Minimal enclosing discs,circumcircles, and circumcenters in normed planes (Part II)

Until now there are almost no results on the precise geometric location of minimal enclosing balls of simplices in finite-dimensional real Banach spaces. We give a complete solution of the two-dimensional version of this problem, namely to locate minimal enclosing discs of triangles in arbitrary normed planes. It turns out that this solution is based on the classification of all possible shapes that the intersection of two norm circles can have, and on a new classification of triangles in normed planes via their angles. We also mention that our results are closely related to basic notions like coresets, Jung constants, the monotonicity lemma, and d-segments.     

Effect of Nb and Cr incorporation on the structural and magnetic properties of rapidly quenched FeCoSiB microwires

Rapidly quenched microwires with a nominal composition of Fe₃₉Co₃₉Si₈B₁₄ (#A_O), Fe₃₇Co₃₇Nb₄Si₈B₁₄ (#A_N) and Fe₃₆Co₃₆Nb₄Cr₂Si₈B₁₄ (#A_NC) have been investigated. Devitrification of as-quenched microwires showed that crystallization temperatures increased with simultaneous incorporation of Nb and Cr as in #A_NC alloy. Addition of these elements also contributed to an increase in activation energy in #A_N and #A_NC alloys. Nb addition reduced the particle size, which became much finer in the case of the Cr-containing alloy. Although Nb addition did not have much effect on lowering the Curie temperature T_C of the amorphous phase, Cr substitution lowered T_C to 698 K from high values of 785 K and 787 K observed in the #A_O and #A_NC alloys, respectively. However, the Cr addition revealed a better Giant magneto-impedance (GMI) response compared to the other alloys. Such improved GMI properties in the Cr-containing alloy are attributed to lower values of the coercivity and magnetostriction in the alloy containing both Nb and Cr.     

H-D exchange on graphite-potassium intercalation compounds

Potassium graphite intercalation compounds are able to activate C-H bonds of hydrocarbons at room temperature. In this paper, the hydrogen-deuterium exchange of CHD(3) in the presence of C(8)K, C(24)K and C(36)K is described.     

Low-Temperature Toluene Oxidation on Fe-Containing Modified SBA-15 Materials

Transition metals as catalysts for total VOC oxidation at low temperatures (150–280 °C) are a big challenge nowadays. Therefore, iron-modified SBA-15, AlSBA-15, and ZrSBA-15 materials with 0.5 to 5.0 wt.% Fe loading were prepared and tested for toluene oxidation. It was found that increasing Fe loading significantly improved the rate of oxidation and lowered the temperature of achieving 100% removal of toluene from above 500 °C for the supports (AlSBA-15 and ZrSBA-15) to below 400 °C for 5FeZrSBA-15. The formation of finely dispersed iron oxide active sites with a particle size less than 5 nm was observed on all the SBA-15, AlSBA-15, and ZrSBA-15 supports. It was found that the surface properties of the mesoporous support due to the addition of Al or Zr predetermined the type of formed iron oxide species and their localization on the support surface. Fe-containing SBA-15 and AlSBA-15 showed activity in total toluene oxidation at higher temperatures (280–450 °C). However, 5 wt. % Fe-containing ZrSBA-15 showed excellent activity in the total oxidation of toluene as a model VOC at lower temperatures (150–380 °C) due to the synergistic effect of Fe-Zr and the presence of accessible and stable Fe²⁺/Fe³⁺ active sites.     

Formation and cleavage of C-H, C-C, and C-O bonds of ortho-methyl-substituted anisoles by late transition metals

2,6-Dimethyl-substituted anisoles can be converted into the corresponding 2-ethyl-6-methylphenols in a several-step reaction mediated by a TpMe2Ir(III) complex; use of the 13C-enriched anisoles, ArO13CH3, shows that the 13C label distributes across the two ethyl sites with a preference for the terminal position.     

Higher homotopy of groups definable in o-minimal structures

It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal covers are contractible.     

Raman spectroscopy of ionic liquids derived from 1‐n‐butyl‐3‐methylimidazolium chloride and niobium chloride or zinc chloride mixtures

Anionic species formed in mixtures of 1‐n‐butyl‐3‐methylimidazolium chloride (BMICl) with different amounts of niobium pentachloride (NbCl₅) or zinc dichloride (ZnCl₂) were investigated by Raman spectroscopy. In the BMICl and NbCl₅ ionic mixtures the presence of the anion NbCl₆⁻ was detected for all compositions (molar fraction, X) and a mixture of this anion and the neutral Nb₂Cl₁₀ in acid ones. Two different anions were observed for basic mixtures of BMICl and ZnCl₂: ZnCl₄²⁻(0 < X < 0.35) and Zn₂Cl₆²⁻(X > 0.3), whereas for acidic ones three species were detected: Zn₂Cl₆²⁻(X < 0.7), Zn₃Cl₈²⁻(X > 0.7) and Zn₄Cl₁₀²⁻(X > 0.7). It has also been observed that in both cases, the formation of larger anions causes a shift of the C H stretching modes to higher wavenumbers as the result of a decrease in the hydrogen bond between Cl and the hydrogens from the cation. Copyright © 2008 John Wiley & Sons, Ltd.     

A new type of orthogonality for normed planes

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d ⩾ 3.     

Application of sensitive hydrogels in chemical and pH sensors

In the present work, pH-sensitive poly(vinyl alcohol)/poly(acrylic acid) (PVA/PAA) blends as well as hydrogels based on poly(N-isopropylacrylamide) (PNIPAAm), which are sensitive to organic solvent concentration in aqueous solutions, were used in silicon micromachined sensors. A sensitivity of approximately 15 mV/pH was obtained for a pH sensor with a 50 μm thick PVA/PAA hydrogel layer in a pH range above the acid exponent of acrylic acid (pK_a=4.7). The output voltage versus pH-value characteristics and the long-term signal stability of hydrogel-based sensors were investigated and the measurement conditions necessary for high signal reproducibility were determined. The influence of the preparation conditions of the hydrogel films on the sensitivity and response time of the chemical and pH sensors is discussed.