given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

To determine the number of maximal mouth pressure manoeuvres needed to obtain a reproducible value of maximal inspiratory mouth pressure (MIP), we studied 44 patients with chronic airflow obstruction, with a mean (SD) % predicted FEV1 value of 53.9 (25), who were clinically stable. Maximal inspiratory mouth pressure was determined with an anaeroid manometer during maximal inspiratory efforts in...

Let G(n; m) be a connected graph without loops and multiple edges which has n vertices and m edges. We ÿnd the graphs on which the zeroth-order connectivity index, equal to the sum of degrees of vertices of G(n; m) raised to the power − 1 2 , attains maximum.

∂tw +A(v)w = f(v) in J̊ , w(0) = 0 has a unique solution w = w(v) ∈W(J). Clearly, a fixed point of the map v 7→ w(v) is a solution of (1). Fixed point arguments of this type are, of course, omnipresent in the study of evolution equations of type (1). The new feature of our work, which distinguishes it from all previous investigations, is that we assume that W(J) is a maximal regularity space and...

The segment minimization problem consists of finding a smallest set of binary matrices (segments), where non-zero values in each row of each matrix are consecutive, each matrix is assigned a positive integer weight (a segment-value), and the weighted sum of the matrices corresponds to the given input intensity matrix. This problem has direct applications in intensitymodulated radiation therapy,...

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

Checking linear dependence of a finite number of vectors is a basic problem in linear algebra. We aim to extend the theory of linear dependence to parametric vectors where the entries are polynomials. This dependency depends on the specifications of the parameters or values of the variables in the polynomials. We propose a new method to check if parametric vectors are linearly dependent. Furthe...

Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. We consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem...

Let K be a p-adic field, R the valuation ring of K, P the maximal ideal of R and q the cardinality of the residue field R/P . Let f be a polynomial over R in n > 1 variables and let χ be a character of R×. Let Mi(u) be the number of solutions of f = u in (R/P i)n for i ∈ Z≥0 and u ∈ R/P i. These numbers are related with Igusa’s p-adic zeta function Zf,χ(s) of f . We explain the connection betwe...