26 research outputs found
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
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