Valuations on Algebras with Involution

Let A be a central simple algebra with involution sigma of first or second kind. Let v be a valuation on the sigma-fixed part F of Z(A). A sigma-special v-gauge g on A is a kind of value function on A extending v on F, such that g(sigma(x) x) = 2g(x) for all x in A. It is shown (under certain restrictions if the residue characteristic is 2) that if v is Henselian, then there is a sigma-special v-gauge g if and only if sigma is anisotropic, and g is unique. If v is not Henselian, it is shown that there is a sigma-special v-gauge g if and only if sigma remains anisotropic after scalar extension from F to the Henselization of F re v; when this occurs, g is the unique sigma-invariant v-gauge on A.Comment: 27 page

On the Pfister Number of Quadratic Forms

The generic quadratic form of even dimension n with trivial discriminant over an arbitrary field of characteristic different from 2 containing a square root of -1 can be written in the Witt ring as a sum of 2-fold Pfister forms using n-2 terms and not less. The number of 2-fold Pfister forms needed to express a quadratic form of dimension 6 with trivial discriminant is determined in various cases.Comment: 13 page

Potential Errors in a Scheme of Universal Quantum Gates in Kane's Model

We re--investigate a plausible proposal for universal quantum gates in Kane's model, in which the authors assumed that electron spin is always downward under a background magnetic field and the value of controlling parameters is varied instantaneously. We demonstrate that a considerable error appears, for example, in the X rotation. As result, the controlled operations don't work. Such a failure is caused by improper choice of the computational bases; actually, the electron spin is not always downward over time during quantum operations.Comment: 11 pages, 3 figures; improved with typos corrected; Accepted for publication in Phys. Rev.

Exact infinite-time statistics of the Loschmidt echo for a quantum quench

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasi-critical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.Comment: 4 pages, 2 figure

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

Sildenafil, a phosphodiesterase type 5 inhibitor, enhances the antidepressant activity of amitriptyline but not desipramine, in the forced swim test in mice

The cholinergic theory of depression highlights the involvement of muscarinic acetylcholine receptors in the neurobiology of mood disorders. The present study was designed to investigate the effect of sildenafil, a phosphodiesterase type 5 inhibitor which exhibits cholinomimetic properties, alone and in combination with scopolamine in the forced swim test in mice. Moreover, we assessed the ability of sildenafil to modify the antidepressant activity of two tricyclic antidepressants with distinct cholinolytic activity, amitriptyline and desipramine. Swim sessions were conducted by placing mice in glass cylinders filled with water for 6 min and the duration of behavioral immobility during the last 4 min of the test was evaluated. Locomotor activity was measured with photoresistor actimeters. To evaluate the potential pharmacokinetic interaction between amitriptyline and sildenafil, brain and serum concentrations of amitriptyline were determined by HPLC. Sildenafil (1.25–20 mg/kg) as well as scopolamine (0.5 mg/kg) and its combination with sildenafil (1.25 mg/kg) did not affect the total immobility time duration. However, joint administration of scopolamine with sildenafil at doses of 2.5 and 5 mg/kg significantly reduced immobility time as compared to control group. Moreover, co-administration of scopolamine with sildenafil at the highest dose (5 mg/kg) significantly decreased immobility time as compared to scopolamine-treated group. Sildenafil (1.25, 2.5 and 5 mg/kg) significantly enhanced the antidepressant activity of amitriptyline (5 mg/kg). No changes in anti-immobility action of desipramine (20 mg/kg) in combination with sildenafil (5, 10 and 20 mg/kg) were observed. Sildenafil did not affect amitriptyline level in both brain and serum. In conclusion, the present study suggests that sildenafil may enhance the activity of antidepressant drugs which exhibit cholinolytic activity

Indirect comparison of interventions using published randomised trials: systematic review of PDE-5 inhibitors for erectile dysfunction

BACKGROUND: There are no randomised and properly blinded trials directly comparing one PDE-5 inhibitor with another in a normal home setting. Valid indirect comparisons with a common comparator must examine equivalent doses, similar duration, similar populations, with the same outcomes reported in the same way. METHODS: Published randomised, double-blind trials of oral PDE-5 inhibitors for erectile dysfunction were sought from reference lists in previous reviews and electronic searching. Analyses of efficacy and harm were carried out for each treatment, and results compared where there was a common comparator and consistency of outcome reporting, using equivalent doses. RESULTS: Analysis was limited by differential reporting of outcomes. Sildenafil trials were clinically and geographically more diverse. Tadalafil and vardenafil trials tended to use enriched enrolment. Using all trials, the three interventions were similar for consistently reported efficacy outcomes. Rates of successful intercourse for sildenafil, tadalafil and vardenafil were 65%, 62%, and 59%, with placebo rates of 23–28%. The rates of improved erections were 76%, 75% and 71%, respectively, with placebo rates of 22–24%, and NNTs of 1.9 or 2.0. Reporting of withdrawals was less consistent, but all-cause withdrawals for sildenafil, tadalafil and vardenafil were 8% 13% and 20%. All three drugs were well tolerated, with headache being the most commonly reported event at 13–17%. There were few serious adverse events. CONCLUSION: There were differences between trials in outcomes reported, limiting comparisons, and the most useful outcomes were not reported. For common outcomes there was similar efficacy between PDE-5 inhibitors