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 type of iron-based matrix formula as a potential substitute for traditional WC-based matrix formula for hot pressed diamond bit was investigated.Iron,phosphor-iron,663-Cu,nickel,cobalt and certain additives were...A new type of iron-based matrix formula as a potential substitute for traditional WC-based matrix formula for hot pressed diamond bit was investigated.Iron,phosphor-iron,663-Cu,nickel,cobalt and certain additives were selected as the studied formula constituents.Among matrix performances,the hardness and wear resistance were chosen as experimental indexes in this paper.Constrained uniform design method was used for the formula design of iron-based matrix.Two forms of regression models of matrix hardness and wear resistance were obtained by regression analysis using MATLAB.Moreover,the optimization of matrix formulae and matrix performances were also achieved through constrained nonlinear programming.It was found that matrix hardness,significantly affected by the factor of Ni-Co-additives and Fe,increased with the increment of Ni-Co-additives,Fe and P-Fe,but reduced with the increase of 663-Cu.On the other hand,matrix wear resistance is mainly affected by Fe;the effect of the interaction between Fe and P-Fe is also relatively obvious. The increment of 663-Cu powder may result in a slight improvement in matrix wear resistance.In addition,the results of nonlinear programming revealed that the predictive optimum value of hardness was 139.5 HRB and the optimum wear resistance was 0.056 g,whereas they could not reach the optimum value at the same time.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
A major obstacle to achieving reasonable strength prediction of a composite only from its constituent information is in the determination of in situ strengths of the matrix. One can measure only the original strengths...A major obstacle to achieving reasonable strength prediction of a composite only from its constituent information is in the determination of in situ strengths of the matrix. One can measure only the original strengths of the pure matrix, on the basis of which the predicted transverse strengths of a unidirectional (UD) composite are far from reality. It is impossible to reliably measure matrix in situ strengths. This paper focuses on the correlation between in situ and original strengths. Stress concentrations in a matrix owing to the introduction of fibers are attributed to the strength variation. Once stress concentration factors (SCFs) are obtained, the matrix in situ strengths are assigned as the original counterparts divided by them. Such an SCF cannot be defined following a classical approach. All of the relevant issues associated with determining it are systematically addressed in this paper. Analytical expressions for SCFs under transverse tension, transverse compression, and transverse shear are derived. Closed-form and compact formulas for all of the uniaxial strengths of a UD composite are first presented in this paper. Their application to strength predictions of a number of typical UD composites demonstrates the correctness of these formulas.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
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 type of iron-based matrix formula as a potential substitute for traditional WC-based matrix formula for hot pressed diamond bit was investigated.Iron,phosphor-iron,663-Cu,nickel,cobalt and certain additives were selected as the studied formula constituents.Among matrix performances,the hardness and wear resistance were chosen as experimental indexes in this paper.Constrained uniform design method was used for the formula design of iron-based matrix.Two forms of regression models of matrix hardness and wear resistance were obtained by regression analysis using MATLAB.Moreover,the optimization of matrix formulae and matrix performances were also achieved through constrained nonlinear programming.It was found that matrix hardness,significantly affected by the factor of Ni-Co-additives and Fe,increased with the increment of Ni-Co-additives,Fe and P-Fe,but reduced with the increase of 663-Cu.On the other hand,matrix wear resistance is mainly affected by Fe;the effect of the interaction between Fe and P-Fe is also relatively obvious. The increment of 663-Cu powder may result in a slight improvement in matrix wear resistance.In addition,the results of nonlinear programming revealed that the predictive optimum value of hardness was 139.5 HRB and the optimum wear resistance was 0.056 g,whereas they could not reach the optimum value at the same time.
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.
文摘A major obstacle to achieving reasonable strength prediction of a composite only from its constituent information is in the determination of in situ strengths of the matrix. One can measure only the original strengths of the pure matrix, on the basis of which the predicted transverse strengths of a unidirectional (UD) composite are far from reality. It is impossible to reliably measure matrix in situ strengths. This paper focuses on the correlation between in situ and original strengths. Stress concentrations in a matrix owing to the introduction of fibers are attributed to the strength variation. Once stress concentration factors (SCFs) are obtained, the matrix in situ strengths are assigned as the original counterparts divided by them. Such an SCF cannot be defined following a classical approach. All of the relevant issues associated with determining it are systematically addressed in this paper. Analytical expressions for SCFs under transverse tension, transverse compression, and transverse shear are derived. Closed-form and compact formulas for all of the uniaxial strengths of a UD composite are first presented in this paper. Their application to strength predictions of a number of typical UD composites demonstrates the correctness of these formulas.
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.
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.
