A standard way of dealing with matrix polynomial eigenvalue problems is to use linearizations. Byers, Mehrmann and Xu have recently defined and studied linearizations of dimensions smaller than the classical ones. In this paper, lower bounds are provided for the dimensions of linearizations and strong linearizations of a given m×n matrix polynomial, and particular linearizations are constructed...

This paper describes an algorithm to implement image filtering and enhancement operations by processing adaptive triangular meshes that represent gray-level images. Experimental results show that these operations are significantly more efficient when they are performed upon triangular meshes than by sequentially processing all the pixels contained in the given images.

In this paper, we study the Bauer-Fike type theorems for regular matrix pairs and its general form. Besides these, we also obtain some bounds for measuring approximate generalized eigenvalues and for the perturbation of generalized eigenvalues concerning an approximate generalized invariant subspace. To estimate all these bounds, p-Hölder norm and an ad hoc pseudo-metric called p-Chordal matric...

The paper describes a set of methods to automatically acquire the Urdu nouns (and its gender) on the basis of inflectional and contextual clues. The algorithms used are a blend of computer's brute force on the corpus and careful design of distinguishing rules on the basis linguistic knowledge. As there are homograph inflections for Urdu nouns, adjectives and verbs, we compare potential inflecti...

where skm are real numbers, pk0(t) ∈ C2[a,b], p00(t)p20(t) = 0, p00(t)/p20(t) > 0 for t ∈ [a,b]. Let s2m < s0m + 2, s2m ≤ s1m + 2, m = 0,1, that is, we consider the case of so-called regular singularities. Operators with irregular singularities possess different qualitative properties and require different investigations. Since the solutions of (1.1) may have singularities at the endpoints of t...

This note contains a short review of the notion of linearization of regular matrix polynomials. The objective is clarification of this notion when the polynomial has an “eigenvalue at infinity”. The theory is extended to admit reduction by locally unimodular analytic matrix functions.

A large part of the modern theory of differential equations in the complex domain is concerned with regular singularities and holonomic systems. However the theory of differential equations with irregular singularities has a long history and has become very active in recent years. Substantial links of this theory to the theory of algebraic groups, commutative algebra, resurgent functions, and G...

Research of protein is pivotal to the drug discovery, since most of the drugs act upon proteins inside human body. Drugs act when they are close to the concave portions, so called “pockets”, of protein surfaces. Therefore, detection and analysis of the pockets are also important for the drug discovery. This paper presents a fast pocket extraction and evaluation technique for protein surfaces. S...