Let k-l,ml,..~+k denote non-negative integers, and suppose the greatest common divisor of ml,...,mk is 1 . We show that if '1, "',sk are sufficiently long blocks of consecutive integers, then the set mlSl+ . ..+mkSk contains a sizable block of consecutive integers. For example; if m and n are relatively prime natural numbers, and U, U ? Vt V are integers with U-u 2 n-l , V-v 2 m-l 1 then the se...

This paper is about an inverse problem. We assume we are given a function f(x) which is some sum of ridge functions of the form ∑m i=1 gi(a i · x) and we just know an upper bound on m. We seek to identify the functions gi and also the directions a i from such limited information. Several ways to solve this nonlinear problem are discussed in this work. §

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic ...

Synthetic aperture radar interferometry (InSAR) has been widely used over the past two decades for such geodetic applications as topographic mapping and ground deformation monitoring. In particular, in contrast to other geodetic techniques, differential InSAR has the capability of measuring surface deformation with a measurement precision of a few millimetres and a spatial resolution of a few t...

This paper proposes a novel pattern classiication approach, called the nearest linear combination (NLC) approach, for eigenface based face recognition. Assume that multiple prototypical vectors are available per class, each vector being a point in an eigenface space. A linear combination of prototypical vectors belonging to a face class is used to deene a measure of distance from the query vect...

We define an extension of λ-calculus with linear combinations, endowing the set of terms with a structure of R-module, where R is a fixed set of scalars. Terms are moreover subject to identities similar to usual pointwise definition of linear combinations of functions with values in a vector space. We then extend β-reduction on those algebraic λ-terms as follows: at+ u reduces to at′ + u as soo...

a0Tn(x) + a1Tn−1(x) + · · ·+ amTn−m(x) where (a0, a1, . . . , am) is a fixed m-tuple of real numbers, a0, am 6= 0, Ti(x) are Chebyshev polynomials of the first kind, n = m, m + 1, m + 2, . . . Here we analyze the structure of the set of zeros of such polynomial, depending on A and its limit points when n tends to infinity. Also the expression of envelope of the polynomial is given. An applicati...

Let µ 1 (G) ≥. .. ≥ µn (G) be the eigenvalues of the adjacency matrix of a graph G of order n, and G be the complement of G. Suppose F (G) is a fixed linear combination of µ i (G) , µ n−i+1 (G) , µ i G ¡ , and µ n−i+1 G ¡ , 1 ≤ i ≤ k. It is shown that the limit lim n→∞ 1 n max {F (G) : v (G) = n} always exists. Moreover, the statement remains true if the maximum is taken over some restricted fa...

In this expository paper, linear combinations of orthogonal polynomials are considered. Properties like orthogonality and interlacing of zeros are presented.

At a conference in Debrecen in October 2010 Nathanson announced some results concerning the arithmetic diameters of certain sets. (See his paper in the present volume.) He proposed some related problems on the representation of integers by sums or differences of powers of 2 and of 3. In this note we prove some results on this problem and the more general problem about the representation by line...