Abstract:
Recently we have shown the presence of catalytically active IgGs, capable to cleave histone H1 and bovine myelin basic protein (MBP), in blood serum of SLE patients. Here we present data that demonstrate the correlation between a) proteolytic activity towards histone H1 and MBP of IgG-antibodies from blood serum of SLE patients and b) disease severity level in these patients. IgGs were isolated from blood serum by chromatography on protein G-sepharose. Commercial preparations of bovine myelin basic proteins (MBP) and calf thymus histone H1 were used as substrates. Analysis of the proteolytic activity showed that 16 of 38 lgG-preparations (42,1%) obtained from blood serum of SLE patients were capable of cleaving both histone H1 and MBP with different efficiency. It was revealed that the presence in blood serum of lgGs possessing proteolytic activity towards both histone H1 and bMBP closely correlates with manifestation of the disease severity in SLE patients.

Abstract:
The contemporary concept of self-defense is complex and confusing. Every country recognizes the right of self-defense under Article 51 of the UN Charter, however, when it comes to any deviation from its wording, disputes arise. The main questions today which remain quite controversial are whether preemptive and preventive strikes are allowed in international law, does desire to protect nationals qualify as a suitable reason for invoking self-defense and whether the self-defense against "terrorism of global reach" is a new, individual concept of international law or if it is an extension of the classic theory, and whether it is self-defense at all. The July War (the Second Lebanon War) sparked many debates among legal scholars, amidst them a question, whether Israel's actions fall within the scope of permissible self-defense. Two years after the conflict, there is nothing but a few articles written on this matter and academics tend to avoid the issue, although the question requires utmost attention. The aim of this paper is to determine whether the events prior to the Israeli attack can be considered valid grounds for self-defense under article 51 of the UN Charter and whether Israel's retaliation complies with public international law.

Abstract:
Modeling method for forecasting of social-economic processes in accordance with methodology of applique fractal crystals growth methods in fuzzy attraction potential field was proposed. Impact of model empirical parameters on appearance of fractal structure fluctuations in the form of creating additional aggregation centers was investigated. Computer experiments give a possibility to simulate structures which are well correlated with experimental data received.

Abstract:
Fluxon transmission through several impurities of different strength and type (i.e., microshorts and microresistors), placed in a long Josephson junction is investigated. Threshold pinning current on the impurities is computed as a function of the distance between them, their amplitudes and the dissipation parameter. It is shown that in the case of consequently placed microshorts or microresistors, the threshold pinning current exhibits a clear minimum as a function of the distance between the impurities. In the case of a microresistor, followed by a microshort, an opposite phenomenon is observed, namely the threshold pinning current exhibits maximum as a function of the distance between the impurities.

Abstract:
An approach to a Unified Field Theory (UFT) is developed as an attempt to establish unification of the Theory of Quantum Fields (QFT) and General Theory of Relativity (GTR) on the background of a covariant differential calculus. A dual State Vector field (DSV)consisting of covariant and contravariant N-component functions of variables of a N-dimensional unified manifod (UM)is introduced to represents matter. DSV is supposed to transform in a way distinct from that of the differentials of the UM variables. Consequently, the hybrid tensors and a hybrid affine tensor (Dynamic Connection, DC) are introduced. The hybrid curvature form (HCF) is introduced as a covariant derivative of DC. A system of covariant Euler-Lagrange (EL) equations for DSV, DC, and a twin couple of the triadic hybrid tensors (Split Metric, SM)is derived. A scalar Lagrangian form is composed based on a set of principles suited for UFT, including the homogeneity in the UM space, differential irreducibility and scale invariance. The type of the manifold geometry is not specified in advance, in neither local (signature) nor regional (topology) aspects. Equations for DSV play role of the Schroedinger-Dirac equation in space of UM. By the correspondent EL equations, DC and SM are connected to DSV and become responsible for the non-linear features of the system i.e. interactions. In this paper we mark breaking of a background paradigm of the modern QFT, the superposition principle. The issue of the UM-MF dimensionality will be addressed, and relations to the principles and methodology of QFT and GTR will be discussed.

Abstract:
A stochastic process with self-interaction as a model of quantum field theory is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with interaction of the form x^{(\alpha)}(t)^4, where $\alpha$ indicates the fractional derivative. Using Bogoliubov's R-operation we investigate ultraviolet divergencies for the various parameters $\alpha$. Ultraviolet properties of this one-dimensional model in the case $\alpha=3/4$ are similar to those in the $\phi^4_4$ theory but there are extra counterterms. It is shown that the model is two-loops renormalizable. For $5/8\leq \alpha < 3/4$ the model has a finite number of divergent Feynman diagrams. In the case $\alpha=2/3$ the model is similar to the $\phi^4_3$ theory. If $0 \leq \alpha < 5/8$ then the model does not have ultraviolet divergencies at all. Finally if $\alpha > 3/4$ then the model is nonrenormalizable. This model can be used for a non-perturbative study of ultraviolet divergencies in quantum field theory and also in theory of phase transitions.

Abstract:
We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is, for the case of weak gravitational fields. Explicit formulae are presented which relate General Relativistic independent variables, Lagrangean mass coordinate and variables in the lab-frame. Conversion of one set of variables into another requires knowing the solution to the set of equations. These formulae allow one to translate the solution to the exact set in General Relativity into the form in which Special Relativistic solutions are usually obtained. This is applicable for comparison of SR-numerical simulations of collapses, GRBs and Supernovae explosions with more precise GR-simulations.

Abstract:
Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice that is driven by the oscillating force is studied. The investigation is focused mostly on the properties of the mode-locked states in the {\it overband} case, when the driving frequency lies above the linear band. With the help of Floquet theory it is demonstrated that the destabilizing of the mode-locked state happens either through the Hopf bifurcation or through the tangential bifurcation. It is also observed that in the overband case the standing mode-locked kink state maintains its stability for the bias amplitudes that are by the order of magnitude larger than the amplitudes in the low-frequency case.

Abstract:
Directed motion and depinning of topological solitons in a strongly discrete damped and biharmonically ac-driven array of Josephson junctions is studied. The mechanism of the depinning transition is investigated in detail. We show that the depinning process takes place through chaotization of an initially standing fluxon periodic orbit. Detailed investigation of the Floquet multipliers of these orbits shows that depending on the depinning parameters (either the driving amplitude or the phase shift between harmonics) the chaotization process can take place either along the period-doubling scenario or due to the type-I intermittency.

Abstract:
In this paper we produce further specification of the geometric and algebraic properties of the earlier introduced superdimensional dual-covariant field theory (SFT) in a N-dimensional manifold [1] as an approach to a unified field theory (UFT). Considerations in the present paper are directed by a requirement of transformational invariance of connections of derivatives of dual state vector (DSV) and unified gauge field (UGF matrices) to these objects themselves established by mean of N split metric matrices of a rank {\mu} (SM, an extended analog of Dirac matrices) in frame of the related Euler-Lagrange equations for DSV, UGF and SM derived in [1]. This requirement is posed on SFT as one of the aspects of the general demand of irreducibility claimed to UFT; it leads to rotational invariance of SM and grand metric tensor (GM) as being structured on SM. Study in this work has led to explication of geometrical nature of SM and DSV as spin-affinors (variable in space of the unified manifold) and dual spin-field, respectively, in accordance with the E. Cartan's theory of spinors [2, 3, 4].