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 BaNi2_{2}V2_{2}O8_{8}

The phase diagram of the quasi two-dimensional antiferromagnet BaNi$_{2}$V$_{2}$O$_{8}$ is studied by specific heat, thermal expansion, magnetostriction, and magnetization for magnetic fields applied perpendicular to $\mathbf{c}$. At $\mu_0H^{*}\simeq1.5$ T, a crossover to a high-field state, where $T_N(H)$ increases linearly, arises from a competition of intrinsic and field-induced in-plane anisotropies. The pressure dependences of $T_N$ and $H^{*}$ 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

Issues Associated with EFF & FDM Ceramic Filled Feedstock Formulation

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