Estimation of stresses and deformation properties of rock masses which is based on the solution of an inverse problem from the measurement data of the free surface displacement

A method is developed of interpreting the measurement data of the variations of displacements and deformations on the free surfaces caused by carrying out mining works. It allows us to quantitatively estimate the horizontal components of the natural stress fields and elastic characteristics of the constructive elements of the excavation technologies of solid mineral deposits. The method is based on the solution of inverse problems for the system of elasticity equations in the domains of an arbitrary shape. The structure of the proposed target functions is studied; the optimal values are determined of the weight coefficients that provide solvability of the inverse problem as well as the limit level of error in the input data of various types is estimated.     

Coherent Polarization Transfer Effects Are Crucial for Interpreting Low-Field CIDNP Data

In this work we demonstrate that low-field chemically induced dynamic nuclear polarization (CIDNP) is strongly affected by re-distribution of polarization, which is formed in the course of spin evolution in transient radical pairs, in diamagnetic reaction products. This phenomenon is of importance when the spins of the reaction product are coupled strongly meaning that spin–spin interactions between them are comparable to the differences in their Zeeman interactions with the external magnetic field. In this case, polarization transfer relies on a coherent mechanism; as a consequence, spins can acquire significant polarization even when they have no hyperfine coupling to the electron spins in the radical pairs, i.e., cannot be polarized directly by CIDNP. This is demonstrated by taking CIDNP of n-butylamine as an example: in this case only the α-CH₂ protons are polarized directly, which is confirmed by high-field CIDNP, whereas the β-CH₂, γ-CH₂ and δ-CH₃ protons get polarized only indirectly due to the transfer of polarization from the α-CH₂ protons. These results show that low-field CIDNP data should be interpreted with care to discriminate between the effects of spin evolution in transient radical pairs and in diamagnetic reaction products.     

Transformations of variables invariant under minimization of binary functions of multivalued arguments

A number of transformations are introduced that are invariant under minimization problems and make it possible to reduce the maximum possible number of distinct columns in the matrix of zeros of an arbitrary binary function of multivalued arguments. As a result, simpler disjunctive normal forms are constructed. Complexity bounds for the constructed disjunctive normal forms of arbitrary binary functions of k-valued arguments are given.     

Academician Kazansky is 75

Chronicle

Academician Kazansky is 75     

On infinite-dimensional Keyfitz-Kranzer systems of conservation laws

For infinite-dimensional generalizations of the Keyfitz-Kranzer system of conservation laws in which the unknown vector ranges in an arbitrary Banach space, we single out the class of strong generalized entropy solutions of the Cauchy problem. Existence and uniqueness theorems are proved in this class.     

Telescopic actions

A group action H on X is called ??telescopic?? if for any finitely presented group G, there exists a subgroup H?? in H such that G is isomorphic to the fundamental group of X/H??. We construct examples of telescopic actions on some CAT[?C1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison??s theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes?? theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.