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

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 $(X,\omega)$ with $c_1(X)\cdot[\omega]>0$. (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

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

Application of therapeutic physical exercises and massage in treatment and rehabilitation of patients with muscular torticollis

The paper presents recommendations for the use of physical exercises and massage in the treatment and rehabilitation of patients withmuscular torticollis. Recommendations are intended for surgeons, doctors and exercise instructors with higher and secondary education, massagetherapists and paediatricians hospitals and clinics

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