Spin excitations in K2_{2}Fe4+x_{4+x}Se5_{5}: linear response approach

Using \emph{ab initio} linear response techniques we calculate spin wave spectra in K$_{2}$Fe$_{4+x}$Se$_{5}$, and find it to be in excellent agreement with a recent experiment. The spectrum can be alternatively described rather well by localized spin Hamiltonian restricted to first and second nearest neighbor couplings. We confirm that exchange coupling between nearest neighbor Fe magnetic moments is strongly anisotropic, and show directly that in the ideal system this anisotropy has itinerant nature which can be imitated by introducing higher order terms in effective localized spin Hamiltonian (biquadratic coupling). In the real system, structural relaxation provides an additional source of the exchange anisotropy of approximately the same magnitude. The dependence of spin wave spectra on filling of Fe vacancy sites is also discussed

Gegenbauer polynomials and the Fueter theorem

The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions f(z) in the complex plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator. In this paper we interpret this theorem on the level of representation theory, as an intertwining map between certain sl(2)-modules

The Stable Equivalence and Cancellation Problems

Let $K$ be an arbitrary field of characteristic 0, and \Aff^n the $n$-dimensional affine space over $K$. A well-known cancellation problem asks, given two algebraic varieties V_1, V_2 \subseteq \Aff^n with isomorphic cylinders V_1 \times \Aff^1 and V_2 \times \Aff^1, whether $V_1$ and $V_2$ themselves are isomorphic. In this paper, we focus on a related problem: given two varieties with equivalent (under an automorphism of \Aff^{n+1}) cylinders V_1 \times \Aff^1 and V_2 \times \Aff^1, are $V_1$ and $V_2$ equivalent under an automorphism of \Aff^n? We call this stable equivalence problem. We show that the answer is positive for any two curves V_1, V_2 \subseteq \Aff^2. For an arbitrary $n \ge 2$, we consider a special, arguably the most important, case of both problems, where one of the varieties is a hyperplane. We show that a positive solution of the stable equivalence problem in this case implies a positive solution of the cancellation problem.Comment: 9 page

Low Energy, Coherent, Stoner-like Excitations in CaFe2_{2}As2_{2}

Using linear-response density-functional theory, magnetic excitations in the striped phase of CaFe$_{2}$As$_{2}$ are studied as a function of local moment amplitude. We find a new kind of excitation: sharp resonances of Stoner-like (itinerant) excitations at energies comparable to the N{\'{e}}el temperature, originating largely from a narrow band of Fe $d$ states near the Fermi level, and coexist with more conventional (localized) spin waves. Both kinds of excitations can show multiple branches, highlighting the inadequacy of a description based on a localized spin model

Assessment of wood microstructural changes after one-stage thermo-hydro treatment (THT) by micro X-ray computed tomography

The microstructural changes in a selection of softwoods and hardwoods resulting from thermo-hydro treatment (THT) at 160°C were examined by means of a state-of-the-art micro X-ray computed tomography. A dedicated X-ray scanning and volumetric processing protocol was developed. All reconstructed volumes had an approximate voxel pitch between 0.8 and 1.2 μm3. The microstructures of the same needle-shaped specimens before and after THT were visualized, and the individual parameters (maximum opening and lumen volume) for various cell types were quantified and compared. The highest values of substance volume were recorded for the ash sapwood (81%) and spruce specimens (72%). After THT, a significant correlation was found between the mass loss determined by gravimetry and the X-ray volume loss. The largest change occurred in the lumen volume of several tissue components, such as libriform fibers, tracheids, and ray parenchyma. The average aspen fiber volume reduction after THT was 31%, a value 2.6 times higher than the volume reduction of the average vessels. The porosity of ash sapwood increased from 41 to 56%, whereas the porosity of birch decreased from 34 to 29%

Generic canonical form of pairs of matrices with zeros

We consider a family of pairs of m-by-p and m-by-q matrices, in which some entries are required to be zero and the others are arbitrary, with respect to transformations (A,B)--> (SAR,SBL) with nonsingular S, R, L. We prove that almost all of these pairs reduce to the same pair (C, D) from this family, except for pairs whose arbitrary entries are zeros of a certain polynomial. The polynomial and the pair (C D) are constructed by a combinatorial method based on properties of a certain graph.Comment: 13 page