A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper ...A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.展开更多
A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu...A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.展开更多
This paper presents a new inductive learning algorithm, HGR (Version 2.0), based on the newly-developed extension matrix theory. The basic idea is to partition the positive examples of a specific class in a given exam...This paper presents a new inductive learning algorithm, HGR (Version 2.0), based on the newly-developed extension matrix theory. The basic idea is to partition the positive examples of a specific class in a given example set into consistent groups, and each group corresponds to a consistent rule which covers all the examples in this group and none of the negative examples. Then a performance comparison of the HGR algorithm with other inductive algorithms, such as C4.5, OC1, HCV and SVM, is given in the paper. The authors not only selected 15 databases from the famous UCI machine learning repository, but also considered a real world problem. Experimental results show that their method achieves higher accuracy and fewer rules as compared with other algorithms.展开更多
This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.
The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the co...The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.展开更多
Machine learning(ML)is a major subfield of artificial intelligence(AI).It has been seen as a feasi- ble way of avoiding the knowledge bottleneck problem in knowledge-based systems development.Re- search on ML has conc...Machine learning(ML)is a major subfield of artificial intelligence(AI).It has been seen as a feasi- ble way of avoiding the knowledge bottleneck problem in knowledge-based systems development.Re- search on ML has concentrated in the main on inductive learning,a paradigm for inducing rules from unordered sets of exmaples.AQ11 and ID3,the two most widespread algorithms in ML,are both induc- tive.This paper first summarizes AQ11,ID3 and the newly-developed extension matrix approach based HCV algorithm;and then reviews the recent development of inductive learing and automatic knowledge acquisition from data bases.展开更多
基金The NSF(11471108) of Chinathe NSF(2015JJ2051,2016JJ2050) of Hunan Provincethe Teaching Reform Foundation(G21316) of Hunan Province
文摘A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.
基金Foundation items:The National Natural Science Foundation of China (No.10571026)the Specialized Research Fund for the Doctoral Program ofHigher Education (No.20060286006)
文摘A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.
文摘This paper presents a new inductive learning algorithm, HGR (Version 2.0), based on the newly-developed extension matrix theory. The basic idea is to partition the positive examples of a specific class in a given example set into consistent groups, and each group corresponds to a consistent rule which covers all the examples in this group and none of the negative examples. Then a performance comparison of the HGR algorithm with other inductive algorithms, such as C4.5, OC1, HCV and SVM, is given in the paper. The authors not only selected 15 databases from the famous UCI machine learning repository, but also considered a real world problem. Experimental results show that their method achieves higher accuracy and fewer rules as compared with other algorithms.
基金supported in part Professor Yuesheng Xu under the program of"One Hundred Outstanding Young Chinese Scientists" of the Chinese Academy of Sciencesthe Graduate Innovation Foundation of the Chinese Academy of Sciences
文摘This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.
基金The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P.1/85/42.
文摘The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.
基金National Natural Science Foundation of Chian(No.60272042)Natural Science Foundation of Henan Province(No.211050300)Natural Science Foundation of Henan University(No.XK01069)
文摘In this paper, we give a survey of matrix approach in wavelet theory , and describe some related results which were obtained by ourselves.
文摘Machine learning(ML)is a major subfield of artificial intelligence(AI).It has been seen as a feasi- ble way of avoiding the knowledge bottleneck problem in knowledge-based systems development.Re- search on ML has concentrated in the main on inductive learning,a paradigm for inducing rules from unordered sets of exmaples.AQ11 and ID3,the two most widespread algorithms in ML,are both induc- tive.This paper first summarizes AQ11,ID3 and the newly-developed extension matrix approach based HCV algorithm;and then reviews the recent development of inductive learing and automatic knowledge acquisition from data bases.
