On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models

Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three integrals of motions are constructed and equations of motion are solved exactly in the special cylindrical coordinates on the base of the method of separation of variables. In Lobachevsky space there exist trajectories of two types, finite and infinite in radial variable, in Riemann space all motions are finite and periodical. The invariance of the uniform magnetic field in tensor description and gauge invariance of corresponding 4-potential description is demonstrated explicitly. The role of the symmetry is clarified in classification of all possible solutions, based on the geometric symmetry group, SO(3,1) and SO(4) respectively

Motion Caused by Magnetic Field in Lobachevsky Space

We study motion of a relativistic particle in the 3-dimensional Lobachevsky space in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in the Euclidean space. Three integrals of motion are found and equations of motion are solved exactly in the special cylindrical coordinates. Motion on surface of the cylinder of constant radius is considered in detail.Comment: 4 page

A note on “The tanh–coth method combined with the Riccati equation for solving nonlinear coupled equation in mathematical physics”

AbstractThe recent paper “The tanh–coth method combined with the Riccati equation for solving nonlinear coupled equation in mathematical physics” (J. King Saud Univ. Sci. 23 (2011) 127–132) is analyzed. We show that the authors of this paper solved equations with the well known solutions. One of these equations is the famous Riccati equation and the other equation is one for the Weierstrass elliptic function. We present the general solutions of these equations. As this takes place, 19 solutions by authors do not satisfy the equation but the other 29 solutions can be obtained from the general solutions

The role of ACTH and glucocorticoids in nonenzymatic fibrinolysis during immobilization stress in animals

The role of the altered hormonal status of an organism in the activation of the anticoagulative system during stress is investigated. The 30 minute immobilization stress was shown to raise significantly the nonenzymatic fibrinolytic activity of blood in rats. Combined with adrenocorticotropin (ACTH) the effect is still greater. Intravenous administration of 0.2 m1 0.01 percent solution of protamine sulphate prevented the nonenzymatic fibrinolysis induced by the stress. Administration of ACTH after protomine sulphate again raised the fibrinolysis. This suggests that ACTH stimulates the release of heparin

The effects of adrenalectomy and corticsteroid injection on the fibrinolytic activity of complex heparin compounds in the blood during immobilization

Total non-enzymatic fibrinolytic activity in the blood of rats increased three times in response to stress caused by 30 minute immobilization, and the activity of epinephrine-heparin complex increased nine times. In adrenalectomized animals, which showed a weak response to the same stress, intraperitoneal injection of hydrocortisone 30 minutes prior to immobilization normalized the response. Obtained results indicate that adrenalectomy leads to sharp reduction of heparin complexing with thromogenic proteins and epinephrine, while substitution therapy with hydrocortisone restores anticoagulation system function

Ultrafast changes in the optical properties of a titanium surface and femtosecond laser writing of one-dimensional quasi-periodic nanogratings of its relief

One-dimensional quasi-periodic nanogratings with spacings in the range from 160 to 600 nm are written on a dry or wet titanium surface exposed to linearly polarized femtosecond IR and UV laser pulses with different surface energy densitiesye

Formation of periodic nanostructures on aluminum surface by femtosecond laser pulses

One-dimensional periodic nanostructures have been produced on the surface of an aluminum specimen using femtosecond laser pulses at wavelengths of 744 and 248 nm. The nanostructurization of the specimen has been conducted in water and in air in the preablation regime. We investigate the dependence that the surface topology has on the parameters of laser radiation, as well as on the medium in contact with the specimen surfaceye