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...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.展开更多
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 an...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.展开更多
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 ...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.展开更多
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...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.展开更多
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 propert...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.展开更多
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 s...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.展开更多
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.
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 fre...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.展开更多
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..
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.
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 ...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.展开更多
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 li...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.展开更多
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...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.展开更多
基金supported by Shanghai Center for Mathematical Sci-ences,China Scholarship Council(201206105015)National Science Foundation of China(11171119,11001057,11571049)Natural Science Foundation of Guangdong Province in China(2014A030313422)
文摘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.
文摘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.
基金This project was surpported by the Natural Science Foundation of Shandong Province of China (Y2004A94)
文摘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.
基金This project was supported by Natural Science Foundation of Shandong Province of China (Y2004A04), Natural ScienceFoundation of Fujian of China (Z051049) and Education Foundation of Fujian of China (JA04268),.
文摘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.
基金supported by the National Natural Science Foundation of China (60364001,70461001)the Hainan Provincial Natural Science Foundation of China (807054)Hainan Provincial Education Office Foundation (HJ 2008-56)
文摘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.
基金This work was supported by the National Natural Science Foundation of China(11771090,11901311)Natural Sciences Foundation of Shanghai(17ZR1402900).
文摘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.
基金Supported by the National Natural Science Foundation of China (10571035)
文摘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.
基金Supported by National Natural Science Foundation of China( 60672072 60832003)Zhejiang Provincial Natural Science Foundation of China(Y106505)
文摘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.
文摘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..
基金supported by the National Natural Science Foundation of China(11571049,11101048)
文摘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.
基金supported by the National Natural Science Foundation of China (60364001, 70461004)the Hainan Provincial Natural Science Foundation of China (807054)Hainan Provincial Eduction Office Foundation (HJ2008-56).
文摘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.
基金supported by the National Natural Science Foundation of China(12171050,12071047)the Fundamental Research Funds for the Central Universities(500421126)。
文摘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.
基金This project was supported by the Natural Science Foundation of Shandong Province of China (Y2004A04)the Natural Science Foundation of Fujian Province of China (A0410026).
文摘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.