Abstract: In this article, experimental situations are considered
where a main effects plan is to be used to study m two-level factors
using n runs which are partitioned into b blocks, not necessarily
of same size. Assuming the block sizes to be even for all blocks,
for the case n ≡ 2 (mod 4), optimal designs are obtained with
respect to type 1 and type 2 optimality criteria in the class of designs
providing estimation of all main effects orthogonal to the block
effects. In practice, such orthogonal estimation of main effects is
often a desirable condition. In the wider class of all available m two
level even sized blocked main effects plans, where the factors do not
occur at high and low levels equally often in each block, E-optimal
designs are also characterized. Simple construction methods based on
Hadamard matrices and Kronecker product for these optimal designs
are presented.
Abstract: In this paper, according to the classical algorithm
LSQR for solving the least-squares problem, an iterative method is
proposed for least-squares solution of constrained matrix equation. By
using the Kronecker product, the matrix-form LSQR is presented to
obtain the like-minimum norm and minimum norm solutions in a
constrained matrix set for the symmetric arrowhead matrices. Finally,
numerical examples are also given to investigate the performance.
Abstract: In this paper, reliable consensus of multi-agent systems
with sampled-data is investigated. By using a suitable
Lyapunov-Krasovskii functional and some techniques such as
Wirtinger Inequality, Schur Complement and Kronecker Product, the
results of such system are obtained by solving a set of Linear Matrix
Inequalities (LMIs). One numerical example is included to show the
effectiveness of the proposed criteria.
Abstract: The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs,
Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.
Abstract: A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.