Finding of the optimal parameters of animated and stereographic rainbow diffractive images

We have considered the basic aspects of the technology of animated and stereographic rainbow images. These images can be included in Optical Security Devices (OSDs) in order to increase their structure complexity and to improve their protective properties. The cited technology provides, on the one hand, a simple identification on the visual level of verification and, on the other hand, the sufficient reliability against counterfeits. The last property is achieved at first by the division of the elemental unit on elemental regions of any adjusted shape with outline of the precision that is inaccessible for the recreation without Electron Beam Lithography Equipment (EBLE) which is used for the recording of OSDs. Second, the used encoding methods also assure the certain reliability. In the context of the paper, the theoretical discussion based a quantitative formulation of the Huygens--Fresnel law of the diffraction on an elemental diffractive grating is carried out. For other definite Conditions of Lighting and Observation of Diffracting Light (CLODL), the correlation between the slope angle of diffraction grating strokes and the corresponding horizontal parallax angle is got; and the parameter which defines the channel selection (the quality of splitting into separate channels) is introduced. The rule for the definition of the wavelength and the intensity of light that diffracts on a given grating under certain CLODL is derived as well. This fact allows one to create the software utility that models the behavior of anigrams or stereograms. An algorithm of the synthesis of anigrams and stereograms as parts of OSDs using the technology of a composite “figure” elemental unit (that is composed from parts of any shape) and applying the halftone encoding by the period, filling, and achromaticity or all these parameters at once is elaborated, and its software implementation is constructed. The criteria for the choice of such anigram’s parameters as the resolution, number of channels, and angle distances between them are elaborated. In order to check them, the results of tests are summarized. The investigation of the optimal parameters of halftone images’ encoding finding is implemented, and the results obtained for the tough and flexible linkings of a channel to the subregion of an elemental unit for hatching images are compared

The Dynamics of a Rigid Body in Potential Flow with Circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte

The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

Multilevel computer-generated holograms for reconstructing 3-D images in combined optical-digital security devices

Computer-generated holograms (CGHs) integrated within combined optical-digital security devices (CO/DSDs) are described in this work. They can restore the monochrome and color 3D images in white light. To record them, the Electron Beam Lithography (EBL) is used. Our investigations on optimization of synthesis and recording the CO/DSDs with the integrated in it multilevel CGHs of 3D images possessed horizontal parallax only (HPO) are presented here. The CGH fabrication process is mainly composed of two parts: calculation of the interferogram data (ID) and their recording. Calculation of the ID is done as follows: firstly, the geometrical and optical constants of recording scheme and the object surface represented by the elemental self-radiating areas, are determined, secondly, the basic parameters accounting for discretization of ID in hologram plane is defined. The ID values can be derived by calculation of the necessary elemental object areas bipolar intensities sum. Next, over suitable quantization of ID, recording the rectangle data appropriate for EBL onto glass coated with non-organic photoresist based on As₄₀S₄₀Se₂₀ is performed. We have also investigated reciprocal influence of an optical part of the CO/DSD and a digital one

The Spinning Particles as a Nonlinear Realizations of the Superworldline Reparametrization Invariance

The superdiffeomorphisms invariant description of $N$ - extended spinning particle is constructed in the framework of nonlinear realizations approach. The action is universal for all values of $N$ and describes the time evolution of $D+2$ different group elements of the superdiffeomorphisms group of the $(1,N)$ superspace. The form of this action coincides with the one-dimensional version of the gravity action, analogous to Trautman's one.Comment: 4 pages, RevTe

Measurement of xF3xF_3 and F2F_2 Structure Functions in Low Q2Q^2 Region with the IHEP-JINR Neutrino Detector

The isoscalar structure functions $xF_3$ and $F_2$ are measured as functions of $x$ averaged over all $Q^2$ permissible for the range of 6 to 28 GeV of incident neutrino (anti-neutrino) energy at the IHEP-JINR Neutrino Detector. The QCD analysis of $xF_3$ structure function provides $\Lambda_{\bar{MS}}^{(4)} = (411 \pm 200)$ MeV under the assumption of QCD validity in the region of low $Q^2$. The corresponding value of the strong interaction constant $\alpha_S (M_Z) = 0.123^{+0.010}_{-0.013}$ agrees with the recent result of the CCFR collaboration and with the combined LEP/SLC result.Comment: 11 pages, 1 Postscript figure, LaTeX. Talk given at the 7th International Workshop on Deep Inelastic Scattering and QCD (DIS 99), Zeuthen, Germany, 19-23 Apr 199

The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.Comment: 13 page