Cp_(2)TiCl_(2) as a Lewis acid precursor and nicotinic acid as a ligand have been used synergistically for the one-pot synthesis of 2-(N-substituted amino)-1,4-naphthoquinones.This method establishes a general strateg...Cp_(2)TiCl_(2) as a Lewis acid precursor and nicotinic acid as a ligand have been used synergistically for the one-pot synthesis of 2-(N-substituted amino)-1,4-naphthoquinones.This method establishes a general strategy for the functionalization and conversion of C-H bonds of 1,4-naphthoquinones into C-N bonds,providing an effective route to synthesize 2-(N-substituted amino)-1,4-naphthoquinone with high yield under mild conditions.Additionally,the synergistic catalytic mechanism was investigated by 1H NMR titration experiments and LC-MS analysis,with experimental results sufficiently and consistently supporting the proposed mechanism of the catalytic cycle.展开更多
By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equ...By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.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
基金2024 Special Talent Introduction Projects of Key R&D Program of Ningxia Hui Autonomous Region(2024BEH04049)the 2024 Guyuan City Innovation-Driven Achievement Transformation Project(2024BGTYF01-47)2025 Ningxia Natural Science Foundation Program(2025AAC030624).
文摘Cp_(2)TiCl_(2) as a Lewis acid precursor and nicotinic acid as a ligand have been used synergistically for the one-pot synthesis of 2-(N-substituted amino)-1,4-naphthoquinones.This method establishes a general strategy for the functionalization and conversion of C-H bonds of 1,4-naphthoquinones into C-N bonds,providing an effective route to synthesize 2-(N-substituted amino)-1,4-naphthoquinone with high yield under mild conditions.Additionally,the synergistic catalytic mechanism was investigated by 1H NMR titration experiments and LC-MS analysis,with experimental results sufficiently and consistently supporting the proposed mechanism of the catalytic cycle.
基金State Natural Science Foundation (59879012) and Doctoral Foundation from State Education Commission (98024832).
文摘By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.
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.
