Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

Influence of isovalent and heterovalent substitution for Bi<Superscript>3+</Superscript> and Fe<Superscript>3+</Superscript> on the properties of Bi<Subscript>2</Subscript>Fe<Subscript>4</Subscript>O<Subscript>9</Subscript>-based solid solutions

Bi_2–хLa_хFe₄O₉ and Bi₂Fe_4–2xTi_xCo_xO₉ ferrites have been prepared by solid-state reactions at a temperature of 1073 K. X-ray diffraction data indicate that, in the Bi_2–хLa_хFe₄O₉ system, the limiting degree of La³⁺ substitution for Bi³⁺ ions in Bi₂Fe₄O₉ does not exceed 0.05 and that the limiting degree of substitution in the Bi₂Fe_4–2xTi_xCo_xO₉ system lies in the range 0.05 < x < 0.1. The specific magnetization and specific magnetic susceptibility of the samples have been measured at temperatures from 5 to 300 K in a magnetic field of 0.86 T. The field dependences of magnetization obtained for the Bi_2–хLa_хFe₄O₉ and Bi₂Fe_4–2xTi_xCo_xO₉ ferrites at temperatures of 300 and 5 K demonstrate that partial isovalent substitution of La³⁺ for Bi³⁺ ions in Bi₂Fe₄O₉ and heterovalent substitution of Ti⁴⁺ and Co²⁺ ions for two Fe³⁺ ions leads to partial breakdown of the antiferromagnetic state and nucleation of a ferromagnetic state.     

Determination of fibrin and fibrinogen split products by their anticoagulant activity

A new diagnostic method to determine fibrinogen and fibrin splitting products is based on the fact that high-molecular fragments acting as specific inhibitors of fibrin self-assembly compose these products. Fibrinogen and fibrin splitting products are detected and determined quantitatively by prolongation of coagulation time in the test with the standard monomeric fibrin. The number of units of anticoagulating activity in the studied urine are the results of the determinations. Sensitivity of the method if necessary may be increased by adding of a certain amount of the fibrinogen and fibrin splitting products to the test that makes a favourable background for the action of the products. The method is rather sensitive, reliable and simple. It may be used in ordinary clinical laboratories. The method proved to be quite satisfactory when testing renal diseases at the clinic. It is of great significance for early detection of the transplanted kidney rejection. The new method is compared with the known immunological method which consist in determination of the inhibitory effect of the fibrinogen and fibrin splitting products on agglutination of erythrocytes of specific antibodies; the erythrocytes being subjected to "tanning" and "loading" with fibrinogen. A satisfactory correlation is found between the results of two methods.     

Monitoring the Fast-Neutron Flux Density and Fluence in a RBMK Core using a Threshold Fission Chamber in a Screen-Absorber

A new method for measuring the flux density and fluence of fast neutrons in a RBMK core, using a threshold ionization fission chamber with a ²³⁸U radiator, and a computational-experimental method based on threshold chambers for fissioning of ²³⁸U with enrichment at least 99.999% are proposed. A method is proposed for taking account of the correction factors for the change in sensitivity of threshold fission chambers with and without screens on the basis of RBMK-1000 fast-neutron spectra determined experimentally by the activation method.__________Translated from Atomnaya Energiya, Vol. 98, No. 4, pp. 260–267, April, 2005.     

Minimizing the distance to one evader while chasing another

To approach a simple game Δ² of P and E = {E₁, E₂} with no a priori evaders' role assignment and the payoff equal to the distance to one evader at an instant of catching another, we introduce a concept of casting and study the games Δ_1,2 and Δ_2,1 for preassigned and Δ_p² for open-loop casting procedures. Since Δ_p² is reduced to Δ_1,2 or Δ_2,1 which, in turn, are distinguished only by their notations, we focus attention mainly on Δ_1,2. According to the tenet of transition, Δ_1,2 is divided into a concatenation of Δ_1,2^b (basic) and Δ_1,2^a (auxiliary) games that model the problem before and after the first instant of E₁ capture. The games Δ_1,2^a, Δ_1,2^b, Δ_1,2 are studied one after another with use of the Isaacs' approach extended by Berkowitz, Breakwell, Bernhard et al.     

Testing a fiber-optic ionizing-radiation detector

A fiber-optic ionizing-radiation detector is composed of a scintillation sensor, an optical fiber, and a photodetector. Due to the miniature size and the high radiation resistance, the detector is capable of measuring the characteristics of powerful neutron and γ-ray fields with a high spatial resolution. A prototype of the detector has been tested using a ⁶⁰Co γ-ray source with a dose rate as great as 200 R/S. The dynamic range of dose measurements is no less than 10⁵. The detector signal is linearly dependent on the radiation dose rate. The ratio of the useful signal to the background due to radioluminescence of the optical fiber is presented for different types of scintillators.     

A Study of Structure Evolution in Pearlitic Steel Wire at Increasing Plastic Deformation

In this work was studied the influence of the plastic deformation's intensity under deep drawing on microstructures of a pearlitic steel containing 0.8% C. Varying the levels of deformation causes diverse dislocation movements as well as modified structural states in the individual phases of the pearlitic eutectoid steel. It is shown that in the course of plastic deformation there is a reduction of interlamellar distance in a pearlite and increase in dislocation density. In some parts partial spheroidisation cementite plates is observed. The bands formed in dislocation structure are found out. The analysis of failure mechanisms of steel with pearlite structure after plastic deformation is carried out. During the deformation of pearlite, the increase in stress at the phase boundary, owing to the elastic strain incompatibility between the ferrite and cementite phases, resembles the stress concentration at grain boundaries. Pores form at the interface between the surface of the ferritic matrix and the spheroidised carbide particles. Such micro pores occur by means of plastic deformation of the ferrite's interstices around the stronger cementite owing to the reduction of the ferritic interstices and their subsequent cracking.     

A Preparative Method for the Isolation of Calponin from Molluscan Catch Muscle

We describe the development of a preparative method to isolate molluscan catch muscle, calponin. This method is based on the ability of calponin to interact with actin in a temperature-dependent manner. After extracting thin filaments, as previously described, the extract was ultracentrifuged at 2 °C. While other surface proteins of thin filaments co-precipitated with actin, calponin, along with some minor contaminants, remained in the supernatant. Calponin was purified through cation-exchange chromatography. The yield of pure protein was four-fold higher than that achieved through high-temperature extraction. To evaluate functionally isolated proteins, we determined the effect of calponin on Mg²⁺-ATPase activity of hybrid and non-hybrid actomyosin. The degree of ATPase inhibition was consistent with previously published data but strongly dependent on the environmental conditions and source of actin and myosin used. Furthermore, at low concentrations, calponin could induce the ATPase activity of hybrid actomyosin. This result was consistent with data indicating that calponin can modulate actin conformation to increase the relative content of “switched on” actin monomers in thin filaments. We assume that calponin obtained by the isolation method proposed herein is a fully functional protein that can both inhibit and induce the ATPase activity.