A common way of computing the roots of a polynomial is to find the eigenvalues of a linearization, such as the companion (when the polynomial is expressed in the monomial basis), colleague (Chebyshev basis) or comrade matrix (general orthogonal polynomial basis). For the monomial case, many studies exist on the stability of linearization-based rootfinding algorithms. By contrast, little seems t...

Reaction of [ (ML,CI),] with TI[9-SMe,-nido-7,8-C,B,H,,1 affords the new compounds [3,3-L2-4-SMe,closo-3.1 ,2-MC,B,Hl,]. Compounds 1 ( M = Rh, L = CO), 2 ( M = Rh, L2 = I12,T12-1,5-C8H12) and 3 (M = Pd, L, = qz,o-5-OMe-C8H,,) were characterised by microanalysis, multinuclear N M R spectroscopy and, in the case of 1 and 2, single-crystal X-ray diffraction studies. The experimentally determined c...

Recently, an extension of the class of matrices admitting a Francis type of multishift QR algorithm was proposed by the authors. These so-called condensed matrices admit a storage cost identical to that of the Hessenberg matrix and share all of the properties essential for the development of an effective implicit QR type method. This article continues along this trajectory by discussing the gen...

Neuronal membrane potential resonance (MPR) is associated with subthreshold and network oscillations. A number of voltage-gated ionic currents can contribute to the generation or amplification of MPR, but how the interaction of these currents with linear currents contributes to MPR is not well understood. We explored this in the pacemaker PD neurons of the crab pyloric network. The PD neuron MP...

We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the lowest pair of electronic states, approximate ”vibronic” (vibration-electronic) ground state wave functions are constructed having the form of simple, closed ex...

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real function defined on the set of finite graphs, by sampling a randomly chosen substructure whose size is independent of the size of the input. Graph parameters that may be successfully estimated in this way are said to be testable or estimable, and the sample complexity qz = qz(ε) of an estimable par...

The electrocardiographic and vectorcardiographic (Frank system) features of the first degree relatives of subjects with documented familial hypertrophic cardiomyopathy were analysed. A total of nine affected members and 29 relatives were examined in four families. THe subjects were considered to be affected when the septal to free posterior wall thickness ratio exceeded 1.3 at M-mode echocardio...