For an iterated function system (IFS) with contractive similarities, the post-critically finite (p.c.f.) condition and H-condition are two important separation conditions in the literature. But their relationship is not clear. In this paper, we show that if the similarity matrices of the IFS...
On matrices whose numerical ranges have circular or weak circular symmetry Linear Algebra Appl., 302/303 (1998), pp. 193-221 Google Scholar [12] R.C. Thompson The upper numerical range of a quaternionic matrix is not a complex numerical range Linear Algebra Appl., 254 (1997), pp. 19-...
7.5 Extension 5: Both the mass and stiffness matrices depend on unknown parameters In Section 6 we considered the adjoint method for a time-dependent problem at the semi-discrete level. We assumed that the mass matrix M was constant, and that only the stiffness matrix K depended on the unkno...
Condition for AB+A+B=0 where A and B are matrices I first tried by assuming the matrices but it was becoming complicated so i tried taking transpose on both sides,it also did not help.So now i could not think of what to do further.Help please. ...
To better understand the results, rearrange the layout of the plots so you can compare the confusion matrices for the four models. Click the Document Actions button located to the far right of the model plot tabs. Select the Tile All option and specify a 2-by-2 layout. In the top right...
for all k, where \(\lambda _{\max }\) and \(\lambda _{\min }\) mean the largest and the smallest eigenvalues of the corresponding matrices. (c) Let \(x^*\) be an accumulation point of \(\{x^k\}\). Then, Q defined in (6) satisfies the generalized Lojasiewicz inequality at...
We used a Non-Negative Matrix Factorization (NMF) that finds two non-negative matrices (W, H) whose product approximates the non-negative matrix Me. This factorization can be used for example for dimensional reduction, source separation, or topic extraction. In our case, we assumed Metrain is...
Contrary to our expectation, mean occurrence for the entire species community, and for forest-associated and migrant species, were highest in bauxite, intermediate in suburban, and lowest in agriculture. Open-associated species had higher occurrences in both bauxite and agricultural matrices, whereas ...
Central to all applications of rotational isomeric state theory is a conformation partition function, Z, that is assembled as a sequential product of n statistical weight matrices11 (1) where U1 is a row, Un is a column, and the internal Ui are rectangular matrices. In most applications, in...
The “odd” DSTs are obtained with similar considerations applied to matrices B5 to B8. These are listed in what follows without more detailed discussion: (2.66)(SN−1V)lk=22N−1sin[2lkπ2N−1],l,k=1,2,…,N−1, (2.67)(SN−1VI)lk=22N−1sin[2(l+12)(k+1)π2N−1...