Self-assembly of miktoarm star-like ABn block copolymer in both selective solvent (A- or B-selective) and miscible homopolymer matrix (A or B homopolymer), that is, formation of micelles, was for the first time investigated by theoretical calculations based on self-consistent mean field theory. Interestingly, the calculation revealed that the size of micelles in solvent was smaller than that in...

Identifying and locating-dominating codes have been studied widely in circulant graphs of type Cn(1, 2, 3, . . . , r) over the recent years. In 2013, Ghebleh and Niepel studied locatingdominating and identifying codes in the circulant graphs Cn(1, d) for d = 3 and proposed as an open question the case of d > 3. In this paper we study identifying, locating-dominating and self-identifying codes i...

To describe the dynamics of stage-structured populations with m stages living in n patches, we consider matrix models of the form SD, where S is a block diagonal matrix with n× n column substochastic matrices S1, . . . , Sm along the diagonal and D is a block matrix whose blocks aren× n nonnegative diagonal matrices. The matrix S describes movement between patches and the matrix D describes gro...

This paper describes Householder reduction of a rectangular sparse matrix to small band upper triangular form. Using block Householder transformations gives good orthogonality, is computationally efficient, and has good potential for parallelization. The algorithm is similar to the standard dense Householder reduction used as part of the usual dense SVD computation. For the sparse algorithm, th...

In this paper, we present a numerical method to solve the palindromic quadratic eigenvalue problem (PQEP) (λA+λQ+A)z = 0 arising from the vibration analysis of high speed trains, where A, Q ∈ Cn×n have special structures: both Q and A are m × m block matrices with each block being k × k, and moreover they are complex symmetric, block tridiagonal and block Toeplitz, and also A has only one nonze...

We investigate the condition number of the matrices that appear in the boundary element method. In particular we consider the Laplace equation with mixed boundary conditions. For Dirichlet boundary conditions, the condition number of the system matrix increases linearly with the number of boundary elements. We extend the research and search for a relation between the condition number and the nu...

In this paper we study the connection between matrix measures and random walks with a block tridiagonal transition matrix. We derive sufficient conditions such that the blocks of the n-step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by m...

A fast approximate inversion method is proposed for the block lower triangular Toeplitz with tri-diagonal blocks (BL3TB) matrix. The BL3TB matrix is approximated by a block ε-circulant matrix, which can be efficiently inverted using the fast Fourier transforms. The error estimation is given to show the high accuracy of the approximation. In applications, the proposed method is employed to solve...

In this work we study in detail the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form. That is the existence of a coordinate frame in which the stiffness matrix takes on these simple forms. The consequences of a block-diagonal or diagonal stiffness matrix for the invariants of the system, principal screws, von Mises’ invaria...

This paper describes Householder reduction of a rectangular sparse matrix to small band upper triangular form Bk+1. Bk+1 is upper triangular with nonzero entries only on the diagonal and on the nearest k superdiagonals. The algorithm is similar to the Householder reduction used as part of the standard dense SVD computation. For the sparse “lazy” algorithm, matrix updates are deferred until a ro...