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121.
以计算循环行列式的方法讨论了拟差集关联矩阵在建立存在性条件中的作用,同时也导出了几个有用的组织式,求和与求积式。 相似文献
122.
矩阵A的伴随矩阵A*是在求其逆矩阵中提出的,是一个重要矩阵。本文研究了伴随矩阵的性质,得到了可逆方阵A的m次伴随矩阵A*m、A*m的逆矩阵及A*m的行列式的表达式,并给出了证明。 相似文献
123.
This paper attempts to prove the D-optimality of the saturated designs X and X of order 22, already existing in the current literature. The corresponding non-equivalent information matrices M=(X)X and M=(X)X have the maximum determinant. Within the application of a specific procedure, all symmetric and positive definite matrices M of order 22 with determinant the square of an integer and det(M) are constructed. This procedure has indicated that there are 26 such non-equivalent matrices M, for 24 of which the non-existence of designs X such that XX =M is proved. The remaining two matrices M are the information matrices M and M. 相似文献
124.
We consider fourth order ordinary differential operators on the half-line and on the line, where the perturbation has compactly supported coefficients. The Fredholm determinant for this operator is an analytic function in the whole complex plane without zero. We describe the determinant at zero. We show that in the generic case it has a pole of order 4 in the case of the line and of order 1 in the case of the half-line. 相似文献
125.
Let A be a(left and right) Noetherian ring that is semiperfect. Let e be an idempotent of A and consider the ring Γ :=(1-e)A(1-e) and the semi-simple right A-module Se := e A/e rad A. In this paper, we investigate the relationship between the global dimensions of A and Γ, by using the homological properties of Se. More precisely, we consider the Yoneda ring Y(e) := Ext_A~*(Se, Se) of e. We prove that if Y(e) is Artinian of finite global dimension, then A has finite global dimension if and only if so does Γ. We also investigate the situation where both A and Γ have finite global dimension. When A is Koszul and finite dimensional, this implies that Y(e) has finite global dimension. We end the paper with a reduction technique to compute the Cartan determinant of Artin algebras. We prove that if Y(e) has finite global dimension, then the Cartan determinants of A and Γ coincide. This provides a new way to approach the long-standing Cartan determinant conjecture. 相似文献
126.
Yaru Fu Xiaoyu Jiang Zhaolin Jiang Seong Tae Jhang 《Journal of Applied Analysis & Computation》2020,10(4):1599-1613
In this paper, tridiagonal Toeplitz matrix (type I, type II) with opposite-bordered rows are introduced. Main attention is paid to calculate the determinants, the inverses and the eigenpairs of these matrices. Specifically, the determinants of an $n\times n$ tridiagonal Toeplitz matrix with opposite-bordered rows can be explicitly expressed by using the $(n-1)$th Fibonacci number, the inversion of the tridiagonal Toeplitz matrix with opposite-bordered rows can also be explicitly expressed by using the Fibonacci numbers and unknown entries from the new matrix. Besides, we give the expression of eigenvalues and eigenvectors of the tridiagonal Toeplitz matrix with opposite-bordered rows. In addition, some algorithms are presented based on these
theoretical results. Numerical results show that the new algorithms have much better computing efficiency than some existing algorithms studied recently. 相似文献
127.
Lei Wang Yi-Tian Gao Feng-Hua Qi 《Journal of Mathematical Analysis and Applications》2010,372(1):110-4055
For the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth of the water, we consider a variable-coefficient variant Boussinesq (vcvB) model with symbolic computation. We construct the connection between the vcvB model and a variable-coefficient Ablowitz-Kaup-Newell-Segur (vcAKNS) system under certain constraints. Using the N-fold Darboux transformation of the vcAKNS system, we present two sets of multi-solitonic solutions for the vcvB model, which are expressed in terms of the Vandermonde-like and double Wronskian determinants, respectively. Dynamics of those solutions are analyzed and graphically discussed, such as the parallel solitonic waves, shape-changing collision, head-on collision, fusion-fission behavior and elastic-fusion coupled interaction. 相似文献
128.
王帅 《数学的实践与认识》2010,40(15)
对于题目中的几个问题,首先给出了一个计算并消除两组划痕数据之间平移误差和转动误差的精确算法,然后利用中值滤波+低通滤波+高斯滤波的方案来消除噪声和误差,最后对过滤后的数据进行分析,提取了一维特征向量并提出了比对特征相关系数作为检验弹头相似程度的标准. 相似文献
129.
Yan Wu 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1121-1123
In this note, a modified Second Derivative Test is introduced for the relative extrema of a single variable function. This improved test overcomes the difficulty of the second derivative vanishing at the critical point, while in contrast the traditional test fails for this case. A proof for this improved Second Derivative Test is presented, followed by an example. 相似文献
130.
给出了广义Vandermonde行列式的一种求法,并运用它给出了Lagrange插值公式的几个证明. 相似文献