The volcanics matrix parameters are variable in different areas and even in different intervals of a same well,due to its complicated mineral compositions and variable mineral contents. The determination of matrix par...The volcanics matrix parameters are variable in different areas and even in different intervals of a same well,due to its complicated mineral compositions and variable mineral contents. The determination of matrix parameters is significant because it has an effect on the porosity calculation accuracy. The authors proposed a simple but useful dual-component model to calculate porosity,and the results are compatible with the core porosity.展开更多
A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix...A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX - EXF = BY and its dual equation XA - FXE = YC are provided. It is also shown that the results obtained can be used easily for observer design. The method proposed in this paper is universally applicable to linear matrix equations.展开更多
By applying the rules for the sum of quark oscillation probabilities for the original CKM matrix and for Wolfenstein’s parameterization, equations were derived in which the CP violating phase for quarks appears as an...By applying the rules for the sum of quark oscillation probabilities for the original CKM matrix and for Wolfenstein’s parameterization, equations were derived in which the CP violating phase for quarks appears as an unknown quantity. Quark oscillations occur in spaces that are on the femtometer scale and they are unmeasurable from the point of view of experiments. However, the consequence of those oscillations is the CP violating phase for quarks, which is measured through unitary triangles in Wolfenstein’s parameterization. Through the mathematical model presented in this paper, the equation in Wolfenstein’s parameterization was derived, the root of which is consistent with measurements in today’s quark physics.展开更多
The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2...The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.展开更多
基金Supported by projects of the National Natural Science Foundation of China (No. 41174096)the Ministry of Science and Technology of China (No.2011ZX05009 No. 2011ZX05044)
文摘The volcanics matrix parameters are variable in different areas and even in different intervals of a same well,due to its complicated mineral compositions and variable mineral contents. The determination of matrix parameters is significant because it has an effect on the porosity calculation accuracy. The authors proposed a simple but useful dual-component model to calculate porosity,and the results are compatible with the core porosity.
基金supported by National Natural Science Foundation of China (No. 60736022, No. 60821091)
文摘A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX - EXF = BY and its dual equation XA - FXE = YC are provided. It is also shown that the results obtained can be used easily for observer design. The method proposed in this paper is universally applicable to linear matrix equations.
文摘By applying the rules for the sum of quark oscillation probabilities for the original CKM matrix and for Wolfenstein’s parameterization, equations were derived in which the CP violating phase for quarks appears as an unknown quantity. Quark oscillations occur in spaces that are on the femtometer scale and they are unmeasurable from the point of view of experiments. However, the consequence of those oscillations is the CP violating phase for quarks, which is measured through unitary triangles in Wolfenstein’s parameterization. Through the mathematical model presented in this paper, the equation in Wolfenstein’s parameterization was derived, the root of which is consistent with measurements in today’s quark physics.
基金supported in part by the Social Science Foundation of Ministry of Education(07JJD790154)the National Science Foundation for Young Scholars (60803076)+2 种基金the Natural Science Foundation of Zhejiang Province (Y6090211)Foundation of Education Department of Zhejiang Province (20070590)the Young Talent Foundation of Zhejiang Gongshang University
文摘The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.
文摘分布式电源(distributed generation,DG)出力的间歇性、随机性和波动性,增加了配电网负荷供应能力(loadsupply capacity,LSC)评估的复杂性。针对传统不确定性方法难以全面地体现LSC的客观不确定性和认知不确定性,提出一种基于仿射数学的变步长重复潮流法(theaffinealgorithm based step-varied repeated power flow method,AA-SVRPF)。利用概率函数的分布参数区间建立风速和光照强度的参数化P-box模型。通过AA直接求得LSC的焦元,结合证据理论生成负荷增长百分比的证据结构体形式。针对计算过程中存在多层循环嵌套、计算效率低的问题,提出基于矩阵运算的快速求解策略,提高了AA-SVRPF的计算效率。为体现不同供电水平时的LSC的不确定性,采用静态负荷供应风险概率作为LSC的度量指标。通过算例的对比分析,结果验证了该方法的可行性和有效性。
