a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

King [3] introduced and examined the concepts of almost A-summable sequence, almost conservative matrix and almost regular matrix. In this paper, we introduce and examine the concepts of λ-almost A-summable sequence, λalmost conservative matrix and λ-almost regular matrix. Also we introduce statistically (V, λ)-summable sequence.

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0’s and 1’s which is not A-summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x. In this paper, definitions for “subsequences of a double sequence” and “Pri...

We describe the generic change of the partial multiplicities at a given eigenvalue λ0 of a regular matrix pencil A0 + λA1 under perturbations with low normal rank. More precisely, if the pencil A0 + λA1 has exactly g nonzero partial multiplicities at λ0, then for most perturbations B0 + λB1 with normal rank r < g the perturbed pencil A0 + B0 + λ(A1 + B1) has exactly g − r nonzero partial multip...

In this paper we present a new diagonal balancing technique for regular matrix pencils λB − A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired from the balancing technique of a square matrix A and has a comparable complexity. Upon convergence, the diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also s...

In this paper, we describe, analyze and compare techniques for extracting spatial knowledge from a terrain model. Specifically, we investigate techniques for extracting a morphological representation from a terrain model based on an approximation of a Morse-Smale complex. A Morse-Smale complex defines a decomposition of a topographic surface into regions with vertices at the critical points and...