Mechanism of mass transfer in the formation of hydrothermal deposits of sulphides [Translation from: Trudy Inst.Geol.rudn.Mesterozh. 16, 80 [pages 44-46 ”Solubility of sulphides of iron” only], 1958]

This partial translation of the original paper provides the summary of this study of the mechanism of mass transfer in the formation of hydrothermal deposits of sulphides. For determining the solubility of sulphides of iron, the radioactive isotope Fe59 was used. The solubility of two sulphides was determined

On residualizing homomorphisms preserving quasiconvexity

H is called a G-subgroup of a hyperbolic group G if for any finite subset M G there exists a homomorphism from G onto a non-elementary hyperbolic group G_1 that is surjective on H and injective on M. In his paper in 1993 A. Ol'shanskii gave a description of all G-subgroups in any given non-elementary hyperbolic group G. Here we show that for the same class of G-subgroups the finiteness assumption on M (under certain natural conditions) can be replaced by an assumption of quasiconvexity

Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length

It is shown that there exist finitely generated infinite simple groups of infinite commutator width and infinite square width on which there exists no stably unbounded conjugation-invariant norm, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.Comment: v4: 41 pages, 6 figures rescaled at 120%; references updated, typos corrected, other minor corrections. v3: minor changes to the title, text and figures. v2: 41 pages, 6 figures; correction: Ore's conjecture was proved in 2008; 2 references added. v1: 40 pages, 6 figure

Topologization of sets endowed with an action of a monoid

Given a set $X$ and a family $G$ of self-maps of $X$, we study the problem of the existence of a non-discrete Hausdorff topology on $X$ with respect to which all functions $f\in G$ are continuous. A topology on $X$ with this property is called a $G$-topology. The answer is given in terms of the Zariski $G$-topology $\zeta_G$ on $X$, that is, the topology generated by the subbase consisting of the sets $\{x\in X:f(x)\ne g(x)\}$ and $\{x\in X:f(x)\ne c\}$, where $f,g\in G$ and $c\in X$. We prove that, for a countable monoid $G\subset X^X$, $X$ admits a non-discrete Hausdorff $G$-topology if and only if the Zariski $G$-topology $\zeta_G$ is non-discrete; moreover, in this case, $X$ admits $2^{\mathfrak c}$ hereditarily normal $G$-topologies.Comment: 10 page

Separable subsets of GFERF negatively curved groups

A word hyperbolic group G is called GFERF if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it. We show that in any such group, the product of finitely many quasiconvex subgroups is closed in the profinite topology on G

Unitary Representations of Lie Groups with Reflection Symmetry

We consider the following class of unitary representations $\pi$ of some (real) Lie group $G$ which has a matched pair of symmetries described as follows: (i) Suppose $G$ has a period-2 automorphism $\tau$, and that the Hilbert space $\mathbf{H} (\pi)$ carries a unitary operator $J$ such that $J\pi =(\pi \circ \tau)J$ (i.e., selfsimilarity). (ii) An added symmetry is implied if $\mathbf{H} (\pi)$ further contains a closed subspace $\mathbf{K}_0$ having a certain order-covariance property, and satisfying the $\mathbf{K}_0$-restricted positivity: $\ge 0$, $\forall v\in \mathbf{K}_0$, where $$ is the inner product in $\mathbf{H} (\pi)$. From (i)--(ii), we get an induced dual representation of an associated dual group $G^c$. All three properties, selfsimilarity, order-covariance, and positivity, are satisfied in a natural context when $G$ is semisimple and hermitean; but when $G$ is the $(ax+b)$-group, or the Heisenberg group, positivity is incompatible with the other two axioms for the infinite-dimensional irreducible representations. We describe a class of $G$, containing the latter two, which admits a classification of the possible spaces $\mathbf{K}_0 \subset \mathbf{H} (\pi)$ satisfying the axioms of selfsimilarity and order-covariance.Comment: 49 pages, LaTeX article style, 11pt size optio

Controlled Transformation of Electrical, Magnetic and Optical Material Properties by Ion Beams

Key circumstance of radical progress for technology of XXI century is the development of a technique which provides controllable producing three-dimensional patterns incorporating regions of nanometer sizes and required physical and chemical properties. Our paper for the first time proposes the method of purposeful direct transformation of the most important substance physical properties, such as electrical, magnetic, optical and others by controllable modification of solid state atomic constitution. The basis of the new technology is discovered by us effect of selective atom removing out of thin di- and polyatomic films by beams of accelerated particles. Potentials of that technique have been investigated and confirmed by our numerous experiments. It has been shown, particularly, that selective atom removing allows to transform in a controllable way insulators into metals, non-magnetics into magnetics, to change radically optical features and some other properties of materials. The opportunity to remove selectively atoms of a certain sort out of solid state compounds is, as such, of great interest in creating technology associated primarily with needs of nanoelectronics as well as many other "nano-problems" of XXI century.Comment: 22 pages, PDF, 9 figure