1,990 research outputs found
Total anti-symmetrische Quasigruppen
Bei der Untersuchung von Prüfziffersystemen über Quasigruppen stößt man auf die so genannten total anti-symmetrischen Quasigruppen. Bislang war ihre Existenz für alle Ordnungen ungeklärt. Ecker und Poch vermuteten 1986, dass es keine total anti-symmetrischen Quasigruppen der Ordnung gibt. In der vorliegenden Arbeit widerlegen wir diese Vermutung und entwickeln Konstruktionen für total anti-symmetrische Quasigruppen der Ordnung für alle . Per Computersuche weisen wir außerdem nach, dass Prüfziffersysteme über einer 2-Quasigruppe der Ordnung 10, ebenso wie Prüfziffersysteme über Gruppen der Ordnung 10, nicht alle (Sprung-)Zwillingsfehler oder Sprung-Transpositionen erkennen können. Als weiteres Ergebnis zeigen wir, dass die Klasse der total anti-symmetrischen Quasigruppen keine Varietät ist
Scaling of magnetic monopoles in the pure compact QED
In the pure U(1) lattice gauge theory with the Villain action we find that
the monopole mass in the Coulomb phase and the monopole condensate in the
confinement phase scale according to simple power laws. This holds outside the
coupling region in which on finite toroidal lattices the metastability
phenomena occur. A natural explanation of the observed accuracy of the scaling
behaviour would be the second order of the phase transition between both phases
in the general space of couplings not far away from the Villain action.Comment: LATTICE99(Topology and Confinement) - 3 pages, 4 fig
Total anti-symmetrische Quasigruppen
Bei der Untersuchung von Prüfziffersystemen über Quasigruppen stößt man auf die so genannten total anti-symmetrischen Quasigruppen. Bislang war ihre Existenz für alle Ordnungen ungeklärt. Ecker und Poch vermuteten 1986, dass es keine total anti-symmetrischen Quasigruppen der Ordnung gibt. In der vorliegenden Arbeit widerlegen wir diese Vermutung und entwickeln Konstruktionen für total anti-symmetrische Quasigruppen der Ordnung für alle . Per Computersuche weisen wir außerdem nach, dass Prüfziffersysteme über einer 2-Quasigruppe der Ordnung 10, ebenso wie Prüfziffersysteme über Gruppen der Ordnung 10, nicht alle (Sprung-)Zwillingsfehler oder Sprung-Transpositionen erkennen können. Als weiteres Ergebnis zeigen wir, dass die Klasse der total anti-symmetrischen Quasigruppen keine Varietät ist
Processing Succinct Matrices and Vectors
We study the complexity of algorithmic problems for matrices that are
represented by multi-terminal decision diagrams (MTDD). These are a variant of
ordered decision diagrams, where the terminal nodes are labeled with arbitrary
elements of a semiring (instead of 0 and 1). A simple example shows that the
product of two MTDD-represented matrices cannot be represented by an MTDD of
polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by
allowing componentwise symbolic addition of variables (of the same dimension)
in rules. It is shown that accessing an entry, equality checking, matrix
multiplication, and other basic matrix operations can be solved in polynomial
time for MTDD_+-represented matrices. On the other hand, testing whether the
determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the
same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing
a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of
CSR 201
Giant crystal-electric-field effect and complex magnetic behavior in single-crystalline CeRh3Si2
Single-crystalline CeRh3Si2 was investigated by means of x-ray diffraction,
magnetic susceptibility, magnetization, electrical resistivity, and specific
heat measurements carried out in wide temperature and magnetic field ranges.
Moreover, the electronic structure of the compound was studied at room
temperature by cerium core-level x-ray photoemission spectroscopy (XPS). The
physical properties were analyzed in terms of crystalline electric field and
compared with results of ab-initio band structure calculations performed within
the density functional theory approach. The compound was found to crystallize
in the orthorhombic unit cell of the ErRh3Si2 type (space group Imma -- No.74,
Pearson symbol: oI24) with the lattice parameters: a = 7.1330(14) A, b =
9.7340(19) A, and c = 5.6040(11) A. Analysis of the magnetic and XPS data
revealed the presence of well localized magnetic moments of trivalent cerium
ions. All physical properties were found to be highly anisotropic over the
whole temperature range studied, and influenced by exceptionally strong
crystalline electric field with the overall splitting of the 4f1 ground
multiplet exceeding 5700 K. Antiferromagnetic order of the cerium magnetic
moments at TN = 4.70(1)K and their subsequent spin rearrangement at Tt =
4.48(1) K manifest themselves as distinct anomalies in the temperature
characteristics of all investigated physical properties and exhibit complex
evolution in an external magnetic field. A tentative magnetic B-T phase
diagram, constructed for B parallel to the b-axis being the easy magnetization
direction, shows very complex magnetic behavior of CeRh3Si2, similar to that
recently reported for an isostructural compound CeIr3Si2. The electronic band
structure calculations corroborated the antiferromagnetic ordering of the
cerium magnetic moments and well reproduced the experimental XPS valence band
spectrum.Comment: 32 pages, 12 figures, to appear in Physical Review
The Safe Lambda Calculus
Safety is a syntactic condition of higher-order grammars that constrains
occurrences of variables in the production rules according to their
type-theoretic order. In this paper, we introduce the safe lambda calculus,
which is obtained by transposing (and generalizing) the safety condition to the
setting of the simply-typed lambda calculus. In contrast to the original
definition of safety, our calculus does not constrain types (to be
homogeneous). We show that in the safe lambda calculus, there is no need to
rename bound variables when performing substitution, as variable capture is
guaranteed not to happen. We also propose an adequate notion of beta-reduction
that preserves safety. In the same vein as Schwichtenberg's 1976
characterization of the simply-typed lambda calculus, we show that the numeric
functions representable in the safe lambda calculus are exactly the
multivariate polynomials; thus conditional is not definable. We also give a
characterization of representable word functions. We then study the complexity
of deciding beta-eta equality of two safe simply-typed terms and show that this
problem is PSPACE-hard. Finally we give a game-semantic analysis of safety: We
show that safe terms are denoted by `P-incrementally justified strategies'.
Consequently pointers in the game semantics of safe lambda-terms are only
necessary from order 4 onwards
Vortex critical behavior at the de-confinement phase transition
The de-confinement phase transition in SU(2) Yang-Mills theory is revisited
in the vortex picture. Defining the world sheets of the confining vortices by
maximal center projection, the percolation properties of the vortex lines in
the hypercube consisting of the time axis and two spatial axis are studied.
Using the percolation cumulant, the temperature for the percolation transition
is seen to be in good agreement with the critical temperature of the thermal
transition. The finite size scaling function for the cumulant is obtained. The
critical index of the finite size scaling function is consistent with the index
of the 3D Ising model.Comment: 4 pages, 4 PS figures, using revtex4, paragraph and refs added, typo
correcte
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