This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise inputdependant bounds on these coefficients. Such bounds are e.g. useful to perform deterministic chinese remaindering of the characteristic or minimal polynomi...

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

conclusions we can conclude that treatment of af using a right-sided minithoracotomy approach and rf energy in patients undergoing cardiac surgery for various valve diseases is feasible, safe, and reproducible. objectives our aim is to evaluate the feasibility, safety, and immediate plus medium-term results of concomitant af ablation therapy in patients undergoing minimally invasive valve surge...

background: one of the main causes of sexually transmitted diseases is group b β- hemolytic streptococci (gbs) multiplying in the genital tracts. penicillin is the most common drug for the treatment of infections caused by these bacteria, but in patients suffering from penicillin allergy, erythromycin and clindamycin are used as alternative therapeutic drugs against gbs. recently, resistance to...

We show that for all n and α such that 1 ≤ n ≤ α ≤ 2 there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.

Acta Crystallographica Section A: Foundations of Crystallography covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic d...

Proof of Claim 1.1: Of course, we assume that {nj}j=1 are all distinct. Let n1 = 1. Then there must exist An2 such that An2 ∩An1 6= ∅. If not, then An1 ∩Aj = ∅ for all j 6= n1. Thus, An1 ⊆ Aj for all j 6= n1. Now, fix some j0 6= n1 such thatAj0 6= An1 . Then, sinceF is a σ-algebra, we have thatAk0 = A c j0 for some k0 6= n1. Thus, setting j = k0 6= n1, An1 ⊆ Ack0 = ( Acj0 )c = Aj0 . The only wa...