require mean stationarity conditions for consistency. Such conditions often do not hold for the models we consider. Our LIQMLEs are based on a two-step control function approach that includes the first stage model residuals for a predetermined or endogenous regressor in the outcome equation. The LIMLEs are more precise than non-linear GMM estimators that are based on the original outcome equation. The LIQMLEs also compare favourably to various alternative (Q)MLEs in terms of precision, robustness and/or ease of computation.

Estimation of the annual runoff frequency distribution under a non-stationarity condition within the Budyko framework

<p>In the past decades, climate change has been leading to non-stationarity in hydrological variables. Therefore, a simple framework within the Budyko framework is proposed to estimate the annual runoff frequency distribution and provide a new method for hydrological design under non-stationarity conditions. In this framework, the mean and standard deviation of annual runoff are derived by the Choudhury-Yang equation. Furthermore, the P-Ш type frequency curve is selected to calculate the annual runoff on a design return period. Based on this framework, the change in water resources in 207 three-level basins across China during 2020-2050 are estimated according to the Coupled Model Inter-comparison Project Phase 5. The results show that the mean annual runoff will decrease by 2.7% for all basins, and the regional difference will decline, i.e., the mean annual runoff will increase in the north of China and decrease in the south of China. However, the inter-annual variability of annual runoff will increase in more than 70% of basins. Additionally, in the wet year, approximately half of the total basins show decreased runoff change, and in the dry year, decreased change appears in ~65% basins. These findings offer a simple and effective way to re-examine the effects of non-stationarity in hydrological design.</p>

Optimization of spacecraft pulsed flights trajectories with the stage discharge into the atmosphere and phase restriction

The paper considers the reducing of the near-Earth space debris due to the stages discharge into the Earth’s atmosphere, introduces the solution for optimizing the impulse transfer between the artificial Earth satellite reference circular orbit and the target elliptical orbit with a phase constraint on the maximum distance of the spacecraft from the Earth. A specially developed numerical-analytical differentiation technology allows us to calculate derivatives under the transversality of Lagrange principle. The paper proposes the transversality and stationarity conditions analysis, which results in the conclusion that the Beletsky — Egorov — Pines integral, and the Hamiltonian are continuous in the moments of all intermediate impulse actions application, including the stage discharge moments. The paper shows that the problem solution for various flight schemes coincides with a similar one without a priori assumption about the impulse effects apsidal nature.

Optimal Control of the Separation Process with Flow Restrictions

Here we formulate the problem of optimal process control with distributed parameters, taking into account the constraints on the control and associated flows. The necessary optimality conditions are obtained. The analysis of the stationarity conditions is carried out and the method for constructing the domain of admissible controls is proposed. The developed optimization method is applied in the automation of industrial distillation plants for the sulfuric acid alkylation of isobutane with butylenes, ortho-xylene production, etc.