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In the Arctic zone of Siberia, large diamond occurrences have been discovered in volcaniclastic, sedimentary-volcaniclastic, volcanosedimentary, and sedimentary rocks of the upper Ladinian strata and the base of the Carnian (Triassic) strata. They are confined to the Primorye mineragenic zone, which is traced along the Laptev Sea water area from the western Verkhoyansk area to eastern Taimyr. We have first identified a specific range of diamonds in these deposits. Among the rounded crystals of varieties I, II, V, and VII, there are grains with a light carbon isotope composition and high nitrogen contents. They have no analogues in typomorphic features in the known primary deposits of Yakutia but are completely similar to diamonds in the Rhaetian, Early Jurassic, Late Jurassic, Early Cretaceous, Neogene, and Quaternary commercial placers and placer occurrences, which suggests their formation as a result of the erosion of Triassic sources.

Pyrolysis-free gas chromatography-mass spectrometry was used to determine the gas phase composition of inclusions in phenocrysts from basalts and rhyolites of the Men’shii Brat Volcano (Medvezh’ya caldera, Iturup Island). Among more than 300 compounds detected in the inclusions, hydrocarbons are predominant (52-92 rel.%). These hydrocarbons (С₁-С₁₇) are alkanes, alkenes, alcohols, polycyclic aromatic hydrocarbons, ethers and esters, aldehydes, ketones, and carboxylic acids as well as sulfonated, nitrogenated, and halogenated organic compounds. Inorganic substances, which are predominantly CO₂, H₂O, SO₂, and N₂, are present in subordinate amounts. The organic compounds are interpreted as products of abiogenic synthesis of hydrocarbons in magmatic gases. This fundamentally new information about the composition of magmatic fluid suggests that mantle and crustal magmas can transport hydrocarbon substance.

The calculated line intensities of the 1-0, 2-0 and 3-0 absorption bands of the radioactive hydrogen chloride isotopologue H³⁶Cl are presented. The line positions were calculated using the Dunham coefficients obtained with the help of the isotopic independent spectroscopic constants. The line intensities of these bands were calculated using the effective dipole moment parameters obtained with the help of the isotopic substitution equations based on the effective dipole moment parameters of the H³⁵Cl isotopologue. The latter were fitted to the line intensities presented in the HITRAN2020 database.

The methane spectrum is studied near R (3) and R (4) multiplets of the first vibrational overtone in the 298-720 K temperature range with a tuning diode laser. We have developed the technique for laser radiation measurement and frequency calibration with the use of a high-stability plain-mirror interferometer. The coefficients of collisional broadening by nitrogen are calculated at different temperatures.

This paper proposes a new method for the numerical solution of a pure Neumann problem for the diffusion equation in a mixed formulation. The method is based on the inclusion of a condition of unique solvability of the problem in one of the equations of the system with a subsequent decrease in its order by using a Lagrange multiplier. The unique solvability of the problem obtained and its equivalence to the original mixed formulation in a subspace are proved. The problem is approximated on the basis of a mixed finite element method. The unique solvability of the resulting saddle system of linear algebraic equations is investigated. Theoretical results are illustrated by computational experiments.

A unitoid matrix is a square complex matrix that can be brought to diagonal form by a Hermitian congruence transformation. The canonical angles of a nonsingular unitoid matrix A are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of A, which is the matrix A^-*A. We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in A^-*A caused by a perturbation in A.

In this paper, we introduce a new convergence mode to deal with the generalized spectrum approximation of two bounded operators. This new technique is obtained by extending the well-known ν-convergence used in the case of classical spectrum approximation. This new vision allows us to see the ν-convergence assumption as a special case of our new method compared to the hypotheses needed in old methods, those required in this paper are weaker. In addition, we prove that the property U holds, which solves the spectral pollution problem arising in spectrum approximation of unbounded operator.

A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on Bernoulli's algorithm for computing the greatest in magnitude root of a polynomial with complex coefficients and the ndelin-Lobachevsky-Graeffe method for squaring the roots. Numerical results on the construction of stability domains of Ams-Bashforth methods of order 3-11 are given.

An experimental study of the efficiency of 3D bounry value problem solvers on the regular subgrids of quasi-structured parallelepipel grids has been carried out. Five solvers are considered: three iterative: the successive over-relaxation method, the implicit alternating direction method, the implicit incomplete factorization method with acceleration by conjugate gradients, as well as two direct methods: PARDISO and HEMHOLTZ - both from the Intel MKL library. The characteristic features of the conducted research are the following: 1) the subgrids contain a small number of nodes; 2) the efficiency is estimated not only for single calculations, but also mainly for a series of calculations, in each of which a large number of repetitions of solving the problem with different bounry conditions on the same same subgrid. On the basis of numerical experiments, the fastest solver under the given conditions was revealed, which turned out to be the method of successive over-relaxation method.

M.M. Lavrentiev's linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev's equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallelization of calculations.