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We study the infinite Jacobi block matrices under the discrete Miura-type transformations which relate matrix Volterra and Toda lattice systems to each other and the situations when the deficiency indices of the corresponding operators are the same. A special attention is paid to the completely indeterminate case (i.e., then the deficiency indices of the corresponding block Jacobi operators are maximal). It is shown that there exists a Miura transformation which retains the complete indeterminacy of Jacobi block matrices appearing in the Lax representation for such systems, namely, if the Lax matrix of Volterra system is completely indeterminate, then so is the Lax matrix of the corresponding Toda system, and vice versa. We consider an implication of the obtained results to the study of matrix orthogonal polynomials as well as to the analysis of self-adjointness of scalar Jacobi operators.

We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments of its Weyl function, can be used in solving initial-boundary value problem for both systems. It is shown that the Miura transformation can be easily described in terms of these moments. Using this description we establish a bijection between the Volterra lattices and the class of Toda lattices which is characterized by positivity of Jacobi operators in their Lax representation. Also, we discuss an implication of the latter result to the spectral theory.

The effects of low-dose radiation exposure remain a controversial topic in radiation biology. This study compares early (0.5, 4, 24, 48, and 72 h) and late (5, 10, and 15 cell passages) post-irradiation changes in γH2AX, 53BP1, pATM, and p-p53 (Ser-15) foci, proliferation, autophagy, and senescence in primary fibroblasts exposed to 100 and 2000 mGy X-ray radiation. The results show that exposure to 100 mGy significantly increased γH2AX, 53BP1, and pATM foci only at 0.5 and 4 h post irradiation. There were no changes in p-p53 (Ser-15) foci, proliferation, autophagy, or senescence up to 15 passages post irradiation at the low dose. [ABSTRACT FROM AUTHOR]

Existing databases of RCS benchmarks lack a complex, low-observable target. This paper describes the design of such a complex and low-observable measurement model. Starting point of the design is the so-called Muldicon model, developed by the NATO/STO/AVT panel. Hot spots of the original model are identified and treated with radar-absorbing materials. Simulations on the treated model demonstrate that the model is indeed low observable. The effect of the manufacturing process of 3D-printing and separable parts is assessed experimentally on a cone-sphere; the effect is found to be negligible. These results give confidence that the model, when built, satisfies the requirements of being complex and low observable; and that artefacts of the manufacturing process will not impair its signature. [ABSTRACT FROM AUTHOR]

We consider the situations, when two unbounded operators generated by infinite Jacobi matrices, are self-adjoint and commute. It is found that if two Jacobi matrices formally commute, then two corresponding operators are either self-adjoint and commute, or admit a commuting self-adjoint extensions. In the latter case such extensions are explicitly described. Also, some necessary and sufficient conditions for self-adjointness of Jacobi operators are studied.

We consider the infinite Jacobi block matrices in the completely indeterminate case, i. e. such that the deficiency indices of the corresponding Jacobi operators are maximal. For such matrices, some criteria of complete indeterminacy are established. These criteria are similar to several known criteria of indeterminacy of the Hamburger moment problem in terms of the corresponding scalar Jacobi matrices and the related systems of orthogonal polynomials.

For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.

This paper proposes a new type of substrate for manufacturing LEDs based on AlInGaN heterostructures. Instead of depositing SiC layers on the surface of Si using the conventional method, a new method involving the coordinated substitution of atoms (MCSA) to form the SiC layer is proposed. This new approach enables the growth of epitaxial GaN layers with low defect content and facilitates transfer to any surface. The paper details the technology of manufacturing LEDs on SiC/Si substrates obtained by the MCSA and elaborates on the benefits of using these substrates in LED production. Additionally, the advantages of the growth interface between SiC and Si materials are discussed. Moreover, it is found that thinner SiC layers (<200 nm) contribute to the scattering of the LED's own radiation in the heterostructure waveguide, which decreases its absorption by silicon. For flip-chip LEDs with the substrate removed, substrates with thicker SiC layers (~400 nm) and a growth porous layer of several microns at the SiC-Si interface is utilized to simplify Si substrate removal and enhance the manufacturing process's cost-effectiveness. [ABSTRACT FROM AUTHOR]

The reserves of highly viscous oils and natural bitumen are several times higher than the stocks of light oils. In the development of such oils by thermal methods, steam is produced, the development of which is accompanied by significant emissions into the atmosphere of flue gases, including carbon dioxide. According to estimates, the extraction of high-viscosity oils annually releases about 34.5 million tons of carbon dioxide into the atmosphere. However, carbon dioxide emissions from steam generation can be reduced to zero by injecting flue gases along with steam into the formation. In addition to environmental benefits, the technology of co-injection of water vapor and combustion gases (nitrogen and carbon dioxide) has a complex (thermal and physico-chemical) effect on the formation with a synergistic effect. The article is devoted to the analysis of the mechanisms affecting the increase in oil recovery during the co-injection of steam with flue gases, the description of equipment for the injection of flue gases into the reservoir, as well as the analysis of field experience in using this technology. The calculations for one of the fields of high-viscosity oil show the high efficiency of co-injection of water steam with flue gases.

As the development of reserves of traditional oil takes place, an important component of the raw material base is the reserves of highly viscous oil and natural bitumen, one of the effective methods for the development of which is the SAGD technology. This paper is devoted to optimizing the length of the horizontal section of wells with the SAGD technology using numerical modeling for one of the fields of high-viscosity Caribbean oil and finding the analytical dependence of the technological characteristics of the method on the parameters of the wells. The solution of the tasks was carried out using a thermohydrodynamic simulator «CMG STARS» (Computer Modeling Group). The paper presents the results of calculations to determine the optimal rate of steam injection and the length of a horizontal wellbore at the SAGD, as well as the analytical dependence of the technological characteristics of the parameters of the well, which can be used for an initial assessment of the effectiveness of technology for specific geological and physical conditions in this area.

In the present work, a new method of growing layers of three main crystal modifications of Ga2O3, namely α-phase, ε-phase, and β-phase, with thickness of 1 µm or more was developed. The method is based on the use of two approaches, namely a combination of Ga2O3 growth using the hydride vapor-phase epitaxy (HVPE) method and the use of a silicon crystal with a buffer layer of dislocation-free silicon carbide as a substrate. As a result, Ga2O3 gallium oxide layers of three major Ga2O3 crystal modifications were grown, namely, α-phase, ε-phase, and β-phase. The substrate temperatures and precursor flux values at which it is possible to grow only α-phase, only ε-phase, or only β-phase without a mixture of these phases were established. It was found that the metastable α- and ε-phases change into the stable β-phase when heated above 900 °C. Experimentally obtained Raman and ellipsometric spectra of α-phase, ε-phase, and β-phase of Ga2O3 are presented. The theoretical study of the Raman spectra and the dependences of dielectric function on photon energy for all three phases was carried out. The vibrations of Ga2O3 atoms corresponding to the main lines of the Raman spectrum of the α-phase, ε-phase, and β-phase were simulated by density functional methods. [ABSTRACT FROM AUTHOR]