Multi-instantons in seven dimensions

We consider the self-dual Yang-Mills equations in seven dimensions. Modifying the t'Hooft construction of instantons in $d=4$, we find $N$-instanton $7d$ solutions which depend on $8N$ effective parameters and are $E_{6}$-invariant.Comment: 9 pages, LaTeX, no figure

Incoherent pion photoproduction on the deuteron in the first resonance region

Incoherent pion photoproduction on the deuteron is studied in the first resonance region. The unpolarized cross section, the beam asymmetry, and the vector and tensor target asymmetries are calculated in the framework of a diagrammatic approach. Pole diagrams and one-loop diagrams with $NN$ scattering in the final state are taken into account. An elementary operator for pion photoproduction on the nucleon is taken in various on-shell forms and calculated using the SAID and MAID multipole analyses. Model dependence of the obtained results is discussed in some detail. A comparison with predictions of other works is given. Although a reasonable description of many available experimental data on the unpolarized total and differential cross sections and photon asymmetry has been achieved, in some cases a significant disagreement between the theory and experiment has been found. Invoking known information on the reactions $\gamma d\to\pi^0 d$ and $\gamma d\to np$ we predict the total photoabsorption cross section for deuterium. We find that our values strongly overestimate experimental data in the vicinity of the $\Delta$ peak.Comment: 22 pages, 23 figure

Self-dual Yang-Mills fields in pseudoeuclidean spaces

The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations are constructed from these solutions.Comment: 9 pages, LaTeX, no figure

1-Hyperreflexivity and Complete Hyperreflexivity

The subspaces and subalgebras of B(H) which are hyperreflexive with constant 1 are completely classified. It is shown that there are 1-hyperreflexive subspaces for which the complete hyperreflexivity constant is strictly greater than 1. The constants for \bC T \otimes B(H) are analyzed in detail.Comment: 41 page

STRAIN CHARACTERISTICS OF SOILS AND THE METHODS OF THEIR DETERMINATIO

A method is proposed for determining the strain characteristics of soils under dynamic loads, based on the results of experiments on dynamic compression of soils in laboratory conditions on a device of dynamic loading and for solving a wave problem, the statement of which is identical to the statement of the experiment. With the proposed method, the dynamic and static compression moduli, the unloading modulus, the viscosity coefficient of loess soil in the range of seismic loads were determined in accordance with the elastic-viscoelastic soil model developed by G.M. Lyakhov

NbS3_{3}: A unique quasi one-dimensional conductor with three charge density wave transitions

Through transport, compositional and structural studies, we review the features of the charge-density wave (CDW) conductor of NbS$_{3}$ (phase II). We highlight three central results: 1) In addition to the previously reported CDW transitions at $T_{P1}$ = 360\,K and $T_{P2}$ = 150\,K, another CDW transition occurs at a much higher temperature $T_{P0}$ = 620-650\,K; evidence for the non-linear conductivity of this CDW is presented. 2) We show that CDW associated with the $T_{P2}$ - transition arises from S vacancies acting as donors. Such a CDW transition has not been observed before. 3) We show exceptional coherence of the $T_{P1}$-CDW at room-temperature. Additionally, we report on the effects of uniaxial strain on the CDW transition temperatures and transport.Comment: 16 pages, 18 figure

Approach to the choice of modernization directions for the system of geodynamic monitoring in cases of using components intensity uncertainty

The problem of the optimum choice of the modernization directions for geodynamic monitoring systems, which is solved in the conditions of changing the parameters of natural-technical systems (NTS) is considered in the work. The solution of the task is creating a list of the components modernization directions and validate ranking the most effective of them. As criterion of modernization the value of decrease in resource intensity of subsystem application is usin

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