This paper examines extensions of a min-max equality (stated in ? Berge, Part I) for the maximum number of nodes in a perfect graph which can be g-coloure&L A system L of linear inequalities in the variables 5 is called TDI if for every linear function cg such that _c is all integers, the dual of the linear program: maximize (~8: x satisfies L} has an integer-valued optimum solution or no optim...

An alternating sign matrix is a square matrix with entries 1, 0 and −1 such that the sum of the entries in each row and each column is equal to 1 and the nonzero entries alternate in sign along each row and each column. To some of the symmetry classes of alternating sign matrices and their variations, G. Kuperberg associate square ice models with appropriate boundary conditions, and give determ...

A letter matrix is an n-by-n matrix whose entries are n symbols, each appearing n times. The row (column) distribution of a letter matrix is an n-by-n nonnegative integer matrix that tells how many of each letter are in each row (column). A row distribution R and a column distribution C are compatible if there exits a letter matrix A whose row distribution is R and whose column distribution is ...

This work deals with the generalized eigenvalue problem for nonsquare matrix pencils A − λB such that matrices A,B ∈ MC (m×n) show a given structure. More precisely, we assume they result from removing the first row of some matrix G ∈ MC ((m+1) , n) in the case of A, and its last row in the case of B. This structured generalized eigenvalue problem can be found in signal processing methods and i...

The ith row of A represents a ±1-valued “square wave” function of j with halfperiod i. Thus xA, where x is a (row) N -vector, gives a picture of the waveform that is a linear combination of square waves with weights in x. Similarly yA finds weights so that a given waveform y is a weighted linear combination of these square waves. This matrix has a surprisingly simple inverse. More generally, we...

An efficient method for the computation to high relative accuracy of the LDU decomposition of an n × n row diagonally dominant M–matrix is presented, assuming that the off–diagonal entries and row sums are given. This method costs an additional O(n) elementary operations over the cost of Gaussian elimination, and leads to a lower triangular, column diagonally dominant matrix and an upper triang...

A square {+1,−1}-matrix of order n with maximal determinant is called a saturated D-optimal design. We consider some cases of saturated Doptimal designs where n > 2, n ≡ 0 mod 4, so the Hadamard bound is not attainable, but bounds due to Barba or Ehlich and Wojtas may be attainable. If R is a matrix with maximal (or conjectured maximal) determinant, then G = RR is the corresponding Gram matrix....

A new method for feature extraction and recognition, namely the fuzzy bidirectional weighted sum criterion (FBWSC) is proposed in this paper. FBWSC defines the row directional fuzzy image optimal image projection matrix. Subsequently, each sample in the original training sample set is transformed using the row directional optimal image projection matrix, and the row directional feature training...

If a matrix .4 transforms a sequence {z„} into the sequence {z, A is said to be regular. The well known necessary and sufficient conditions for A to be regular are1 (a) X^-i |g»,*| Wo, (b) limn^oo an,k = 0 for every fixed fe, (c) XXi a»j»«A»—»1 as w-»°o. It is known2 that if a regular matrix s...