We shall show that any two quadrangulations on the sphere with n vertices can be transformed into each other by at most 6n− 32 diagonal slides and rotations, up to homeomorphism, if n ≥ 9.

If A is a square matrix with distinct eigenvalues and D a nonsingular matrix, then the angles between rowand column-eigenvectors of D~XAD differ from the corresponding quantities of A. Perturbation analysis of the eigenvalue problem motivates the minimization of functions of these angles over the set of diagonal similarity transforms ; two such functions which are of particular interest are the...

Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...

A 54-year-old man with exertional angina of 2 months’ evolution came to the hospital for pain that had lasted 1.45 h. The electrocardiogram showed ST segment elevation of 2 mm in leads I and aVL. Clopidogrel and acetylsalicylic acid were administered. Angiography disclosed a filling defect in the left main coronary artery (LMCA) consistent with a large thrombus, occlusion of the first diagonal ...

A generic matrix A ∈ Cn×n is shown to be the product of circulant and diagonal matrices with the number of factors being 2n−1 at most. The demonstration is constructive, relying on first factoring matrix subspaces equivalent to polynomials in a permutation matrix over diagonal matrices into linear factors. For the linear factors, the sum of two scaled permutations is factored into the product o...

Let $mathbf{c}_0$ be the real vector space of all real sequences which converge to zero. For every $x,yin mathbf{c}_0$, it is said that $y$ is block diagonal majorized by $x$ (written $yprec_b x$) if there exists a block diagonal row stochastic matrix $R$ such that $y=Rx$. In this paper we find the possible structure of linear functions $T:mathbf{c}_0rightarrow mathbf{c}_0$ preserving $prec_b$.

Response modification factor (R factor) is one of the seismic design parameters to be considered in evaluating the performance of buildings during strong motions. This paper has tried to evaluate the response modification factor of concrete coupled shear wall structures with various length/depth ratios of spandrel beams. The effect of diagonal reinforcement of spandrel beam was also evaluated o...

Assume that a1j 6= 0 for j = 2 . . . n. Then the (1, 1) element of A∗A is equal to a11+a12+. . .+a1n. The (1, 1) element of AA∗ is equal to a11. Since A is normal, a 2 11 + a 2 12 + . . . + a 2 1n = a 2 11 and, therefore, a1j = 0 for j = 2 . . . n. Now assume that a2j 6= 0 for j = 3 . . . n. Using the above proven fact that a12 = 0 we can compare the (2,2) entries of A∗A and AA∗ to show that al...