LIMITING DIRECTIONS OF JULIA SETS OF ENTIRE SOLUTIONS TO COMPLEX DIFFERENTIAL EQUATIONS

In this paper,we mainly investigate the dynamical properties of entire solutions of complex differential equations.With some conditions on coefficients,we prove that the set of common limiting directions of Julia sets of solutions,their derivatives and their primitives must have a definite range of measure.

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.

Function S-Rough sets and its applications

Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

S-rough sets and the discovery of F-hiding knowledge

Singular rough sets （S-rough sets） have three classes of forms： one-directional S-rough sets, dual of onedirectional S-rough sets, and two-directional S-rough sets. Dynamic, hereditary, mnemonic, and hiding properties are the basic characteristics of S-rough sets. By using the S-rough sets, the concepts of f-hiding knowledge, F-hiding knowledge, hiding degree, and hiding dependence degree are given. Then, both the hiding theorem and the hiding dependence theorem of hiding knowledge are proposed. Finally, an application of hiding knowledge is discussed.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

Function S-rough sets and two law forecast

Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough sets namely the two law forecast model is proposed, which includes upper law forecast model and lower law forecast model; and its＇ implement algorithm is given. Finally, the validity of the model is demonstrated by the forecast for region economic development of Hainan Province.

Optimality for Henig Proper Efficiency in Vector Optimization Involving Dini Set-Valued Directional Derivatives

This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.

A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS

Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related limiting directions is verified.

基于Vague Sets-topsis理论的爆破方案优选

为了解决复杂框架结构楼房爆破拆除过程中如何选择爆破方案的技术难题,建立改进的Vague Sets-topsis综合评价指标模型,对爆破方案进行优选。首先对爆破方案中的关键参数建立评审指标集;然后利用逼近理想解的排序法,计算出各个方案的综合优越度,从而确定各个爆破方案的优劣;最后以铁四院前大楼爆破为例,采用改进的Vague Sets-topsis理论模型对"内向折叠爆破"(S1)、"双向折叠爆破"(S2)和"单向折叠双切口爆破"(S3)等不同方案的关键参数进行综合对比分析,得到方案的最优排序为:S3>S2>S1。实际爆破拆除实例表明:S3拆除效果良好,证明采用改进的Vague Sets-topsis理论模型可以用于复杂框架结构楼房控制爆破拆除优选。

JULIA LIMITING DIRECTIONS OF ENTIRE SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS

For entire or meromorphic function f,a value θ∈[0,2π)is called a Julia limiting direction if there is an unbounded sequence{z_(n)}in the Julia set satisfying limn→∞ arg z_(n)=θ.Our main result is on the entire solution f of P(z,f)+F(z)f^(s)=0,where P(z,f)is a differential polynomial of f with entire coefficients of growth smaller than that of the entire transcendental F,with the integer s being no more than the minimum degree of all differential monomials in P(z,f). We observe that Julia limiting directions of f partly come from the directions in which F grows quickly.

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.

Image Filter for Removal of Impulse Noise Based on Directional Derivatives

One of the most common image processing tasks involves the removal of noise from images. Noise can be introduced during image capture, during transmission, or during storage. For design purposes, noise sources are frequently approximated by random variables with a known probability distribution. One common noise model corrupts a signal by introducing impulses. And the surface of the image disturbed by impulse noise displays many peaks or vales. According to the characteristic of impulse noise, a novel algorithm is proposed to the detection of impulse noise point from images based on directional derivatives. First, the theory of calculus on directional derivatives is introduced in detail. Then it is applied to the field of image to removing noise with the discrete form derived from its continuous mathematical model. And a number of contrasting simulations illustrate that our algorithm not only can preserve the structure information while removing impulse noise but also can mostly save the gray value of the pixels undisturbed by noise. In addition, the comparisons of the filtering performance for removing impulse noise are analyzed in detail in the case of different noise densities, and also show that the algorithm suggested outperforms the conventional filter algorithms such as mean filter, median filter and so on in speed and impulse noise reduction, especially in random-valued impulse noise reduction. So it is a very good alternative to the existing schemes.

A NOTE ON q-DIFFERENCE OPERATOR AND RELATED LIMIT DIRECTION

The growth of entire functions under the q-difference operators is studied inthis paper, and then some properties of Julia set of entire functions under the higher orderq-difference operators are obtained.

On Limiting Directions of Julia Sets of Entire Solutions of Complex Differential Equations

Assume that f is a transcendental entire function.The ray arg z=θ∈[0,2π]is said to be a limiting direction of the Julia set J(f)of f if there exists an unbounded sequence{z_(n)}■J(f)such that lim rn→∞ arg z_(n)=θ.In this paper,we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations F(z)f^(n)(z)+P(z,f)=0,and f^(n)+A(z)P(z,f)=h(z),where P(z,f)is a differential polynomial in f and its derivatives,F(z),A(z)and h(z)are entire functions.We demonstrate the existence of close relationships Petrenko's deviations of the coefficients and the measures of limiting directions of entire solutions of the above two equations.

Designing a Protection Scheme in Micro-Grid Systems with DG Using Central Protection Unite and Multiple Setting Group Protection Relays

Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this continuous changes in generation condition, the fault current level in network will be affected, this changes in fault current level will affect in the coordination between protection relays and to keep the coordination at right way, an adaptive protection system is required that can adaptive its setting according to generation changes, the fault current level in each case is evaluated using ETAP software, and the required relay setting in each case is also evaluated using Grey Wolf Optimizer (GWO) algorithm, and to select suitable setting which required in each condition, to select the active setting group of protection relay according to generation capacity, central protection unite can be used, and to improve protection stability and minimizing relays tripping time, a proposed method for selecting suitable backup relay is used, which leads to decrease relays tripping time and increase system stability, output settings for relays in all cases achieved our constrains.

TABLE BASED METHOD FOR COMPETENCE SET EXPANSION

Each directed graph with the asymmetric costs defined over its arcs,can be represented by a table,which we call an expansion table.The basic properties of cycles and spanning tables of the expansion table corresponding to the cycles and spanning trees of the directed graph is first explored.An algorithm is then derived to find a minimum spanning table corresponding to a minimum spanning tree in the directed graph.Finally,how to use the algorithm to find the optimal expansion of competence set and related problems are discussed.

Directional Derivative and Subgradient of Cone-Convex Set-Valued Mappings with Applications in Set Optimization Problems

In this paper,we introduce a new directional derivative and subgradient of set-valued mappings by using a nonlinear scalarizing function.We obtain some properties of directional derivative and subgradient for cone-convex set-valued mappings.As applications,we present necessary and sufficient optimality conditions for set optimization problems and show that the local weak l-minimal solutions of set optimization problems are the global weak l-minimal solutions of set optimization problems under the assumption that the objective mapping is cone-convex.

S-Rough communication and its characteristics

In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication model. S-rough communication has two kinds of forms： one-direction S-rough communication and two-direction S-rough communication. The mathematical structure and characteristics of the one-direction S-rough communication and the two-direction S-rough communication, the relationship theorem between the one-direction S-rough communication and the two-direction S-rough communication are also presented. The S-rough communication is a dynamic communication method, and it is a novel research direction in rough sets field.

Model Predictive Control-Based Direct Torque Control for Matrix Converter-Fed Induction Motor with Reduced Torque Ripple

To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed in this paper.Two new look-up tables are proposed,these are derived on the basis of the control of the electromagnetic torque and stator flux using all the feasible voltage vectors and their associated switching states.Finite control set model predictive control(FCS-MPC)has then been adopted to select the optimal switching state that minimizes the cost function related to the electromagnetic torque.Finally,the experimental results are shown to verify the reduced torque ripple performance of the proposed MPC-based DTC method.