The recovery of the acoustic stiffness coefficient

We are concerned with the reconstruction of a non‐differentiable acoustic stiffness reactance coefficient of a one‐dimensional hyperbolic equation using the smallest possible number of boundary readings generated by classical initial conditions. To this end, a complete set of spectral data of a string is extracted from either a single or at most two readings of the trace of the solution on the boundary. The sought coefficient is then uniquely recovered by the Krein inverse spectral theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Imidazolium chloride organophosphate antidotes

The structures of four imidazolium oxime derivatives were solved by direct methods. These compounds have been shown to be effective in the treatmen of organophosphate poisoning. Despite substantial differences in the nature of the substituent on N1, all four compounds have similar shapes when viewed down the plane of the imidazole ring. The potency of these compounds in the treatment of organophosphate poisoning correlates well with the distance between the imidazole ring and the oxygen moiety on the side chain. 2-(hydroxyimino)methyl-3-methyl-1-[1-(3-methyl-sulfonylpropyloxy) methyl]imidazolium chooride (1) crystallizes in the triclinic space groupPī (Z=2). The unit cell parametersa, b, c (Å) and α, β, and γ (^o) were: 8.506(2), 8.787(4), 10.070(4), 73.68(3), 81.37(3), 85.39(3). 2-(hydroxyimino)-methyl-3-methyl-1-(2′-N-phenylsulfonylamino-1′-ethyl) imidazolium chloride (2) crystallizes in the monoclinic space groupP2 ₁ la(Z=4). The unit cell parametersa, b, c (Å) and β (^o) were: 12.690(2), 6.317(4), 20.193(4), 91.47(2). 1-(2′-ethyl-2′-trifluoromethanesulfonyl-aminoethyl)-2-(hydroxyimino) methyl-3-methylimidazolium chloride (3) crystallizes in the triclinic space groupPī (Z=2). The unit cell parametersa, b, c (Å) and α, β, and γ (^o) were: 6.635(1), 11.333(2), 12.274(3), 115.05(3), 98.46(3), 90.11(3). 2-(hydroxyimino)-methyl-3-methyl-1-[2-(2-methyl-3-nitrobutyloxy) methyl]-imidazolium chloride (4) crystallizes in the orthorhombic space groupP2₁2₁2₁ (Z=4). The unit cell parametersa, b, andc (Å) were: 10.034(1), 11.401(2), 13.352(2).     

Imidazolium chloride organophosphate antidotes

The structures of four imidazolium oxime derivatives were solved by direct methods. These compounds have been shown to be effective in the treatmen of organophosphate poisoning. Despite substantial differences in the nature of the substituent on N1, all four compounds have similar shapes when viewed down the plane of the imidazole ring. The potency of these compounds in the treatment of organophosphate poisoning correlates well with the distance between the imidazole ring and the oxygen moiety on the side chain. 2-(hydroxyimino)methyl-3-methyl-1-[1-(3-methyl-sulfonylpropyloxy) methyl]imidazolium chooride (1) crystallizes in the triclinic space groupPī (Z=2). The unit cell parametersa, b, c (?) and α, β, and γ (^o) were: 8.506(2), 8.787(4), 10.070(4), 73.68(3), 81.37(3), 85.39(3). 2-(hydroxyimino)-methyl-3-methyl-1-(2′-N-phenylsulfonylamino-1′-ethyl) imidazolium chloride (2) crystallizes in the monoclinic space groupP2 ₁ la(Z=4). The unit cell parametersa, b, c (?) and β (^o) were: 12.690(2), 6.317(4), 20.193(4), 91.47(2). 1-(2′-ethyl-2′-trifluoromethanesulfonyl-aminoethyl)-2-(hydroxyimino) methyl-3-methylimidazolium chloride (3) crystallizes in the triclinic space groupPī (Z=2). The unit cell parametersa, b, c (?) and α, β, and γ (^o) were: 6.635(1), 11.333(2), 12.274(3), 115.05(3), 98.46(3), 90.11(3). 2-(hydroxyimino)-methyl-3-methyl-1-[2-(2-methyl-3-nitrobutyloxy) methyl]-imidazolium chloride (4) crystallizes in the orthorhombic space groupP2₁2₁2₁ (Z=4). The unit cell parametersa, b, andc (?) were: 10.034(1), 11.401(2), 13.352(2).     

Steric effects in the hypervalent iodine oxidation of ketones

Oxidation of 3-cholestanone (1) with C₆H₅I(OAc)₂ or o-OIC₆H₄COOH or C₆H₅IO₂ in KOH/MeOH yields 2 α-carbomethoxy-A-norcholestane (2). This result is interpreted on mechanistic grounds and compared with the course of the reaction with other sterically hindered ketones such as friedelin, 3-keto, 12-keto, 17-keto steroids, and 2,2,6,6-tetramethyl-4-piperidone.     

Synthesis,Crystal Structure and Spectroscopic Characterisation of Mono‐ and Dinuclear 5,5‐Diethylbarbiturato Complexes of Chromium(0) and Rhenium(I)

Addition of 5,5‐diethylbarbituric acid (H₂debarb, 1 ) to [CpCr(NO)₂Cl], [Re(CO)₅Br] or [(PPh₃)Re(CO)₄Br] in the presence of triethylamine and AgO₃SCF₃ (= AgOTf) resulted in the mono‐barbiturato complexes [CpCr(NO)₂(Hdebarb)] ( 2 ), [PPh₃Re(CO)₄(Hdebarb)] ( 3 ) and [Re(CO)₅(Hdebarb)] ( 4 ), respectively. Bis‐barbiturato complex [{(CO)₅Re}₂(debarb)] ( 5 ) with a doubly deprotonated barbiturate dianion formed when a molar ratio of metal complex to ligand of 2:1 was used. In the case of the rhenium complexes, AgO₃SCF₃ must be used additionally to cleave off bromide. All of the complexes were fully characterised by means of IR, mass and ¹H, ¹³C and ³¹P NMR spectra and elemental analysis. In addition, their solid‐state structures were determined by single‐crystal X‐ray diffraction studies. The complexes exhibit distorted pseudo‐tetrahedral ( 2 ) or pseudo‐octahedral ( 3 – 5 ) configuration around the metal atom. In all complexes the ring system of the Hdebarb ligand is essentially planar.     

Use of hypervalent iodine oxidation for the C(3)-hydroxylation of chromone,flavone and α-naphthoflavone

C(3)-Hydroxylation of chromone (1a) , flavone (1b) and α-naphthoflavone (4) via acid-catalysed hydrolysis of the corresponding β-methoxy-α-hydroxydimethylacetals (2a, 2b , and 5) formed by iodobenzene diacetate-potassium hydroxide methanol oxidation is described.     

Objectifying the adjacent and opposite angles: a cultural historical analysis

The angle topic is central to the development of geometric knowledge. Two of the basic concepts associated with this topic are the adjacent and opposite angles. It is the goal of the present study to analyze, based on the cultural historical semiotics framework, how high-achieving seventh grade students objectify the adjacent and opposite angles’ concepts. We videoed the learning of a group of three high-achieving students who used technology, specifically GeoGebra, to explore geometric relations related to the adjacent and opposite angles’ concepts. To analyze students’ objectification of these concepts, we used the categories of objectification of knowledge (attention and awareness) and the categories of generalization (factual, contextual and symbolic), developed by Radford. The research results indicate that teacher's and students’ verbal and visual signs, together with the software dynamic tools, mediated the students’ objectification of the adjacent and opposite angles’ concepts. Specifically, eye and gestures perceiving were part of the semiosis cycles in which the participating students were engaged and which related to the mathematical signs that signified the adjacent and the opposite angles. Moreover, the teacher's suggestions/requests/questions included/suggested semiotic signs/tools, including verbal signs that helped the students pay attention, be aware of and objectify the adjacent and opposite angles’ concepts.