A proposed directional function and wind-wave directional spectrum

A directional function for frequencies equal to and larger than the peak frequency of a wind-wave frequency spectrum is constructed by fitting the angular spreading based on the analytically derived directional spectrum of Wen et al. (1993, Journal of Oceanography, 49(2), 131～147, 149～172). For frequencies smaller than the peak frequency, the directional function is obtained by comparing and analyzing existing formulas. The nondimensional wind-wave frequency spectrum of Wen et al. (1994, Progress in Natural Seience, 4(4). 407～427;4 (5), 586～596) has been used together with the directional function just mentioned to obtain the directional spectrum for easier application.

Robust H_∞ directional control for a sampled-data autonomous airship

A robust H∞ directional controller for a sampled-data autonomous airship with polytopic parameter uncertainties was proposed. By input delay approach, the linearized airship model was transformed into a continuous-time system with time-varying delay. Sufficient conditions were then established based on the constructed Lyapunov-Krasovskii functional, which guarantee that the system is mean-square exponentially stable with H∞ performance. The desired controller can be obtained by solving the obtained conditions. Simulation results show that guaranteed minimum H∞ performance γ=1.4037 and fast response of attitude for sampled-data autonomous airship are achieved in spite of the existence of parameter uncertainties.

ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS

In this paper, we prove that for an algebroid function w（z）, the singular direction argz = φ0, satisfying that for arbitrary ε（0 〈 ε 〈 2/π） and any given α ∈ C^^,limr→＋∞ log τ/n（τ,φ0-ε,φ0＋ε,w=a）=＋∞ holds with at most; 2v possible exceptional values of a, is the Ncvanlinna direction of w（z）.

Frame Work of Data Envelopment Analysis—A Model to Evaluate the Environmental Efficiency of China'S Industrial Sectors

Objective To evaluate the environmental and technical efficiencies of China＇s industrial sectors and provide appropriate advice for policy makers in the context of rapid economic growth and concurrent serious environmental damages caused by industrial pollutants. Methods A data of envelopment analysis （DEA） framework crediting both reduction of pollution outputs and expansion of good outputs was designed as a model to compute environmental efficiency of China＇s regional industrial systems. Results As shown by the geometric mean of environmental efficiency, if other inputs were made constant and good outputs were not to be improved, the air pollution outputs would have the potential to be decreased by about 60% in the whole China. Conclusion Both environmental and technical efficiencies have the potential to be greatly improved in China, which may provide some advice for policy-makers.

F-rough law and the discovery of rough law

By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.

F-Law collision and system state recognition

Using function one direction S-rough sets （function one direction singular rough sets）, f-law and F- law and the concept of law distance and the concept of system law collided by F-law are given. Using these concepts, state characteristic presented by system law collided by F-law and recognition of these states characteristic and recognition criterion and applications are given. Function one direction S-rough sets is one of basic forms of function S-rough sets （function singular rough sets）. Function one direction S-rough sets is importance theory and is a method in studying system law collision.

F-generation law and recognition of system law

If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.

Hiding dependence-discovery of F-hiding laws and system laws

Function one direction S-rough sets have dynamic characteristics and law characteristics. By using the function one direction S-rough sets, this article presents the concepts of the f-hiding law, F-hiding law, f-hiding law dependence and F-hiding law dependence. Based on the concepts above, this article proposes the hidingdependence theorem of f-hiding laws, the hiding-dependence theorem of F-hiding laws, the hiding-dependence separation theorem, the hiding dependence-discovery principle of unknown laws. Finally, the application of the hiding dependence of hiding laws in the discovery of system laws is given.

Numerical Simulation of 3-D Wave Crests

A clear definition of 3-D wave crest and a description of the procedures to detect the boundary of wave crest are presented in the paper. By using random wave theory and directional wave spectrum, a MATLAB-platformed program is designed to simulate random wave crests for various directional spectral conditions in deep water. Statistics of wave crests with different directional spreading parameters and different directional functions are obtained and discussed.

■-law collision and system state recognition

Using dual function one direction S-rough sets, this article gives the f-law, the F-law, law distance and the concept of system law collided by the F-law. The characteristics presented by the system law collided by the F-law, the recognition of these characteristics and recognition criterion are also proposed. The dual function one direction S-rough sets is one of the basic forms of function S-rough sets. Its basic theory and application in the study of system law collision are reviewed.

Statistics of Wave Crest Characteristics

The statistical distribution of wave crest characteristics such as crest length, crest height, joint crest height and length are analyzed based on numerical simulation of 3-D random waves. The effects of directional functions and wave crest defining methods on crest characteristics are also studied. The results show that wave crests are no longer uniform and continuous in directional wave field; the distribution of crest length is obviously influenced by the directional function; the statistics of crest characteristics obtained by the two different methods are almost the same.

Function S-rough Sets and Their Law Characteristic

Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.

Energy Efficiency and Emissions Reduction Potential of China's Industrial Sector

Based on the total-factor energy efficiency framework,this paper calculates China's industrial energy efficiency and CO2 emissions reduction potential from 2000 to 2009 by utilizing the directional distance function and data envelopment analysis.The empirical results show that:China's industrial overall energy efficiency is relatively lower while the emis-sions reduction potential is relatively greater,given the optimum production frontier.Significant indus-trial disparities of energy efficiency and emissions reduction potential exist.Energy efficiency and emis-sions reduction potential significantly show different tendencies of industrial dynamic variation.This paper suggests the Chinese government impose differential carbon taxes,flexibly utilize carbon market mecha-nism,strengthen energy-saving technological R&D,promote the utilization of renewable energy,and strengthen environmental supervision and regulation,so as to improve China's industrial energy efficiency and reduce CO2 emissions.

THE FEKETE-SZEG PROBLEM FOR CLOSE-TO-CONVEX FUNCTIONS WITH RESPECT TO THE KOEBE FUNCTION

An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.

An Empirical Study on Environmental Regulatory Costs &Environmental TFP

This paper examines the cost of environmental regulation and the environmental total factor productivity （TFP） with directional distance function and the Malmquist-Luenberger （ALL） index respectively, using inputs and output data of 36 two-digit industries over the period 1998- 2010. It finds that Chinese industries incur a relatively high environmental regulatory cost and that China has paid a high price fulfilling its promise to emissions mitigation. A comparison between conventional and environmental TFP shows that the two indicators for all industries declined on average, but a hypothesis test reveals insignificant difference between the two. In addition, the rise in environmental TFP is mainly due to technological progress, which is consistent with findings of many researches; analysis demonstrates signs of absolute convergence of environmental TFP.

Evolution of Word-updating Dynamical Systems (WDS) on Directed Graphs

This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential dynamical systems(SDS)on graphs.Some properties on WDS,especially some results on NOR-WDS,which are different from that on NOR-SDS,are obtained.

The Hiding Characteristic of F-interior Hiding Image and Its Applications

By using function one direction S-rough sets,the concept of F-interior hiding image is presented; the theorem of F-interior hiding and the recognition criteria of interior hiding are proposed; and the applications of F-interior hiding image are given. F-interior hiding image is a new application area of function S-rough sets,and function S-rough sets is a new theory and new tools for iconology research.

Star-shaped Differentiable Functions and Star-shaped Differentials

Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.

Operational and investment efficiency of investment trust companies:Do foreign firms outperform domestic firms?

This study examines the efficiency of investment trust companies(ITCs)from 2011 to 2020 using a meta-frontier two-stage network data envelopment analysis(DEA)based on the directional distance function(DDF).We improved the accuracy of the efficiency measurement and added a network-based ranking component to rank the topperforming entities.In the group-specific technology assessment,foreign ITCs excel in investment efficiency.Meanwhile,in the meta-technology assessment,domestic ITCs outperform foreign ITCs in terms of both investment and operational efficiencies.Group-specific technology efficiency scores were found to be lower than or equal to the meta-technology efficiency scores for both the operational and investment stages.Based on the network-based ranking approach,Yuan Ta,a domestic ITC that ranked fourth in the operational stage and first in the investment stage,can be used as a reliable benchmark.This study will enable practitioners to gain a better understanding of the performance of ITCs operating under heterogeneous technologies.

Re-measuring Productivity, Energy and Environmental Factors of China＇s New Industrialization

This paper identifies low-carbon, energy-efficient, and green economic growth as the primary goals of China＇s new industrialization and defines productivity under new industrialization which; unlike conventional productivity, simultaneously satisfies these goals. In contrast to conventional methods for measuring productivity, this paper employs a non-radial, non-angular SBM directional distance function to estimate new industrialization productivity of industrial sectors across 30 Chinese provinces, municipalities and autonomous regions between 1998 and 2008. Our research shows that conventional measurements of productivity overestimate industrial growth in China＇s central and western regions. On the whole, prospects for growth performance of China＇s industrial sectors are not optimistic. The degree of new industrialization is higher in eastern region than in central and western regions, where balancing industrial growth with resources and the environment is a daunting task. This paper＇s conclusions support ＂environmental Kuznets curve＂ and ＂Porter hypothesis＂ but reject ＂pollution asylum hypothesis ＂.