Low‐frequency scattering by a penetrable body with an eccentric soft or hard core

A plane wave is scattered by an acoustically soft or hard sphere, covered by a penetrable non‐concentric spherical lossless shell that disturbs the propagation of the incident wave field. The dimensions of the coated sphere are much smaller than the wavelength of the incident field. Low‐frequency theory reduces this scattering problem to a sequence of potential problems, which can be solved iteratively. Exactly one bispherical coordinate system exists that fits the given geometry of the obstacle. For the case of a soft and hard core, the exact low‐frequency coefficients of the zeroth and the first‐order for the near field as well as the first‐ and second‐order coefficients for the normalized scattering amplitude are obtained and the cross sections are calculated. Discussion of the results and their physical meaning is included. Copyright © 2009 John Wiley & Sons, Ltd.     

Fundamental Solutions of Linear Differential Equations in the Sense of Mnemofunctions

In this paper we discuss the definition and construction of the fundamental solution of a linear differential equation with constant coefficients in the algebra of mnemofunctions. This algebra contains the tempered distributions. We also present some examples including a physical illustration of our results for the equation u = .     

Vibrational spectra of spinels with cation ordering on the octahedral sites

Infrared and Raman spectra are reported for compounds with 1 : 1, 1 : 3, and 1 : 2 mixed ordering on the octahedral sites of the spinel structure. The spectra of the superstructures are complex with many more bands observed than occur in the parent spinel structure, although less than were predicted by group theoretical analysis. A qualitative interpretation of the spectra can be made through the large Brillouin zone concept.     

Anisotropic exchange interactions in hetero-one-dimensional Ln–M systems (Ln = Er,Yb; M = Cr,FeLS): Magnetometry and Dual Mode X-band Electron Paramagnetic Resonance spectroscopic studies

A recently introduced experimental and theoretical procedure is presented in order to calculate the magnitude and anisotropy of interaction between a lanthanide and a 3d-metal ion. The general formula of the hetero-one-dimensional molecular compounds is trans-[M(CN)₄(μ-CN)₂Ln(H₂O)₄(bpy)]_n·nH₂O · 1.5nbpy (M = Fe³⁺, Cr³⁺; Ln = Er³⁺, Yb³⁺), where bpy = 2,2′-bipyridine, abbreviated as [LnM] from now on. The main parts of this procedure are: (a) the evaluation of the effective g-parameters of the lanthanide ion with the help of EPR measurements; (b) the use of dual-mode EPR spectroscopy to define the anisotropic exchange interactions with the help of an anisotropic Hamiltonian model; (c) use of the same magnetic model to fit magnetization and susceptibility data in order to verify the EPR findings.     

Preparation and characterization of electrophoretically deposited high-temperature superconductor coatings

The high-temperature superconductor, YBa₂Cu₃O_7–x (x = 0.1–0.2) [YBCO], was prepared using an optimized calcination and sintering process. Thin layers of a few microns of this material were deposited on a silver substrate by applying a simplified electrophoretic deposition technique in a suspension of the fine, < 10 m, superconductor powder in a non-aqueous liquid. To get a uniform and strongly adherent coating, the deposition process is repeated several times, followed by an appropriate sintering procedure. The initially prepared YBCO powder and the coatings produced were characterized for their superconducting properties by X-ray diffraction analysis (XRD), magnetization measurements with a Superconducting Quantum Interference Device (SQUID) and electrical resistivity measurements. By scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) the grain size of the YBCO film, its thickness and impurity content, respectively, were estimated.     

On a new edge function on complete weighted graphs and its application for locating Hamiltonian cycles of small weight

In this paper, we define a new combinatorial function on the edges of complete weighted graphs. This function assigns to each edge of the graph the sum of the weights of all Hamiltonian cycles that contain the edge. Since this function involves the factorial function, whose exact calculation is intractable due to its superexponential asymptotic rate of increase, we also introduce a normalized version of the function that is efficiently computable. From this version, we derive an upper bound to the weight of the minimum weight Hamiltonian cycle of the graph based on the weights of the graph edges. Then we investigate the possible algorithmic applications of this normalized function using the Nearest Neighbor Heuristic and a smallest edge first heuristic. As evidence for its applicability, we show that the use of this function as a criterion for the selection of the next edge, improves the performance of both heuristics for approximating the minimum weight Hamiltonian cycles in Euclidean plane graphs. Moreover, our experimental results show that the use of the function is more suitable with the structure of the smallest edge first heuristic since it provides a solution closer to the best known solution of known hard TSP instances but in \(O(n^3)\) time.     

The concept of "capacity" in zeolite ion-exchange systems

In the present paper a study is conducted in order to distinguish the several types of capacity used in the literature on zeolite ion-exchange systems, to verify the use of each capacity type, and to analyze the several experimental methods used for capacity determination. Although the study is focused on zeolite clinoptilolite as a characteristic paradigm, its theoretical approaches and experimental findings and methods could also apply to other zeolites.     

Samarium Based High Surface Area Perovskite Type Oxides SmFe1-XAlXO3 (X=0.00, 0.50, 0.95).Part I, Synthesis and Characterization of Materials

High specific surface area (ssa) perovskite type solids based on samarium (SmFe_1-xAl_xO₃, x = 0.00, 0.50, 0.95) were prepared using hexadecyltrimethyl-ammonium bromide C16TAB as a precursor and gelating agent. The structure of perovskite is fully developed at 600oC for the SmFeO3 solid but not for the other materials. The ssa of the solids varies (33.5 m²g^-1 - 1 m²g^-1) depending on composition and calcination temperature.     

Successive Michael reactions on chromone derivatives with dimethyl 1,3-acetonedicarboxylate: one-pot synthesis of functionalized benzophenones, benzo[c]chromones and hydroxybenzoylfuroates

Chromones were reacted with dimethyl acetonedicarboxylate in the presence of DBU in THF at room temperature to furnish good yields of products, their structure depending on the substituent at 3-position. Unsubstituted chromones lead to methyl 7-hydroxy-6-oxo-6H-benzo[c]chromone-8-carboxylates 2, whereas by using 3-bromochromone, the methyl furoate 3c along with the unexpected furylcyclopropyl-chromene carboxylate 4c was isolated. Finally, from 3-formyl-chromones functionalized benzophenones 5 were isolated, in good yields. Plausible mechanisms are proposed.