Global asymptotic stability of a higher order rational difference equation

In this note, we consider the following rational difference equation:

     

A simple equilibrium model for shallow-cumulus-topped mixed layers

A new equilibrium model for shallow-cumulus-topped mixed layers is presented. A variant on the w _* closure for the shallow-cumulus mass flux is applied that retains the convective area-fraction in its formulation. As opposed to being constant, the fraction is explicitly modeled using a statistical closure as a function of the saturation deficit and humidity variance at cloud base. As a consequence, important new interactions are introduced between the convective transport, humidity, and depth of the mixed layer. This mechanism, which we call the mass-flux humidity feedback, helps determine the character of the equilibrium state such that the mixed-layer top is maintained close to the cloud-base height. Due to the strong sensitivity of the mass flux to the area fraction, the latter thus acts as a regulator or valve mechanism on moist convective transport. As a consequence, the mixed-layer model is able to explain the robustness of many aspects of the shallow-cumulus boundary layer that is typically found in observations and large-eddy simulations (LESs). The model is evaluated for a single-LES case as well as for global climatology obtained from a 40-year reanalysis of meteorological data by the European Centre for Medium-range Weather Forecasts (ECMWF). LES characteristics of convective mass flux, cloud fraction, humidity variance, cloud-base height, and surface fluxes of heat and humidity are reproduced. The solution on reanalysis fields reproduces the spatial structure of mixed-layer temperature and humidity and their associated surface fluxes in the subtropical Atlantic and Pacific trade wind regions. Furthermore, the spatial structure of the convective area-fraction matches that of synoptic surface observations of frequency of occurrence of shallow cumulus. Particularly striking is the smooth onset of the convective area-fraction and mass flux along the trade-wind trajectory that is reproduced, from zero to typical trade-wind values. The cumulus onset represents the necessity for shallow-cumulus mass flux to occur in order to close the mixed-layer budgets of heat, moisture, and mass, as a response to the changing magnitude of large-scale subsidence and free tropospheric humidity along the trajectory. Finally, the mass flux model is implemented in an intermediate-complexity tropical climate model to study its behavior when fully interactive with the larger-scale flow. A climate run then shows that the model is stable, due to the mass-flux humidity feedback acting to keep the shallow-cumulus boundary layer close to its equilibrium state for long, climatological timescales.     

Removal of reactive dye brilliant red HE-3B from aqueous solutions by hydrolyzed polyacrylonitrile fibres: equilibrium and kinetics modelling

A cheap and efficient fibrous hydrolyzed polyacrylonitrile (HPAN) sorbent was obtained by alkaline hydrolysis of Romanian polyacrylonitrile fibres. Scanning electronic microscopy and infrared spectroscopy were used to characterize the hydrolyzed product and to confirm its functionalization. The adsorptive potential of the proposed sorbent for reactive dye Brilliant Red HE-3B removal from aqueous solutions of pH=2 was examined by the batch technique as a function of dye concentration, temperature solution and contact time. The Freundlich, Langmuir and Dubinin-Radushkevich adsorption models were applied to describe equilibrium sorption data and to determine the corresponding isotherm constants. The thermodynamic parameters ΔG, ΔH and ΔS were also determined; the values obtained show that sorption of reactive dye on HPAN fibres is a spontaneous, endothermic and entropy-driven process. The kinetics of sorption of the reactive dye were analyzed using pseudo-first order and pseudo-second order kinetic models. The kinetic data fitted well to pseudo-second order kinetics, indicating the chemisorption of reactive dye onto the fibrous sorbent. The sorption mechanism of the dye onto hydrolyzed fibres was confirmed by FTIR spectroscopy. The dye-loaded HPAN sorbent can be regenerated by treatment with 0.1M NaOH and the regenerated sorbent may be reused in several adsorption-desorption cycles. The results of this study provided evidence that the HPAN fibres are effective for removing reactive dye Brilliant Red HE-3B from aqueous effluents.      

Vehicular motion in 2D city traffic network with signals controlled by phase shift

We study the dynamic behavior of vehicular traffic through the series of traffic lights controlled by phase shift in two-dimensional (2D) city traffic network. The nonlinear-map model is presented for the vehicular traffic. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. There are two traffic lights for the movement to north or that to east at each crossing. The traffic lights are controlled by the cycle time, split, and phase shift. The vehicle moves through the series of signals on a path selected by the driver. The city traffic with a heterogeneous density distribution is also studied. The dependence of the arrival time on cycle time, split, phase shift, selected path, and density is clarified for 2D city traffic. It is shown that the vehicular traffic is efficiently controlled by the phase shift.     

Topological vector spaces admissible in economic equilibrium theory

In models of economic equilibrium in markets with infinitely many commodities, the commodity space is an ordered topological vector space endowed with additional structure. In the present paper, we consider ordered topological vector spaces which are admissible (for equilibrium analysis) in the sense that every economy which is reasonably well behaved posesses an equilibrium. It turns out that this condition may be characterized in terms of topology and order. This characterization implies that the commodity space has the structure of a Kakutani space.     

广生马灭马氏链（Ⅱ）

本文在文献[1]的基础上继续讨论了广生灭马氏链,求出了向下的首达时间分布及各级矩,给出了广生灭马氏链遍历的充分必要条件以及平均反回时间的计算公式,并且在遍历的条件下,求出了其平稳分布。     

微波暗室辐射问题的动态平衡解法

利用动态平衡原理,给出了一种微波暗室辐射问题的求解方法,并进行了计算机迭代仿真,证明了该方法的可行性.     

假期中顾客以概率p进入的单重休假M/G/1排队

本文考虑单重休假M/G/1排队系统,其中在服务员休假中到达的顾客以概率p(0≤p≤1)进入系统,采用一种较简单的分析方法,得到了队长瞬态分布的拉普拉斯变换的递推表达式和稳态分布的递推表达式.另外,通过本文的研究直接导出了一些特殊情况下的相应结果.     

On general hemiequilibrium problems

In this paper, we introduce and analyze a new class of equilibrium problems known as general hemiequilibrium problems. It is shown that this class includes hemiequilibrium problems, hemivariational inequalities and complementarity problems as special cases. We use the auxiliary principle techniques to suggest some iterative-type methods for solving multivalued hemiequilibrium problems. We also analyze the convergence analysis of these new iterative methods under some mild conditions. As special cases, we obtain several new and known methods for solving variational inequalities and equilibrium problems.     

Impact of some parameters on investments in oligopolistic electricity markets

It is seldom the case that one has the opportunity to compare investments as projected by a long-term multi-period model to what is eventually realized in practice. Further, although sensitivity analysis is of common use in any optimization setting, the impact of some parameters on strategic investments is not yet fully assessed in the context of the deregulated electricity industry. Starting with a benchmark model of the Finnish industry, we precisely explore the impact on equilibrium investments of varying such parameters as direct- and cross-price elasticities, length of the planning horizon and the depreciation rate of capacity. We run the model with different parameter values and compare the predicted equilibrium with what companies have actually done. The model is a stochastic dynamic game involving three players and played over a ten-year period.Our results show the depreciation rate and the planning horizon have a notable effect on investment levels, whereas price elasticities seem to play a lesser role. Although the model’s results are rather well aligned to total industry investments, it diverges from individual levels. This may be due to the cost parameter used and/or to the open-loop information structure adopted in the computations. In any event, these results should be of methodological and practical interest to scholars and practitioners involved in strategic investment in the electricity industry.