This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ...This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ratio of fault throw to the distance between a shale oil well and the nearest fault. Based on CO_2 content, state of water, oil production and logging response of shale oil formations, the classification of shale oils was established, i.e., a fracture-type shale oil well has a fracture development coefficient greater than 0.2, while a matrix-type one has a fracture development coefficient less than 0.2. Furthermore, the key control factors of matrix- and fracture-type shale oil enrichment were analyzed using typical anatomical and statistical methods. For matrix-type shale oil enrichment, these factors are lithofacies, total organic carbon（TOC）, shale porosity and abnormal pressure; for fracture-type shale oil enrichment, they are lithofacies, extent of fracture development, and abnormal pressure. This study also first described the differences between matrix- and fracture-type shale oils. The results provide reference for the exploration of terrestrial faulted basins in eastern China.展开更多
To investigate correlation of expressions of membrane-type 1, 2, and 3 matrix metalloproteinases (MT1, MT2, and MT3-MMP) to the invasion and metastases in laryngeal cancer. Methods Reverse transcription-polymerase cha...To investigate correlation of expressions of membrane-type 1, 2, and 3 matrix metalloproteinases (MT1, MT2, and MT3-MMP) to the invasion and metastases in laryngeal cancer. Methods Reverse transcription-polymerase chain reaction (RT-PCR) was used to examine the mRNA level of MT1, MT2, and MT3-MMP in 24 patients with laryngeal cancer. The relationships of these three MT-MMP expressions to clinico-pathology were analyzed by statistics. Results The expressions of MT1, MT2, and MT3-MMP were significantly higher in laryngeal cancer tissues than those in para-tumorous tissues (P < 0.01) and had a close relationship with invasive depth (P < 0.05). But no significantly different expressions of these three MT-MMPs were found in different primary location and different histological grade of laryngeal cancer (P > 0.05). The expression of MT1-MMP was obviously higher in patients with metastatic lymph nodes than that in patients without metastatic lymph nodes (P < 0.05). Conclusion MT1, MT2, and MT3-MMP play an important role in the progression of laryngeal cancer, and MT1-MMP may serve as a reliable marker in estimating invasive and metastatic potency of laryngeal cancer. Suppressing expressions of MT1, MT2, and MT3-MMP early may inhibit the invasion and metastases of laryngeal cancer.展开更多
Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exp...Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing and for computing with many espectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing for a fixed matrix A with many t ≥ 0.展开更多
Matrix effect primarily impacts the accuracy and precision of zircon LA-ICP-MS U-Pb data.This paper describes three types of matrix effect in zircon LA-ICPMS U-Pb dating,i.e.,the element matrix effect,high Ddpa or ura...Matrix effect primarily impacts the accuracy and precision of zircon LA-ICP-MS U-Pb data.This paper describes three types of matrix effect in zircon LA-ICPMS U-Pb dating,i.e.,the element matrix effect,high Ddpa or uranium matrix effect and alpha dose matrix effect,and illustrates the correction of these three effects.In addition,we point out the limitation and possible problems of the existing correction methods.展开更多
An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to swit...An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.展开更多
For the lower bound about the determinant of Hadamard product of A and B, where A is a n × n real positive definite matrix and B is a n × n M-matrix, Jianzhou Liu [SLAM J. Matrix Anal. Appl., 18(2)(1997): 30...For the lower bound about the determinant of Hadamard product of A and B, where A is a n × n real positive definite matrix and B is a n × n M-matrix, Jianzhou Liu [SLAM J. Matrix Anal. Appl., 18(2)(1997): 305-311]obtained the estimated inequality as follows det(A o B)≥a11b11 nⅡk=2(bkk detAk/detAk-1+detBk/detBk-1(k-1Ei=1 aikaki/aii))=Ln(A,B),where Ak is kth order sequential principal sub-matrix of A. We establish an improved lower bound of the form Yn(A,B)=a11baa nⅡk=2(bkk detAk/detAk-1+akk detBk/detBk-1-detAdetBk/detak-1detBk-1)≥Ln(A,B).For more weaker and practical lower bound, Liu given thatdet(A o B)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB(nⅡk=2 k-1Ei=1 aikaki/aiiakk)=(L)n(A,B).We further improve it as Yn(A,B)=(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)+max1≤k≤n wn(A,B,k)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)≥(L)n(A,B).展开更多
In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps.Meanw...In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps.Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.展开更多
In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-know...In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.展开更多
In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fracti...In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained.展开更多
To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the es...To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the estimations for determinants of Dashnic-Zusmanovich type matrices are studied.For a Dashnic-Zusmanovich type matrix,we transform it into a diagonally dominant matrix by using scaling matrices.Then we obtain the upper and lower bounds for the determinant of the Dashnic-Zusmanovich type matrix.Numerical examples are given to illustrate the effectiveness of the proposed results.展开更多
基金supported by the National Basic Research Program of China(973 Program)(Grant No2014CB239104)
文摘This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ratio of fault throw to the distance between a shale oil well and the nearest fault. Based on CO_2 content, state of water, oil production and logging response of shale oil formations, the classification of shale oils was established, i.e., a fracture-type shale oil well has a fracture development coefficient greater than 0.2, while a matrix-type one has a fracture development coefficient less than 0.2. Furthermore, the key control factors of matrix- and fracture-type shale oil enrichment were analyzed using typical anatomical and statistical methods. For matrix-type shale oil enrichment, these factors are lithofacies, total organic carbon（TOC）, shale porosity and abnormal pressure; for fracture-type shale oil enrichment, they are lithofacies, extent of fracture development, and abnormal pressure. This study also first described the differences between matrix- and fracture-type shale oils. The results provide reference for the exploration of terrestrial faulted basins in eastern China.
文摘To investigate correlation of expressions of membrane-type 1, 2, and 3 matrix metalloproteinases (MT1, MT2, and MT3-MMP) to the invasion and metastases in laryngeal cancer. Methods Reverse transcription-polymerase chain reaction (RT-PCR) was used to examine the mRNA level of MT1, MT2, and MT3-MMP in 24 patients with laryngeal cancer. The relationships of these three MT-MMP expressions to clinico-pathology were analyzed by statistics. Results The expressions of MT1, MT2, and MT3-MMP were significantly higher in laryngeal cancer tissues than those in para-tumorous tissues (P < 0.01) and had a close relationship with invasive depth (P < 0.05). But no significantly different expressions of these three MT-MMPs were found in different primary location and different histological grade of laryngeal cancer (P > 0.05). The expression of MT1-MMP was obviously higher in patients with metastatic lymph nodes than that in patients without metastatic lymph nodes (P < 0.05). Conclusion MT1, MT2, and MT3-MMP play an important role in the progression of laryngeal cancer, and MT1-MMP may serve as a reliable marker in estimating invasive and metastatic potency of laryngeal cancer. Suppressing expressions of MT1, MT2, and MT3-MMP early may inhibit the invasion and metastases of laryngeal cancer.
文摘Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing and for computing with many espectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing for a fixed matrix A with many t ≥ 0.
文摘Matrix effect primarily impacts the accuracy and precision of zircon LA-ICP-MS U-Pb data.This paper describes three types of matrix effect in zircon LA-ICPMS U-Pb dating,i.e.,the element matrix effect,high Ddpa or uranium matrix effect and alpha dose matrix effect,and illustrates the correction of these three effects.In addition,we point out the limitation and possible problems of the existing correction methods.
文摘An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.
文摘For the lower bound about the determinant of Hadamard product of A and B, where A is a n × n real positive definite matrix and B is a n × n M-matrix, Jianzhou Liu [SLAM J. Matrix Anal. Appl., 18(2)(1997): 305-311]obtained the estimated inequality as follows det(A o B)≥a11b11 nⅡk=2(bkk detAk/detAk-1+detBk/detBk-1(k-1Ei=1 aikaki/aii))=Ln(A,B),where Ak is kth order sequential principal sub-matrix of A. We establish an improved lower bound of the form Yn(A,B)=a11baa nⅡk=2(bkk detAk/detAk-1+akk detBk/detBk-1-detAdetBk/detak-1detBk-1)≥Ln(A,B).For more weaker and practical lower bound, Liu given thatdet(A o B)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB(nⅡk=2 k-1Ei=1 aikaki/aiiakk)=(L)n(A,B).We further improve it as Yn(A,B)=(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)+max1≤k≤n wn(A,B,k)≥(nⅡi=1 bii)detA+(nⅡi=1 aii)detB-(detA)(detB)≥(L)n(A,B).
文摘In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps.Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.
基金Project supported by National Natural Science Foundation of China (Grant No .10271074)
文摘In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.
文摘In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained.
基金supported by the National Natural Science Foundation of China(No.12171323)the Natural Science Foundation of Guangxi Province(No.2023GXNSFAA026514)。
文摘To estimate the determinant of a matrix is a hot issue in numerical algebra.The class of H-matrices has a wide range of applications in many fields such as computational mathematics,control theory.In this paper,the estimations for determinants of Dashnic-Zusmanovich type matrices are studied.For a Dashnic-Zusmanovich type matrix,we transform it into a diagonally dominant matrix by using scaling matrices.Then we obtain the upper and lower bounds for the determinant of the Dashnic-Zusmanovich type matrix.Numerical examples are given to illustrate the effectiveness of the proposed results.
