In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some propert...In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.展开更多
Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quant...Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.展开更多
Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient condi...Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient conditions for A in the semigroup Gn（C） to be primitive are given. We also show that Gc（Jn） is a subsemigroup of Gn（C）.展开更多
The popularly used circulant matrix model of deconvolution is mostly heavily ill-posed or singular and it is not suitable to many blind deconvolution problems. The aperiodic matrix model can improve the condition numb...The popularly used circulant matrix model of deconvolution is mostly heavily ill-posed or singular and it is not suitable to many blind deconvolution problems. The aperiodic matrix model can improve the condition number of deconvolution problems and its accommodation is much wider than the circulant one's. This paper discusses a comparison of the two models including their ill-posedness, the rationality of the approximation by the models, and their computational efficiency. The comparison shows that the aperiodic model is promising in the development of new restoration algorithms.展开更多
In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented ...In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented respectively.In addition,two algorithms for the inverse of a factor block circulant matrix over the quaternion division algebra are proposed.展开更多
[Objectives] To observe the clinical effects of activating blood circulation to resolve blood stasis and glucosamine hydrochloride capsules therapy on post-traumatic knee osteoarthritis treatment,to measure the expres...[Objectives] To observe the clinical effects of activating blood circulation to resolve blood stasis and glucosamine hydrochloride capsules therapy on post-traumatic knee osteoarthritis treatment,to measure the expression of matrix metalloproteinase in post-traumatic knee osteoarthritis patients before and after treatment,and to explore its relevant molecular mechanisms. [Methods]A total of 60 patients with posttraumatic knee osteoarthritis in early stage in Affiliated Hospital of Shannxi University of Chinese Medicine from January 2015 to December2017 were selected and randomly divided into the control group( n = 30) and the observation group( n = 30). The control group was given oral administration of glucosamine hydrochloride capsules for 6 courses of the treatment. The observation group was using the activating blood circulation to resolve blood stasis therapy for 6 courses of treatment. The recovery of traumatic knee osteoarthritis and the symptom of traditional Chinese medicine( TCM) in 2 groups was compared before and after treatment. The symptoms and the quantitative assessment rating scale of knee osteoarthritis,the pain index of knee and the TCM symptom scores were recorded in both groups. And the synovial fluid and serum of patients were collected to detect the expression of matrix metalloproteinase. [Results]The symptoms and the quantitative assessment rating scale of knee osteoarthritis,the pain index of knee and TCM symptom scores of the 2 groups in the 1 st week,the 12 th week and the 24 th week after the treatment were significantly lower than those before the treatment,and the difference was statistically significant( P < 0. 05). Two therapeutic methods had certain therapeutic effects on the recovery from traumatic knee osteoarthritis,and could significantly improve the TCM syndrome. There were better therapeutic effects on oral decoction of traditional Chinese medicine than oral glycosaminoglycans hydrochloride capsules on treating traumatic knee osteogenesis( P < 0. 05). The expression level of MMP3 was decreased significantly in both groups( P <0. 001),while the expression level of MMP13 had no significant change in both groups( P >0. 05). The expression level of MMP1 was decreased significantly in the observation group( P < 0. 001),but there was no significant change in the control group after treatment( P >0. 05). [Conclusions]Two treatment methods have been effective in this clinical study. We found that the expression level of MMP3 was decreased significantly after treatment in 2 therapies,which can be clinically applied.展开更多
Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major proper...Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm’s matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.展开更多
A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matr...A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for? . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.展开更多
文摘In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.
基金supported by the National Natural Science Foundation of China(Grant Nos.62071015 and 62171264)。
文摘Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances.
基金Supported by the National Natural Science Foundation of China(11071272,11101087)the Postdoctoral Science Foundation of China(2013M531785)+1 种基金the Natural Science Foundation of Fujian Province(2013J05006)the Foundation of Fuzhou University(2012-XQ-30)
文摘Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient conditions for A in the semigroup Gn（C） to be primitive are given. We also show that Gc（Jn） is a subsemigroup of Gn（C）.
基金Supported by the National Natural Science Foundation of China(2 0 0 0 CG0 1 0 3) the Fund of"The Developing Program for Outstanding Person"in NPUS & T Innovation Foundation for Young Teachers of Northwestern Polytechnical University.
文摘In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.
文摘The popularly used circulant matrix model of deconvolution is mostly heavily ill-posed or singular and it is not suitable to many blind deconvolution problems. The aperiodic matrix model can improve the condition number of deconvolution problems and its accommodation is much wider than the circulant one's. This paper discusses a comparison of the two models including their ill-posedness, the rationality of the approximation by the models, and their computational efficiency. The comparison shows that the aperiodic model is promising in the development of new restoration algorithms.
基金The research is partially supported by the 35th Postdoctoral Work of the National Science Foundation of China(2004035684).
文摘In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented respectively.In addition,two algorithms for the inverse of a factor block circulant matrix over the quaternion division algebra are proposed.
基金Supported by Shaanxi Administration of Traditional Chinese Medicine(LCPT034)
文摘[Objectives] To observe the clinical effects of activating blood circulation to resolve blood stasis and glucosamine hydrochloride capsules therapy on post-traumatic knee osteoarthritis treatment,to measure the expression of matrix metalloproteinase in post-traumatic knee osteoarthritis patients before and after treatment,and to explore its relevant molecular mechanisms. [Methods]A total of 60 patients with posttraumatic knee osteoarthritis in early stage in Affiliated Hospital of Shannxi University of Chinese Medicine from January 2015 to December2017 were selected and randomly divided into the control group( n = 30) and the observation group( n = 30). The control group was given oral administration of glucosamine hydrochloride capsules for 6 courses of the treatment. The observation group was using the activating blood circulation to resolve blood stasis therapy for 6 courses of treatment. The recovery of traumatic knee osteoarthritis and the symptom of traditional Chinese medicine( TCM) in 2 groups was compared before and after treatment. The symptoms and the quantitative assessment rating scale of knee osteoarthritis,the pain index of knee and the TCM symptom scores were recorded in both groups. And the synovial fluid and serum of patients were collected to detect the expression of matrix metalloproteinase. [Results]The symptoms and the quantitative assessment rating scale of knee osteoarthritis,the pain index of knee and TCM symptom scores of the 2 groups in the 1 st week,the 12 th week and the 24 th week after the treatment were significantly lower than those before the treatment,and the difference was statistically significant( P < 0. 05). Two therapeutic methods had certain therapeutic effects on the recovery from traumatic knee osteoarthritis,and could significantly improve the TCM syndrome. There were better therapeutic effects on oral decoction of traditional Chinese medicine than oral glycosaminoglycans hydrochloride capsules on treating traumatic knee osteogenesis( P < 0. 05). The expression level of MMP3 was decreased significantly in both groups( P <0. 001),while the expression level of MMP13 had no significant change in both groups( P >0. 05). The expression level of MMP1 was decreased significantly in the observation group( P < 0. 001),but there was no significant change in the control group after treatment( P >0. 05). [Conclusions]Two treatment methods have been effective in this clinical study. We found that the expression level of MMP3 was decreased significantly after treatment in 2 therapies,which can be clinically applied.
文摘Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm’s matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.
文摘A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for? . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.
