315 research outputs found
On total reality of meromorphic functions
We show that if a meromorphic function of degree at most four on a real
algebraic curve of an arbitrary genus has only real critical points then it is
conjugate to a real meromorphic function after a suitable projective
automorphism of the image.Comment: 13 page
Second harmonic electromagnetic emission of a turbulent magnetized plasma driven by a powerful electron beam
The power of second harmonic electromagnetic emission is calculated for the
case when strong plasma turbulence is excited by a powerful electron beam in a
magnetized plasma. It is shown that the simple analytical model of strong
plasma turbulence with the assumption of a constant pump power is able to
explain experimentally observed bursts of electromagnetic radiation as a
consequence of separate collapse events. It is also found that the
electromagnetic emission power calculated for three-wave interaction processes
occurring in the long-wavelength part of turbulent spectrum is in
order-of-magnitude agreement with experimental results
Homology class of a Lagrangian Klein bottle
It is shown that an embedded Lagrangian Klein bottle represents a non-trivial
mod 2 homology class in a compact symplectic four-manifold with
. (In versions 1 and 2, the last assumption was missing.
A counterexample to this general claim and the first proof of the corrected
result have been found by Vsevolod Shevchishin.) As a corollary one obtains
that the Klein bottle does not admit a Lagrangian embedding into the standard
symplectic four-space.Comment: Version 3 - completely rewritten to correct a mistake; Version 4 -
minor edits, added references; AMSLaTeX, 6 page
Finiteness and quasi-simplicity for symmetric K 3-surfaces
We compare the smooth and deformation equivalence of actions of finite groups on K3-surfaces by holomorphic and antiholomorphic transformations. We prove that the number of deformation classes is finite and, in a number of cases, establish the expected coincidence of the two equivalence relations. More precisely, in these cases we show that an action is determined by the induced action in the homology. On the other hand, we construct two examples to show first that, in general, the homological type of an action does not even determine its topological type, and second that K3-surfaces X and X̄ with the same Klein action do not need to be equivariantly deformation equivalent even if the induced action on H2,0(X) is real, that is, reduces to multiplication by ±1
On the number of components of a complete intersection of real quadrics
Our main results concern complete intersections of three real quadrics. We prove that the maximal number B0 2 (N) of connected components that a regular complete intersection of three real quadrics in ℙN may have differs at most by one from the maximal number of ovals of the submaximal depth [(N −1)/2] of a real plane projective curve of degree d = N +1. As a consequence, we obtain a lower bound 1/4 N2 +O(N) and an upper bound 3/8 N2+O(N) for B0 2 (N). © Springer Science+Business Media, LLC 2012
Lines on quartic surfaces
We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic. © 2016, Springer-Verlag Berlin Heidelberg
A search for disordered (glassy) phase in solid 3He deformed in situ
A disordered (glassy) state has been searched in solid 3He deformed in the
course of experiment employing precise measurements of pressure. The analysis
of the temperature dependence of the crystal pressure measured at a constant
volume shows that the main contribution to the pressure is made by the phonon
subsystem, the influence of the disordered phase being very weak. Annealing of
the deformed crystal does not affect this state. The results obtained differ
greatly from the corresponding data for solid 4He measured in the region of
supersolid effects where a pressure excessive in comparison to the phonon one
was registered. The excess pressure had a quadratic dependence on temperature,
which is typical of a disordered system. Absence of the excess pressure in
solid 3He is unclear yet, some speculative interpretations are suggested.Comment: 9 pages, 4 figure
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