186 research outputs found
Thin subsets of groups
For a group and a natural number , a subset of is called
-thin if, for each finite subset of , there exists a finite subset
of such that for every . We
show that each -thin subset of a group of cardinality , can be partitioned into 1-thin subsets. On the
other side, we construct a group of cardinality and point
out a 2-thin subset of which cannot be finitely partitioned into 1-thin
subsets
The comb-like representations of cellular ordinal balleans
Given two ordinal and , let be a function such that, for each , We define a mapping by the rule: if then , . The pair is called a comb defined by . We show that each cellular
ordinal ballean can be represented as a comb. In {\it General
Asymptology}, cellular ordinal balleans play a part of ultrametric spaces.Comment: 5 pages, preprin
Extraresolvability of balleans
summary:A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space
Nanoparticles as a possible moderator for an ultracold neutron source
Ultracold and very cold neutrons (UCN and VCN) interact strongly with
nanoparticles due to the similarity of their wavelengths and nanoparticles
sizes. We analyze the hypothesis that this interaction can provide efficient
cooling of neutrons by ultracold nanoparticles at certain experimental
conditions, thus increasing the density of UCN by many orders of magnitude. The
present analytical and numerical description of the problem is limited to the
model of independent nanoparticles at zero temperature. Constraints of
application of this model are discussed
Centrifugal quantum states of neutrons
We propose a method for observation of the quasi-stationary states of
neutrons, localized near the curved mirror surface. The bounding effective well
is formed by the centrifugal potential and the mirror Fermi-potential. This
phenomenon is an example of an exactly solvable "quantum bouncer" problem that
could be studied experimentally. It could provide a promising tool for studying
fundamental neutron-matter interactions, as well as quantum neutron optics and
surface physics effects. We develop formalism, which describes quantitatively
the neutron motion near the mirror surface. The effects of mirror roughness are
taken into account.Comment: 13 pages, 10 figure
Quantum motion of a neutron in a wave-guide in the gravitational field
We study theoretically the quantum motion of a neutron in a horizontal
wave-guide in the gravitational field of the Earth. The wave-guide in question
is equipped with a mirror below and a rough absorber above. We show that such a
system acts as a quantum filter, i.e. it effectively absorbs quantum states
with sufficiently high transversal energy but transmits low-energy states. The
states transmitted are mainly determined by the potential well formed by the
gravitational field of the Earth and the mirror. The formalism developed for
quantum motion in an absorbing wave-guide is applied to the description of the
recent experiment on the observation of the quantum states of neutrons in the
Earth's gravitational field
Research of interferential factors of accounting and evaluation of cryptocurrency in the practical business model of a company
Cryptocurrency is a modern phenomenon of the digital economy, which is gradually becoming part of the business processes of companies of various profiles and economic sectors. The presence of unsettled issues at the legislative level of jurisdictions, as well as the ambiguity of approaches to the classification and assessment of cryptocurrency in financial reporting, gives rise to discussions of both practical and scientific nature. For trade organizations, the need to resolve this issue is evident, since already now businesses are considering the possibility of accepting payment for goods with some types of cryptocurrencies, as well as using cryptocurrencies to pay for the resources the company needs
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