194 research outputs found
Hereditarily finite sets and identity trees
AbstractSome asymptotic results about the sizes of certain sets of hereditarily finite sets, identity trees, and finite games are proven
The Wonder of Colors and the Principle of Ariadne
The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli
and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to
the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne
and proposes the Ariadne Game, showing that the Principle of Ariadne,
corresponds precisely
to a winning strategy for the Ariadne Game. Some relations to other
alternative. set-theoretical principles
are also briefly discussed
An Exponential Lower Bound for the Latest Deterministic Strategy Iteration Algorithms
This paper presents a new exponential lower bound for the two most popular
deterministic variants of the strategy improvement algorithms for solving
parity, mean payoff, discounted payoff and simple stochastic games. The first
variant improves every node in each step maximizing the current valuation
locally, whereas the second variant computes the globally optimal improvement
in each step. We outline families of games on which both variants require
exponentially many strategy iterations
FREE-CARRIER PLASMONS AS A NOVEL TOOL IN SEMICONDUCTOR PHYSICS*
It is demonstrated that free-carrier plasmons, being well defined collective excitations of the electron gas in the range of small wave vectors, can serve as a sensitive tool to investigate the optical processes related to the small momentum transfers. As an example the system HgSe:Fe is analysed both experimentally and theoretically. It is well known that the excitation of the free-carrier plasma in the light absorption process is possible only in the presence of defects breaking the translational invariance of the system. Due to the overall momentum conservation requirement there must exist a momentum source to make the photon absorption *This work is supported in part by CPBP 01.06. (141
The combinatorics of the Baer-Specker group
Denote the integers by Z and the positive integers by N.
The groups Z^k (k a natural number) are discrete, and the classification up
to isomorphism of their (topological) subgroups is trivial. But already for the
countably infinite power Z^N of Z, the situation is different. Here the product
topology is nontrivial, and the subgroups of Z^N make a rich source of examples
of non-isomorphic topological groups. Z^N is the Baer-Specker group.
We study subgroups of the Baer-Specker group which possess group theoretic
properties analogous to properties introduced by Menger (1924), Hurewicz
(1925), Rothberger (1938), and Scheepers (1996). The studied properties were
introduced independently by Ko\v{c}inac and Okunev. We obtain purely
combinatorial characterizations of these properties, and combine them with
other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and
Scheepers.Comment: To appear in IJ
Around the Hossz\'u-Gluskin theorem for -ary groups
We survey results related to the important Hossz\'u-Gluskin Theorem on
-ary groups adding also several new results and comments. The aim of this
paper is to write all such results in uniform and compressive forms. Therefore
some proofs of new results are only sketched or omitted if their completing
seems to be not too difficult for readers. In particular, we show as the
Hossz\'u-Gluskin Theorem can be used for evaluation how many different -ary
groups (up to isomorphism) exist on some small sets. Moreover, we sketch as the
mentioned theorem can be also used for investigation of
-independent subsets of semiabelian -ary groups for some
special families of mappings
Coexistence of Anomalous Hall Effect and Weak Net Magnetization in Collinear Antiferromagnet MnTe
Anomalous Hall effect (AHE) plays important role in the rapidly developing
field of antiferromagnetic spintronics. It has been recently discussed that it
can be a feature of not only uncompensated magnetic systems but also in
altermagnetic materials. Hexagonal MnTe belongs to this appealing group of
compounds exhibiting AHE and is commonly perceived as magnetically compensated.
Here, we demonstrate that bulk form of MnTe exhibits small but detectable
magnetic moment correlating with hysteretic behaviour of the AHE. We formulate
a phenomenological model which explains how this feature allows to create a
disbalance between states with opposite N\'eel vector and prevent the AHE
signal from averaging out to zero. Moreover, we show how the dependence of AHE
on the N\'eel vector arises on microscopical level and highlight the
differences in Berry curvature between magnetically compensated and
uncompensated systems
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