738 research outputs found
On Congruence Lattices of Nilsemigroups
We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ \u3eΔ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite
Finite Nilsemigroups with Modular Congruence Lattices
This paper continues the joint work [2] of the author with P. Jones. We describe all finitely generated nilsemigroups with modular congruence lattices: there are 91 countable series of such semigroups. For finitely generated nilsemigroups a simple algorithmic test to the congruence modularity is obtained
FINITE NILSEMIGROUPS WITH MODULAR CONGRUENCE LATTICES
This paper continues the joint work [2] of the author with P. Jones. We describe all finitely generated nilsemigroups with modular congruence lattices: there are 91 countable series of such semigroups. For finitely generated nilsemigroups a simple algorithmic test to the congruence modularity is obtained
Importance of In-Plane Anisotropy in the Quasi Two-Dimensional Antiferromagnet BaNiVO
The phase diagram of the quasi two-dimensional antiferromagnet
BaNiVO is studied by specific heat, thermal expansion,
magnetostriction, and magnetization for magnetic fields applied perpendicular
to . At T, a crossover to a high-field state,
where increases linearly, arises from a competition of intrinsic and
field-induced in-plane anisotropies. The pressure dependences of and
are interpreted using the picture of a pressure-induced in-plane
anisotropy. Even at zero field and ambient pressure, in-plane anisotropy cannot
be neglected, which implies deviations from pure
Berezinskii-Kosterlitz-Thouless behavior.Comment: 4 pages, 4 figure
Dipole-active optical phonons in YTiO_3: ellipsometry study and lattice-dynamics calculations
The anisotropic complex dielectric response was accurately extracted from
spectroscopic ellipsometry measurements at phonon frequencies for the three
principal crystallographic directions of an orthorhombic (Pbnm) YTiO_3 single
crystal. We identify all twenty five infrared-active phonon modes allowed by
symmetry, 7B_1u, 9B_2u, and 9B_3u, polarized along the c-, b-, and a-axis,
respectively. From a classical dispersion analysis of the complex dielectric
functions \tilde\epsilon(\omega) and their inverses -1/\tilde\epsilon(\omega)
we define the resonant frequencies, widths, and oscillator strengths of the
transverse (TO) and longitudinal (LO) phonon modes. We calculate
eigenfrequencies and eigenvectors of B_1u, B_2u, and B_3u normal modes and
suggest assignments of the TO phonon modes observed in our ellipsometry spectra
by comparing their frequencies and oscillator strengths with those resulting
from the present lattice-dynamics study. Based on these assignments, we
estimate dynamical effective charges of the atoms in the YTiO_3 lattice. We
find that, in general, the dynamical effective charges in YTiO_3 lattice are
typical for a family of perovskite oxides. By contrast to a ferroelectric
BaTiO_3, the dynamical effective charge of oxygen related to a displacement
along the c-axis does not show the anomalously large value. At the same time,
the dynamical effective charges of Y and ab-plane oxygen exhibit anisotropy,
indicating strong hybridization along the a-axis.Comment: 8 pages, 7 figure
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