Abstract:
Reconnection rate is found for the canonical simplest case of steady-state two-dimensional symmetric reconnection in an incompressible plasma by matching of outer Petschek solution and internal diffusion region solution. The reconnection rate obtained naturally incorporates both Sweet-Parker and Petschek regimes, the latter seems to be possible only for the case with strongly localized resistivity.

Abstract:
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.

Abstract:
The spatial local anomalies of the concentration ratios for isotopes ^{143}Nd/^{144}Nd (or εNd) and ^{87}Sr/^{86}S in Lukkulaisvaara intrusion (North Karelia) were discovered. The physical mechanisms and the descriptions of the effect of an arising of those anomalies were developed and presented. The base of the proposed mechanisms is the phenomena of the migration (diffusion) of components, due to the (T, P (or D)) gradients. The description of the processes of an arising of the gradients of a temperature (T), of a pressure (P) and of a deformation (D) in the layered inhomogeneous intrusion during its formation and evolution, were obtained. It was shown that the gradients can induce the spatial redistribution of the chemical elements and their isotopes in the intrusion. The redistribution, in turn, can lead to the observed spatial concentration anomalies for these components. It was first obtained the expressions for the diffusion additions to the isotope’s parameter ε (εNd, in part).

Abstract:
In the MHD description of plasma phenomena the concept of magnetic field lines frozen into the plasma turns out to be very useful. We present here a method of introducing Lagrangian coordinates into relativistic MHD equations in general relativity, which enables a convenient mathematical formulation for the behaviour of flux tubes. With the introduction of these Lagrangian, so--called ``frozen--in'' coordinates, the relativistic MHD equations reduce to a set of nonlinear 1D string equations, and the plasma may therefore be regarded as a gas of nonlinear strings corresponding to flux tubes. Numerical simulation shows that if such a tube/string falls into a Kerr black hole, then the leading portion loses angular momentum and energy as the string brakes, and to compensate for this loss, momentum and energy is radiated to infinity to conserve energy and momentum for the tube. Inside the ergosphere the energy of the leading part turns out to be negative after some time, and the rest of the tube then gets energy from the hole. In our simulations most of the compensated positive energy is also localized inside the ergosphere because the inward speed of the plasma is approximately equal to the velocity of the MHD wave which transports energy outside. Therefore, an additional physical process has to be included which can remove energy from the ergophere. Magnetic reconnection seems fills this role releasing Maxwellian stresses and producing a relativistic jet.

Abstract:
The reconnection rate is obtained for the simplest case of 2D symmetric reconnection in an incompressible plasma. In the short note (Erkaev et al., Phys. Rev. Lett.,84, 1455 (2000)), the reconnection rate is found by matching the outer Petschek solution and the inner diffusion region solution. Here the details of the numerical simulation of the diffusion region are presented and the asymptotic procedure which is used for deriving the reconnection rate is described. The reconnection rate is obtained as a decreasing function of the diffusion region length. For a sufficiently large diffusion region scale, the reconnection rate becomes close to that obtained in the Sweet-Parker solution with the inverse square root dependence on the magnetic Reynolds number, determined for the global size of the current sheet. On the other hand, for a small diffusion region length scale, the reconnection rate turns out to be very similar to that obtained in the Petschek model with a logarithmic dependence on the magnetic Reynolds number. This means that the Petschek regime seems to be possible only in the case of a strongly localized conductivity corresponding to a small scale of the diffusion region.

Abstract:
The article shows that inflation could be controled in the consumer market through reducing its rates and reducing inflation risks. The approach lies in consideration of risks of ingredients of the consumer choice as a component of a common consumer basket and not that of individual units. The level of correlations of price growth of goods of consumer choice lies in the centre of attention of the offered strategy of control. It is necessary to note that realisation of such measures as regulation of consumer demand and purposeful change of the structure of consumption – is a task, which could be solved only within the framework of the state policy. The state should use its power in the field of taxation, expenditures and monetary policy when eliminating economic instability. Показано, что инфляцией на потребительском рынке можно управлять, снижая ее темпы и уменьшая инфляционные риски. Сущность подхода заключена в том, чтобы рассматривать риски ингредиентов потребительского набора, как составляющую единой потребительской корзины, а не отдельно взятых единиц. В центре внимания предлагаемой стратегии управления находится уровень корреляций ценовых ростов товаров потребительского набора. Необходимо отметить, что реализация таких мер, как регулирование потребительского спроса, целенаправленное изменение структуры потребления ? это задача, которая может быть решена только в рамках государственной политики. Государство должно использовать свою власть в области налогообложения. расходов и денежной политики при устранении экономической нестабильности.

Abstract:
Lactaptin, the proteolytic fragment of human milk kappa-casein, induces the death of various cultured cancer cells. The mechanisms leading to cell death after lactaptin treatment have not been well characterized. In this study the in vivo and in vitro effects of a recombinant analogue of lactaptin (RL2) were examined. Following treatment with the recombinant analogue of lactaptin strong caspase -3, -7 activation was detected. As a consequence of caspase activation we observed the appearance of a sub-G1 population of cells with subdiploid DNA content. Dynamic changes in the mRNA and protein levels of apoptosis-related genes were estimated. No statistically reliable differences in p53 mRNA level or protein level were found between control and RL2-treated cells. We observed that RL2 constitutively suppressed bcl-2 mRNA expression and down regulated Bcl-2 protein expression in MDA-MB-231 cells. We demonstrated that RL2 penetrates cancer and non-transformed cells. Identification of the cellular targets of the lactaptin analogue revealed that α/β-tubulin and α-actinin-1 were RL2-bound proteins. As the alteration in cellular viability in response to protein stimulus can be realized not only by way of apoptosis but also by autophagy, we examined the implications of autophagy in RL2-dependent cell death. We also found that RL2 treatment induces LC3-processing, which is a hallmark of autophagy. The autophagy inhibitor chloroquine enhanced RL2 cytotoxicity to MDA-MB-231 cells, indicating the pro-survival effect of RL2-dependent autophagy. The antitumour potential of RL2 was investigated in vivo in mouse xenografts bearing MDA-MB-231 cells. We demonstrated that the recombinant analogue of lactaptin significantly suppressed the growth of solid tumours. Our results indicate that lactaptin could be a new molecule for the development of anticancer drugs.

Abstract:
A research of inductive conductometric cell is presented. An equivalent circuit and a mathematical model of inductive cell are given in the article. The model takes into account sample-coil capacity (i.e. capacity formed by the coil and the sample under study) and eddy currents. It is sample-coil capacity that makes inductive cell applicable for measurement of electrical conductivity of low conductive samples (specific conductance is less than 1S/m). The model can be used to calculate impedance of inductive cell for different characteristics of sample, materials and dimensions of cell without numerical solving of partial differential equations. Results of numerical simulation were verified by experiment for several devices with inductive cell. Some features that an engineer has to hold in mind while designing a conductometer based on inductive cell are discussed. Presented model can be useful for those who study inductively coupled plasma.

Abstract:
We show how to translate the task of computing the multiplicative structure of a Chow ring of a projective homogeneous variety into an easily understandable combinatorial task of calculating in the corresponding polynomial ring. The algorithms are also presented as a Maple package. Then we proceed to compute the multiplicative structure of the Chow rings for projective homogeneous varieties E6/P1, E7/P7, and E8/P8.

Abstract:
GU "wobble" pair may contain either the enol form of uracil and the keto form of guanine or the enol form of guanine and the keto form of uracil. A direct proof of uracil existence in enol form can be obtained by using NMR spectroscopy. In HNN-COSY experiments the GU pair imitates the GC pair due to the enolization of uracil.