The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Phasic modulation of corticomotor excitability during passive movement of the upper limb: effects of movement frequency and muscle specificity

Modulations in the excitability of spinal reflex pathways during passive rhythmic movements of the lower limb have been demonstrated by a number of previous studies [4]. Less emphasis has been placed on the role of supraspinal pathways during passive movement, and on tasks involving the upper limb. In the present study, transcranial magnetic stimulation (TMS) was delivered to subjects while undergoing passive flexion-extension movements of the contralateral wrist. Motor evoked potentials (MEPs) of flexor carpi radialis (FCR) and abductor pollicus brevis (APB) muscles were recorded. Stimuli were delivered in eight phases of the movement cycle during three different frequencies of movement. Evidence of marked modulations in pathway excitability was found in the MEP amplitudes of the FCR muscle, with responses inhibited and facilitated from static values in the extension and flexion phases, respectively. The results indicated that at higher frequencies of movement there was greater modulation in pathway excitability. Paired-pulse TMS (sub-threshold conditioning) at short interstimulus intervals revealed modulations in the extent of inhibition in MEP amplitude at high movement frequencies. In the APE muscle, there was some evidence of phasic modulations of response amplitude, although the effects were less marked than those observed in FCR. It is speculated that these modulatory effects are mediated via Ia afferent pathways and arise as a consequence of the induced forearm muscle shortening and lengthening. Although the level at which this input influences the corticomotoneuronal pathway is difficult to discern, a contribution from cortical regions is suggested. (C) 2001 Published by Elsevier Science B.V.

The impact of dose escalation and resistance modulation in older patients with acute myeloid leukaemia and high risk myelodysplastic syndrome: the results of the LRF AML14 trial.:the results of the LRF AML14 trial

The acute myeloid leukaemia (AML)14 trial addressed four therapeutic questions in patients predominantly aged over 60 years with AML and High Risk Myelodysplastic Syndrome: (i) Daunorubicin 50 mg/m(2) vs. 35 mg/m(2); (ii) Cytarabine 200 mg/m(2) vs. 400 mg/m(2) in two courses of DA induction; (iii) for part of the trial, patients allocated Daunorubicin 35 mg/m(2) were also randomized to receive, or not, the multidrug resistance modulator PSC-833 in a 1:1:1 randomization; and (iv) a total of three versus four courses of treatment. A total of 1273 patients were recruited. The response rate was 62% (complete remission 54%, complete remission without platelet/neutrophil recovery 8%); 5-year survival was 12%. No benefits were observed in either dose escalation randomization, or from a fourth course of treatment. There was a trend for inferior response in the PSC-833 arm due to deaths in induction. Multivariable analysis identified cytogenetics, presenting white blood count, age and secondary disease as the main predictors of outcome. Although patients with high Pgp expression and function had worse response and survival, this was not an independent prognostic factor, and was not modified by PSC-833. In conclusion, these four interventions have not improved outcomes in older patients. New agents need to be explored and novel trial designs are required to maximise prospects of achieving timely progress.