Vol 487, No 4 (2019)

We study measurable dependence of measures on a parameter in the Kantorovich optimal transportation problem with a parameter. Broad sufficient conditions are obtained for the existence of proper conditional measures measurably depending on a parameter in the case of parametric families of measures and mappings.

The main results of the Aronszajn-Donoghue-Kac theory are extended to the case of n-dimensional (in the resolvent sense) perturbations à of an operator A_{0 =} A_0^* defined on a Hilbert space H. Applying technique of boundary triplets we describe singular continuous and point spectra of extensions A_B of a symmetric operator A acting in H in terms of the Weyl function M(·) of the pair {A, A₀} and boundary n-dimensional operator B = B^*. Assuming that the multiplicity of singular spectrum of A₀ is maximal it is established orthogonality of singular parts E^s_Aв and E^s_Ao of the spectral measures E_Aв and E_Ao of the operators A_B and A₀, respectively. It is shown that the multiplicity of singular spectrum of special extensions of direct sums A = A⁽¹⁾ ⊕ A⁽²⁾ cannot be maximal as distinguished from multiplicity of the absolutely continuous spectrum. In particular, it is obtained a generalization of the Kac theorem on multiplicity of singular spectrum of Schrodinger operator on the line as well as its clarification. The multiplicity of singular spectrum of special extensions of direct sums A = A⁽¹⁾ ⊕ A⁽²⁾ are investigated. In particular, it is shown that it cannot be maximal as distinguished from multiplicity of the absolutely continuous spectrum. This result generalizes the Kac theorem on multiplicity of singular spectrum of Schrodinger operator on the line and clarifies it.

The problem of generation of waves on the surface of a water layer placed on an elastic base is considered. It is assumed that the generating source is located inside the elastic half-space. The Podyapolskii approach is used which is based on study of the solutions to the common linear system of equations of the theory of elasticity in the half-space and the theory of water waves linked at the interface by the corresponding boundary conditions. The previously obtained simplified dispersion relation for the water mode with account for the elastic base effect is used to derive a simple integral formula which associates the initial perturbation of a special kind in the elastic half-space and the amplitude of the surface water waves generated by this source. The obtained solutions are compared with the solutions based on the well-known piston model of long wave generation.

The paper shows the integrability of certain classes of seventh-order dynamic systems that are homogeneous in part, in which the system on the tangent bundle to three-dimensional manifolds is distinguished. In this case, the force fields have various dissipation and generalize the previously considered ones.

A new method for the synthesis of high-purity fine-crystalline aluminum-magnesium spinel MgAl₂O₄ was been proposed. The procedure includes treatment of mixture finely dispersed MgO and hydroxide Al(OH)₃ or aluminum oxyhydroxide AlOOH by water fluid under supercritical conditions (T = 380-400 °С, P_H2O =  22,8-23,0 MPa). It was been shown that the process of formation of the structure of aluminum-magnesium spinel proceeds through a solid-phase mechanism. By varying the conditions of synthesis, the new method of synthesis allows to adjust the size (from 20 nm to 5 µm) and shape (spherical, lamellar, bipyramidal) of particles of synthesized aluminum-magnesium spinel MgAl₂O₄.

The promise of СuO-CeO₂/γ-Al₂O₃ catalysts for partial oxidation of dimethyl ether (DME) to hydrogen-rich gas for fuel cell feeding was demonstrated. The catalysts provided complete conversion of DME to hydrogen-rich gas with low (≤ 0,8 vol.%) CH₄ content and Н₂ productivity ~3,1 l/(g_cat · h) at 350 °C under ambient pressure using a reaction mixture (molar ratio): DME : O₂ : N₂ = 1 : 1 : 4 (DME : air = 1 : 5) at a flow rate 7 l/(g_cat · h).

The paper seeks to explain in new ways the change in the geodynamic regime at the eastern margin of the Eurasian paleocontinent in the Early Cretaceous from the convergent type of plate boundary to the transform boundary. Certain global geodynamic characteristics were analyzed in the 200-65 Ma interval, which reflect the processes both at depth and on the Earth’s surface and are seemingly unrelated directly to the formation of the transform boundary in the east of Asia. The change of geodynamic regimes is found to occur within the 115 to 110 million years ago time range.

Two new localities of Mesozoic mammals have been discovered: Bol’shoi Ilek and Berezovaya River (Russia, Krasnoyarsk Territory, Lower Cretaceous, Ilek Formation). Bol’shoi Ilek locality yields an edentulous fragment of the maxillary of Docodonta indet. A fragment of dentary without teeth attributed to Mammalia indet. (presumably eutriconodontan or symmetrodontan) is presented in the Berezovaya River locality. New localities fill the geographical gap between previously known mammalian localities of Ilek Formation in the basins of Kiya and Bol’shoi Kemchug rivers.

The Early Mesozoic Baga-Khentey pluton is the fragment of the Dauria-Khentey batholith, which could have formed due by the mantle plume action on lower horizons of the continental crust within the zone of collisional compression by closing of the Mongol-Okhotsk ocean. The batholith and their peripheral zones possibly formed from the mantle and crustal sources of magma. The Ikh-Narotin-Khid Massif is located on the border of the rifting zones on periphery of the Late Mesozoic area. The petrographic and geochemical affinity of granitoids of the Ikh-Narotin-Khid massif and composition of gneisses from the country rocks might indicate that this was the substratum in formation of palingenic granites of the calc-alkali series. The distinctions in rock composition of the large plutons consist in minor differentiation of the Baga-Khentey Massif rocks probably related to the anatexis conditions and origin of melts in the collisional compression setting. The granites of the Ikh-Narotin-Khid Massif formed in the extension setting favorable for deep differentiation of magmatic melts.

A find of coesite in a kyanite graphite-diamond-bearing eclogite xenolith from the Udachnaya-Vostochnaya kimberlite pipe is described in this paper. The coesite relics were found in intensely fractured garnet indicating some influence of the kimberlite melt, which is supported by the typical secondary mineral assemblage around this inclusion. These data indicate that shallower diamond-free coesite rocks (2,7 GPa) underwent metamorphism distinct from diamond-bearing coesite eclogites (~4 GPa). The metasomatic alteration of rock interacting with C-O-H fluid during diamond crystallization may be another possible reason for the missing coesite in diamond-bearing xenoliths.

The morphometric indicators of the relief significantly affect the debris flow features in the mountains. The key characteristics are the angles of inclination and height, and when considering heights in the first place we pay attention not to their absolute values, but to the nature of the distribution. In the presented study, the analysis of the numerical values of these two indicators for the Western, Central and Eastern Caucasus was carried out on the basis of the original digital model of the relief. The average value of the tilt angles in the Western Caucasus is 0,5° more than in the Central and Eastern, which contributes to more active debris flows. On the other hand, the Western Caucasus is distinguished by smaller elevation differences. From the position of this factor, the Central Caucasus is the most dangerous. Thus, the nature of the distribution of absolute altitudes, along with high forestation, neutralizes the factor of more significant angles of inclination of surfaces and causes less debris flow danger in the Western Caucasus relative to the Central and Eastern.

The paper gives a quantitative characteristic of the Chukchi Sea bottom sediments’ color and considers its correlations with the content of grain-size fractions, chemical elements, and biogenic components taking into account the diagenetic factor. The prospect for lithostratigraphy of such a colorimetric index as saturation S is noted.

Psoriasis therapy remains extremely relevant area of modern drug design, due to necessity of adverse reactions reduction, inherent for actual methods of therapy. It has been established that two of serine proteases are key agents in psoriasis development: neutrophil elastase 1 (HNE1) and cathepsin G (CatG). Collected molecular data for presented targets forms the basis of molecular modeling strategy for search and identification of new target-specific inhibitors. The result of work is a group of high-priority small-molecule compounds with double-targeted affinity with ability to suppress pro-psoriatic processes, induced by observed serine proteases in the initial stage of disease.

The effect of pinacidil was studied on calcium-loaded rat heart mitochondria (RHM) in the presence of succinate and rotenone. In experiments with pinacidil, the swelling of these mitochondria increased in media with NH₄NO₃ or K‑acetate, but the inner membrane potential DΨ_mito and state 3 or 2,4-dinitrophenol-uncoupled respiration of these organelles were decreased due to opening of the mitochondrial permeability transition pore in the inner membrane. These effects were inhibited by cyclosporin A and ADP. It was concluded that the protective effect of pinacidil in the cardiac muscle ischemia/reperfusion may be associated with stimulation mitochondrial swelling and a decrease in RHM calcium overload resulted in a decrease in DΨ_mito due to the soft uncoupling pinacidil effect.

Recent distribution in the Southern Russian Far East of the most hazardous parasitoses caused by trematodes, cestodes and nematodes is demonstrated. Decelerating expansion of the trematode Clonorchis sinensis, an agent of clonorchiasis towards the southern Primorye Territory from the Amur River basin, that began 10-15 years ago, was revealed. A prognosis was made on the activation of natural foci of endemic paragonimosis. It has been established experimentally that freshwater gastropods belonging to endemic genus Parajuga and local species of the genus Stenothyra were resistant to infection by that trematode. These facts do not exclude possible introduction of the P. heterotremus on the Russian Far East using susceptible gastropods from other genera.