Hydroxylammonium fluorometalates: Synthesis and characterisation of a new fluorocuprate and fluorocobaltate

The first layered hydroxylammonium fluorometalates, (NH₃OH)₂CuF₄ and (NH₃OH)₂CoF₄, were prepared by the reaction of solid NH₃OHF and the aqueous solution of copper or cobalt in HF. Both compounds crystallize in monoclinic, P2₁/c, unit cell with parameters: a = 7.9617(2) Å, b = 5.9527(2) Å, c = 5.8060(2) Å, β = 95.226(2)° for (NH₃OH)₂CuF₄ and a = 8.1764(3) Å, b = 5.8571(2) Å, c = 5.6662(2) Å, β = 94.675(3)° for (NH₃OH)₂CoF₄, respectively. Magnetic susceptibility was measured between 2 K and 300 K giving the effective Bohr magneton number of 2.1 for Cu and 5.2 BM for Co. At low temperatures both complexes undergo a transition to magnetically ordered phase. The thermal decomposition of both compounds was studied by TG, DSC and X-ray powder diffraction. The thermal decomposition of (NH₃OH)₂CuF₄ is a complex process, yielding NH₄CuF₃ as an intermediate product and impure Cu₂O as the final residue, while (NH₃OH)₂CoF₄ decomposes in two steps, obtaining CoF₂ after the first step and CoO as the final product.     

Skew quantum Murnaghan–Nakayama rule

We extend recent results of Assaf and McNamara on a skew Pieri rule and a skew Murnaghan–Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf–McNamara’s original proof, and one via Lam–Lauve–Sotille’s skew Littlewood–Richardson rule. We end with some conjectures for skew rules for Hall–Littlewood polynomials.     

Particularism and resultance

Moral particularism is a promising new approach which understands itself as a subchapter of holism in the theory of reasons. So particularism may be extended to other areas, such as metaphysics. One of the bases for this kind of move is elaborated by particularism itself as resultance, a strategy for providing the relevant basis that is opposed to various forms of generalism (the thin property of goodness is constituted by several thick properties, such as being good humoured, being pleasant; the property of this being a table is constituted from properties of there being four legs, a plate, a certain arrangement). It is claimed that resultance or emergence needs a background structure in order to get off the ground.     

Triangularizability of Polynomially Compact Operators

An operator on a complex Banach space is polynomially compact if a non-zero polynomial of the operator is compact, and power compact if a power of the operator is compact. Theorems on triangularizability of algebras (resp. semigroups) of compact operators are shown to be valid also for algebras (resp. semigroups) of polynomially (resp. power) compact operators, provided that pairs of operators have compact commutators.     

Divisibility of generalized Catalan numbers

We define a q generalization of weighted Catalan numbers studied by Postnikov and Sagan, and prove a result on the divisibility by p of such numbers when p is a prime and q its power.     

Stochastic nature of earthquake ground motion

In this paper, we analyze the irregular behavior of earthquake ground motion as recorded during the Kraljevo M5.4 earthquake, which occurred on November 3rd, 2010 in Serbia. We perform the analysis for the ground accelerations recorded at 6 seismological stations: Grua, Ruda, Rada, Bara, Zaga and Bdva. The latter were carefully chosen based on their corresponding tectonic zone and the local geological setting. For each station, we analyze the horizontal component of the ground acceleration in the north–south direction, which is the one of primary interest for engineering design. We employ surrogate data testing and methods of nonlinear time series analysis. The obtained results indicate that strong ground accelerations are stochastic, in particular belonging to a class of linear stationary stochastic processes with Gaussian inputs or distorted by a monotonic, instantaneous, time-independent nonlinear function. This type of motion is detected regardless of the corresponding tectonic setting and the local geological conditions. The revealed stochastic nature is in disagreement with the frequently assumed deterministically chaotic nature of earthquake ground motion.     

Thermodynamic analysis of the interaction of partially hydrophobic cationic polyelectrolytes with sodium halide salts in water

Isothermal titration calorimetry was used to determine the temperature and concentration dependence of the enthalpy of mixing of 3,3- and 6,6-ionene fluorides, bromides, and iodides with low molecular weight salts (NaF, NaCl, NaBr, and NaI) in water. The magnitudes of the enthalpies, measured in the temperature range from 273 to 318 K, depended on the number of methylene groups on the ionene polyion (hydrophobicity), and on the anion of the added salt (ion-specificity). All enthalpies of mixing of 3,3- and 6,6-ionene fluorides with low molecular weight salts (NaCl, NaBr, and NaI) were negative, which is in contrast to the predictions of standard theories of polyelectrolyte solutions. This fact was interpreted in the light of the ion–water short-range interactions that are not accounted for in those theories. In contrast, the enthalpies of mixing of 3,3- and 6,6-ionene bromides and iodides with NaF were positive, being in accord with theory. Using the calorimetric data, we performed a model thermodynamic analysis of the polyelectrolyte–salt mixing process to obtain changes in the apparent standard Gibbs free energy, enthalpy, entropy, and heat capacity relative to the pure ionene fluorides in water. The results prove that halide ions replace fluoride counterions with a strength increasing in the order chloride < bromide < iodide. The process is enthalpy governed, accompanied by a positive change in the heat capacity.     

Numerical simulation of particles movement in cellular flows under the influence of magnetic forces

A numerical model of particle motion in fluid flow under the influence of hydrodynamic and magnetic forces is presented. As computational tool, a flow solver based on the Boundary Element Method is used. The Euler-Lagrange formulation of multiphase flow is considered. In the case of a particle with a magnetic moment in a nonuniform external magnetic field, the Kelvin body force acts on a single particle. The derived Lagrangian particle tracking algorithm is used for simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient, added mass and magnetophoretic force. As a benchmark test case the magnetite particle motion in cellular flow field of water is computed with and without the action of the magnetic force. The effect of the Kelvin force on particle motion and separation from the main flow is studied for a predefined magnetic field and different values of magnetic flux density. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)