The rearrangement of some cyclopentanone-aryloximes: synthesis of (±)-aplysin, (±)-filiformin and of their debromo analogues.

Upon acid catalyzed rearrangement after Sheradsky, the aryloximes A gave the tricyclic aminals C, which suffered hydrolysis to lactols E. The unique alcohol 29 was then prepared through a highly stereoselective equilibration-reductive alkylation of the epimeric mixture of lactols 22a,b. Two routes, one of which was stereospecific, allowed cyclization of 29 to (±)-aplysin 34. The yield was 2.5 % from oximes 2a,b. The isomeric epi-aplysin 35 and filiformin 36 were also obtained from 29. The debromo analogues 37,38 and 39 and their trideutero derivatives 41,42 and 43 were synthesized along similar line and allowed unequivocal structure elucidation by NMR spectroscopy.     

A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem

We develop in this article an a posteriori error estimator for the P₁‐nonconforming finite element approximation, for a diffusion‐reaction equation. We adopt the error in a constitutive law approach in two and three dimensional space, for not necessary piecewise constant data of problems. The efficiency and the reliability of our estimators are proved, neither Helmholtz decomposition of the error nor saturation assumption. The constants are explicitly given, which prove the robustness of these estimators. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 950–976, 2015     

Structures and energetics of C3H6S isomers: a Gaussian-3 ab initio study

Twenty-two isomers/conformers of C₃H₆S^+√ radical cations have been identified and their heats of formation (ΔH_f) at 0 and 298 K have been calculated using the Gaussian-3 (G3) method. Seven of these isomers are known and their ΔH_f data are available in the literature for comparison. The least energy isomer is found to be the thioacetone radical cation (4⁺) with C_2v symmetry. In contrast, the least energy C₃H₆O^+√ isomer is the 1-propen-2-ol radical cation. The G3 ΔH_f298 of 4⁺ is calculated to be 859.4 kJ mol⁻¹, ca. 38 kJ mol⁻¹ higher than the literature value, ≤821 kJ mol⁻¹. For allyl mercaptan radical cation (7⁺), the G3 ΔH_f298 is calculated to be 927.8 kJ mol⁻¹, also not in good agreement with the experimental estimate, 956 kJ mol⁻¹. Upon examining the experimental data and carrying out further calculations, it is shown that the G3 ΔH_f298 values for 4⁺ and 7⁺ should be more reliable than the compiled values. For the five remaining cations with available experimental thermal data, the agreement between the experimental and G3 results ranges from fair to excellent.

Cation CH₃CHSCH₂^+√ (10⁺) has the least energy among the eleven distonic radical cations identified. Their ΔH_f298 values range from 918 to 1151 kJ mol⁻¹. Nevertheless, only one of them, CH₂=SCH₂CH₂^+√ (12⁺), has been observed. Its G3 ΔH_f298 value is 980.9 kJ mol⁻¹, in fair agreement with the experimental result, 990 kJ mol⁻¹.

A couple of reactions involving C₃H₆S^+√ isomers CH₂=SCH₂CH₂^+√ (12⁺) and trimethylene sulfide radical cation (13⁺) have also been studied with the G3 method and the results are consistent with experimental findings.     

Reaktionen des [η2-{P–PtBu2}Pt(PPh3)2] und [η2-{P–PtBu2}Pt(dppe)] mit Metallcarbonylen. Bildung von [η2-{(CO)5M · PPtBu2}Pt(PPh3)2] (M = Cr,W) und [η2-{(CO)5Cr · PPtBu2}Pt(dppe)]

Coordination Chemistry of P-rich Phosphanes and Silylphosphanes. XVI [1] Reactions of [g²-{P–P^tBu₂}Pt(PPh₃)₂] and [g²-{P–P^tBu₂}Pt(dppe)] with Metal Carbonyls. Formation of [g²-{(CO)₅M · PP^tBu₂}Pt(PPh₃)₂] (M = Cr, W) and [g²-{(CO)₅Cr · PP^tBu₂}Pt(dppe)] [η²-{P–P^tBu₂}Pt(PPh₃)₂] 4 reacts with M(CO)₅ · THF (M = Cr, W) by adding the M(CO)₅ group to the phosphinophosphinidene ligand yielding [η²-{(CO)₅Cr · PP^tBu₂}Pt(PPh₃)₂] 1 , or [η²-{(CO)₅W · PP^tBu₂}Pt(PPh₃)₂] 2 , respectively. Similarly, [η²-{P–P^tBu₂}Pt(dppe)] 5 yields [η²-{(CO)₅Cr · PP^tBu₂}Pt(dppe)] 3 . Compounds 1 , 2 and 3 are characterized by their ¹H- and ³¹P-NMR spectra, for 2 and 3 also crystal structure determinations were performed. 2 crystallizes in the monoclinic space group P2₁/n (no. 14) with a = 1422.7(1) pm, b = 1509.3(1) pm, c = 2262.4(2) pm, β = 103.669(9)°. 3 crystallizes in the triclinic space group P1 (no. 2) with a = 1064.55(9) pm, b = 1149.9(1) pm, c = 1693.2(1) pm, α = 88.020(8)°, β = 72.524(7)°, γ = 85.850(8)°.     

Postbuckling of imperfect stiffened cylindrical shells under combined external pressure and heating

1.IntroductionStiffenedcylindricalshellsarewidelyusedinmanytypesofstructures.Inpracticetheyoftensubjecttovarioustypesofcombinedthermalandmechanicalloadingandmayhavesignificantandunavoidableinitialgeometricalimperfections.Therefore,thepostbucklingbehaviorofimperfectstiITenedcylindricalshellsundercombinedexternalpress.ureandthermalloadingmustbewellunderstood.Manypostbucklingstudieshavebeenmadetbrstiffenedcylindricalshellsunderpureaxialcompression,uniformexternalpressureortheircombinations,where…     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

Magnetic properties of the cyclic spincluster Fe6:bicine

The magnetic properties of the cyclic compound [Fe₆(bicine)₆] LiClO₄ ^. 2MeOH are reported. The cluster Fe₆(bicine)₆ forms an antiferromagnetically coupled ring structure of Fe ^III ions. The magnetic susceptibility is measured between 2 and 300 K and yields the exchange coupling of J/k _B = - 27.5±0.5 K. The field dependence of the magnetic moment is studied at 3 and 6 K in magnetic fields up to 5 T. The zero-field splitting of the first excited spin states with S = 2 and 3 are determined by ESR at 94 GHz. The intra-molecular interactions of the Fe ^III ions are analyzed and the on-site anisotropy of the Fe ^III due to the ligand-configuration is determined to d /k _B = - 0.633±0.008K. Received 28 October 2002 / Received in final form 22 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bernd@piobelix.physik.uni-karlsruhe.de     

Independence polynomials of k-tree related graphs

An independent set of a graph G is a set of pairwise non-adjacent vertices. Let α(G) denote the cardinality of a maximum independent set and f_s(G) for 0≤s≤α(G) denote the number of independent sets of s vertices. The independence polynomial defined first by Gutman and Harary has been the focus of considerable research recently. Wingard bounded the coefficients f_s(T) for trees T with n vertices: for s≥2. We generalize this result to bounds for a very large class of graphs, maximal k-degenerate graphs, a class which includes all k-trees. Additionally, we characterize all instances where our bounds are achieved, and determine exactly the independence polynomials of several classes of k-tree related graphs. Our main theorems generalize several related results known before.     

Strict inequalities for the derivatives of functions satisfying certain boundary conditions

For functions satisfying the boundary conditions