The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi...The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.展开更多
The network characteristic of the central neural system has been widely accepted as a basic fabric form. However,the matrix characteristics of neural network are still not fully understood. If we ignore the matrix cha...The network characteristic of the central neural system has been widely accepted as a basic fabric form. However,the matrix characteristics of neural network are still not fully understood. If we ignore the matrix characteristics of the neural networks and just pay close attention to its connection mode,we are likely to fall into the theory of mechanical reductionism. This can lead to a problem in representing consciousness in a disadvantageous situation. It can also be a barrier to further improving the global workspace theory. Incomplete elucidation of the mechanisms of consciousness representation can also affect the assessment of the surgical outcome of partial epilepsy with conscious injury. Therefore,this paper reviews the epistemological development of neuroscience. We will initially describe the matrix characteristics of the neural system and their significance to the information processing mechanism,and further explore the role of neural matrix in identifying cases of partial epilepsy with little effect on the resection of the lesion.展开更多
The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensi...The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.展开更多
Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study m...Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.展开更多
It is well-known that partial stability is an active modern problem. About stationary linear systems, a lot of results on partial stability have been obtained. For time-varying linear systems, however, the general the...It is well-known that partial stability is an active modern problem. About stationary linear systems, a lot of results on partial stability have been obtained. For time-varying linear systems, however, the general theories of partial stability have not been established.展开更多
文摘The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.
文摘The network characteristic of the central neural system has been widely accepted as a basic fabric form. However,the matrix characteristics of neural network are still not fully understood. If we ignore the matrix characteristics of the neural networks and just pay close attention to its connection mode,we are likely to fall into the theory of mechanical reductionism. This can lead to a problem in representing consciousness in a disadvantageous situation. It can also be a barrier to further improving the global workspace theory. Incomplete elucidation of the mechanisms of consciousness representation can also affect the assessment of the surgical outcome of partial epilepsy with conscious injury. Therefore,this paper reviews the epistemological development of neuroscience. We will initially describe the matrix characteristics of the neural system and their significance to the information processing mechanism,and further explore the role of neural matrix in identifying cases of partial epilepsy with little effect on the resection of the lesion.
文摘The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.
基金supported by National Natural Science Foundation of China(Nos.11601195,11601538,11571073)Natural Science Foundation of Jiangsu Province of China(No.BK20160289)+1 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.16KJB110005)Jiangsu Qing Lan Project
文摘Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.
基金Project supported by the National Natural Science Foundation of China
文摘It is well-known that partial stability is an active modern problem. About stationary linear systems, a lot of results on partial stability have been obtained. For time-varying linear systems, however, the general theories of partial stability have not been established.
