In order to expand the sources of raw materials for edible fungus cultivation, reduce the use of wood, and realize the harmless treatment and efficient utilization of bamboo sawdust, bamboo sawdust was used to partial...In order to expand the sources of raw materials for edible fungus cultivation, reduce the use of wood, and realize the harmless treatment and efficient utilization of bamboo sawdust, bamboo sawdust was used to partially replace the broad-leaved wood sawdust in the conventional formula, and the growth of Ganoderma lucidum and Stropharia rugosoannulata mycelia in a large test tube in different matrix formulas was studied. The results show that the mycelia of the two edible fungi could grow normally in the matrices with bamboo sawdust;the growth of the mycelia in various formulas was different, and the performances of different strains of the same species were also different. Compared with the conventional formula, the suitable substitution amount of bamboo sawdust for the G. lucidum strains was 30%-45%, and that for S. rugosoannulata strains was 16%-32%.展开更多
A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar de...A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.展开更多
In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix eleme...In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.展开更多
OBJECTIVE:To determine the effects of Bushenhuoxue formula(BHF) on interleukin-1 beta(IL-1β),transforming growth factor beta 1(TGF-β1),discoidin domain receptor 2(DDR2) and matrix metalloproteinase-1(MMP-1) levels i...OBJECTIVE:To determine the effects of Bushenhuoxue formula(BHF) on interleukin-1 beta(IL-1β),transforming growth factor beta 1(TGF-β1),discoidin domain receptor 2(DDR2) and matrix metalloproteinase-1(MMP-1) levels in a rat model of osteoarthritis(OA).METHODS:Sprague-Dawley rats were used to establish an OA model and subjected to various treatments over 6 weeks.Rats were treated with BHF,glucosamine sulfate(G5),or starch as a control.Serum levels of IL-1β and MMP-1 and joint fluid levels of IL-1 β were determined by means of ELISAs.We used immunohistochemistry to determine DDR2 levels in knee cartilage.Gene expression levels of MMP-1 in joint synovial tissue were assessed using reverse transcription polymerase chain reaction assays.RESULTS:Serum IL-1β levels were unchanged throughout the study.Levels of IL-1β in joint fluid and MMP-1 in sera from the BHF- and GS-treated groups were significantly reduced.DDR2 levels in knee cartilage were also significantly reduced in the BHF group.Expression of the MMP-1 gene was significantly reduced by BHF treatment.CONCLUSION:BHF might be beneficial in the inhibition and alleviation of local inflammatory responses and cartilage degeneration in OA.展开更多
The present paper offers two likely neglected applications of the classical Lagrange expansion formula. One is a unified approach to some age-old derivative identities originally due to Pfaff and Cauchy. Another is tw...The present paper offers two likely neglected applications of the classical Lagrange expansion formula. One is a unified approach to some age-old derivative identities originally due to Pfaff and Cauchy. Another is two explicit matrix inversions which may serve as common generalizations of some known inverse series relations.展开更多
Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The lin...Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.展开更多
The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed for...The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed form and an inverse form of the classical Faa di Bruno formula.展开更多
Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonst...Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.展开更多
基金Supported by the Science and Technology Project of Guizhou Province ((2022)YB176,[2020]1Y073,(2019)2773,[2019]3007)。
文摘In order to expand the sources of raw materials for edible fungus cultivation, reduce the use of wood, and realize the harmless treatment and efficient utilization of bamboo sawdust, bamboo sawdust was used to partially replace the broad-leaved wood sawdust in the conventional formula, and the growth of Ganoderma lucidum and Stropharia rugosoannulata mycelia in a large test tube in different matrix formulas was studied. The results show that the mycelia of the two edible fungi could grow normally in the matrices with bamboo sawdust;the growth of the mycelia in various formulas was different, and the performances of different strains of the same species were also different. Compared with the conventional formula, the suitable substitution amount of bamboo sawdust for the G. lucidum strains was 30%-45%, and that for S. rugosoannulata strains was 16%-32%.
文摘A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.
文摘In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.
基金Supported by the Shandong Provincial Department of Education(Mechanism of Bushenhuoxue Formula Protecting Chondrocytes of Osteoarthritis,No.J07YD08)the Shandong Provincial Administration of Traditional Chinese Medicine(Relationship between Bushenhuoxue Formula and the Osteoarthritis Signaling Molecule DDR2,No.2007-027)
文摘OBJECTIVE:To determine the effects of Bushenhuoxue formula(BHF) on interleukin-1 beta(IL-1β),transforming growth factor beta 1(TGF-β1),discoidin domain receptor 2(DDR2) and matrix metalloproteinase-1(MMP-1) levels in a rat model of osteoarthritis(OA).METHODS:Sprague-Dawley rats were used to establish an OA model and subjected to various treatments over 6 weeks.Rats were treated with BHF,glucosamine sulfate(G5),or starch as a control.Serum levels of IL-1β and MMP-1 and joint fluid levels of IL-1 β were determined by means of ELISAs.We used immunohistochemistry to determine DDR2 levels in knee cartilage.Gene expression levels of MMP-1 in joint synovial tissue were assessed using reverse transcription polymerase chain reaction assays.RESULTS:Serum IL-1β levels were unchanged throughout the study.Levels of IL-1β in joint fluid and MMP-1 in sera from the BHF- and GS-treated groups were significantly reduced.DDR2 levels in knee cartilage were also significantly reduced in the BHF group.Expression of the MMP-1 gene was significantly reduced by BHF treatment.CONCLUSION:BHF might be beneficial in the inhibition and alleviation of local inflammatory responses and cartilage degeneration in OA.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1107118311471237)
文摘The present paper offers two likely neglected applications of the classical Lagrange expansion formula. One is a unified approach to some age-old derivative identities originally due to Pfaff and Cauchy. Another is two explicit matrix inversions which may serve as common generalizations of some known inverse series relations.
基金the Science and Technology Research Project of Education Department, Heilongjiang Province (Grant No.11513095)the Science andTechnology Foundation of Heilongjiang Institute of Science and Technology(Grant No.04 -25).
文摘Shannon’s information measure is a crucial concept in Information Theory. And the research, for the mathematics structure of Shannon’s information measure, is to recognize the essence of information measure. The linear relation between Shannon’s information measures and some signed measure space by using the formal symbols substitution rule is discussed. Furthermore, the coefficient matrix recurrent formula of the linear relation is obtained. Then the coefficient matrix is proved to be invertible via mathematical induction. This shows that the linear relation is one-to-one, and according to this, it can be concluded that a compact space can be generated from Shannon’s information measures.
基金Supported by the National Natural Science Foundation of China(Grant No.11401237)
文摘The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed form and an inverse form of the classical Faa di Bruno formula.
文摘Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.
