143 research outputs found
Generic algebras with involution of degree 8m
The centers of the generic central simple algebras with involution are
interesting objects in the theory of central simple algebras. These fields also
arise as invariant fields for linear actions of projective orthogonal or
symplectic groups. In this paper, we prove that when the characteristic is not
2, these fields are retract rational, in the case the degree is and is
odd. We achieve this by proving the equivalent lifting property for the class
of central simple algebras of degree with involution. A companion paper
([S3]) deals with the case of , and where stronger rationality
results are proven.Comment: 7 page
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
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
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.
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
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