Quasi-exactly solvable quartic: elementary integrals and asymptotics

We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an interesting identity which is used to describe the spectral locus. We also establish some asymptotic properties of the QES spectral locus.Comment: 20 pages, 1 figure. Added Introduction and several references, corrected misprint

Magnetic resonance study of the spin-reorientation transitions in the quasi-one-dimensional antiferromagnet BaCu2Si2O7

A quasi-one dimensional antiferromagnet with a strong reduction of the ordered spin component, BaCu2Si2O7, is studied by the magnetic resonance technique in a wide field and frequency range. Besides of conventional spin-flop transition at the magnetic field parallel to the easy axis of spin ordering, magnetic resonance spectra indicate additional spin-reorientation transitions in all three principal orientations of magnetic field. At these additional transitions the spins rotate in the plane perpendicular to the magnetic field keeping the mutual arrangement of ordered spin components. The observed magnetic resonance spectra and spin-reorientation phase transitions are quantitatively described by a model including the anisotropy of transverse susceptibility with respect to the order parameter orientation. The anisotropy of the transverse susceptibility and the strong reduction of the anisotropy energy due to the quantum spin fluctuations are proposed to be the reason of the spin reorientations which are observed.Comment: RevTeX, 9 pages, 7 figure

Characteristics of anomalously high multiplicity cosmic ray interactions

Six events with the number of secondaries ranging from 250 to several thousands were registered by an installation consisting of a thin graphite target, above and under which are placed photolayers followed by the usual lead X-ray film and emulsion chambers. Data concerning the number of secondaries and their angular distribution are given. The variance of the angular distribution is compared with data obtained at accelerator energies

<i>Bacillus anthracis</i> Siderophores

Iron is an essential for growth and reproduction of bacteria element. One of the ways of its acquisition by Bacillus anthracis is utilization of high-affinity chelating agents of iron ions - bacillibactin and petrobactin siderophores, extracting the iron from transferring and ferritin of a host cell. Bacillibactin and petrobactin functions are realized on different stages of B. anthracis growth in vivo, whereas petrobactin synthesis is also necessary for manifestation of microbe virulence. Awareness of siderophore biosynthesis pathways facilitates the development of medicines against anthrax, which can block them up. The review contains the data on the structure, genetics, and functions of B. anthracis siderophores

Uncertainty of the implementation time of geodynamic monitoring system in multi-criteria ranking of alternatives

The paper deals with the problem of ranking alternatives to geodynamic monitoring systems in the case of uncertainty of their implementation time. The problem is characterized by the fact that the choice of alternatives and the effect of it depends on the quality properties of the applied organizational and technical solutions, taking into account the time of implementation. The ordering of alternatives is proposed taking into account the uncertainty of the implementation time factors. Ranking is realized by comparing the trees of functional characteristics of alternatives taking into account the compliance of their characteristics with time-varying requirement

Development of neural network model of the multiparametric technological object

At present, there are a large number of methods for identifying the technological objects on the basis of data of their industrial operation [1-3]. The most promising direction is the construction of a model, which will allow to take into account the multifactorial nature of the object, and the nonlinearity of interrelation between variables. This will make it possible to control the object, taking into account the change in its states, and based on the current data,to predict the change in the output value with different input characteristics[4-6]. All this will provide the opportunity to create an operating system, based on the currently measured technological indicators. In order to implement this approach, a comparative study of the regression analysis models, using polynomials of various types and neural network algorithms, for the synthesis of a complex technological unit model, was carried out in the work. In the regression analysis, the following models were investigated: polynomials, linear, fractional and exponential functions, Kolmogorov-Gabor polynomial. In the process of the research of neural networks to solve this problem, their structure was varied, with subsequent learning according to the Levenberg-Marcardt algorithm. In the process of simulation of the object models in the Matlab package, the degree of similarity of the outputs for each of the obtained models and the actual output of the object were estimated. Quadratic criterion and the coefficient of correlation were calculated, that made it possible to judge the accuracy of the constructed models. The best structure of the model was established for identifying a complex multiparameter object, using the example of statistics for the operation of a ball mill.It was a network with three hidden layers and 50, 35 and 25 neurons in them, with activation functions, respectively by layers - hyperbolic tangent, sigmoid function in 2 layers, and a linear activation function in the output layer. The vector, including 15 parameters, was supplied to the network input: the volume of ore supply to the mill, the volume of water supply to the mill and the mill’strommel, the signals with the first-, the second-, and the thirdorder lags, and the signal of current with the first-, the second-, and the third-order lags. This approach to identification has increased the accuracy of the object model, that ultimately will affect the quality of the developed control system of the unit as a whole, allowing to improve the quality of the ball millcontrol