Vibrations of nearly annular and circular plates

A general procedure is presented to determine the natural frequencies and mode shapes of nearly annular and circular plates. A straightforward perturbation procedure is used with a transfer of the boundary conditions to obtain solutions given by simple expressions. As well as yielding good accuracy quantitatively, the method accurately predicts qualitative behavior. Numerical results are presented for clamped elliptical and square plates.     

Studies toward the total synthesis of angelmicin B (hibarimicin B): synthesis of a model CD-D' arylnaphthoquinone

[structure: see text] A synthesis of arylnaphthoquinone 22 corresponding to the CD-D' unit of angelmicin B via the Suzuki coupling of the D' arylboronic acid 15 with the CD bromonaphthoquinone 21 is described. The mild conditions for the Suzuki cross-coupling leading to 22 may prove to be useful for the eventual late-stage coupling of the two highly functionalized halves of angelmicin B.     

Photolysis of (3-methyl-2H-azirin-2-yl)-phenylmethanone: direct detection of a triplet vinylnitrene intermediate

The photoreactivity of (3-methyl-2H-azirin-2-yl)-phenylmethanone, 1, is wavelength-dependent (Singh et al. J. Am. Chem. Soc. 1972, 94, 1199-1206). Irradiation at short wavelengths yields 2P, whereas longer wavelengths produce 3P. Laser flash photolysis of 1 in acetonitrile using a 355 nm laser forms its triplet ketone (T(1K), broad absorption with λ(max) ~ 390-410 nm, τ ~ 90 ns), which cleaves and yields triplet vinylnitrene 3 (broad absorption with λ(max) ~ 380-400 nm, τ = 2 μs). Calculations (B3LYP/6-31+G(d)) reveal that T(1K) of 1 is located 67 kcal/mol above its ground state (S(0)) and has a long C-N bond (1.58 ?), and the calculated transition state to form 3 is only 1 kcal/mol higher in energy than T(1K) of 1. The calculations show that 3 has significant 1,3-carbon iminyl biradical character, which explains why 3 reacts efficiently with oxygen and decays by intersystem crossing to the singlet surface. Photolysis of 1 in argon matrixes at 14 K produced ketene imine 7, which presumably is formed from 3 intersystem crossing to 7. In comparison, photolysis of 1 in methanol with a 266 nm laser produces mainly ylide 2 (λ(max) ~ 380 nm, τ ~ 6 μs, acetonitrile), which decays to form 2P. Ylide 2 is formed via singlet reactivity of 1, and calculations show that the first singlet excited state of the azirine chromophore (S(1A)) is located 113 kcal/mol above its S(0) and that the singlet excited state of the ketone (S(1K)) is 85 kcal/mol. Furthermore, the transition state for cleaving the C-C bond in 1 to form 2 is located 49 kcal/mol above the S(0) of 1. Thus, we theorize that internal conversion of S(1A) to a vibrationally hot S(0) of 1 forms 2, whereas intersystem crossing from S(1K) to T(1K) results in 3.     

A common approach to pyrrolizidine and indolizidine alkaloids; formal synthesis of (−)-isoretronecanol, (−)-trachelanthamidine and an approach to the synthesis of (−)-5-epitashiromine and (−)-tashiromine

A common and short stereoselective route is described for the formal synthesis of pyrrolizidine alkaloids, (−)-isoretronecanol and (−)-trachelanthamidine. An approach to the synthesis of indolizidine alkaloids (−)-5-epitashiromine and (−)-tashiromine utilizing ring closing metathesis is also described starting from commercially available and inexpensive l-proline.     

A novel sugar based intramolecular Ugi 3CC for the N-alkyl-3-oxo-4-aryl-octahydrofuro[2,3-f][1,4]oxazepine-5-carboxamides

An intramolecular Ugi reaction of 3-carboxy tethered sugar aldehyde with aryl amines and isocyanides has been accomplished to produce a novel class of carbohydrate derivatives, 3-oxo-4-aryl-octahydrofuro[2,3-f][1,4]oxazepine-5-carboxamides in good yields. The stereochemistry of the products was assigned by NMR studies. This is the first report on intramolecular Ugi reaction of 3-carboxy tethered sugar aldehyde, aryl amine, and isonitrile.     

Locally ideal formulations for piecewise linear functions with indicator variables

In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context.     

Sequential C-N and C-O bond formation in a single pot: synthesis of 2H-benzo[b][1,4]oxazines from 2,5-dihydroxybenzaldehyde and amino acid precursors

Functionalized β-aryl alanine ester derivatives were found to undergo rapid C-N and C-O bond formation with quinol carbonyl compounds to afford 2H-benzo[b][1,4]oxazines in good to excellent yields. This unprecedented finding reported herein offers a straightforward, highly efficient, and rapid method for the synthesis of 2H-benzo[b][1,4]oxazines.     

Experimental and numerical investigations of the texture evolution in copper wire drawing

Polycrystalline copper wires are drawn in a single and multiple step for the equivalent area reduction (RA) of ∼33% The single step and multiple step drawing process was simulated using a rate independent crystal plasticity with finite strain, which is implemented as a user routine in commercial finite element package ABAQUS. The texture of the copper wires were characterized by X-ray diffraction (XRD) and compared with the texture based finite element (FE) simulation predictions. Initial 〈10 0〉 fiber decreases during the drawing process and is replaced by 〈1 1 1〉 fiber. The 〈1 1 1〉 oriented grains are predominant in a single step drawing compared to a multiple step of the equivalent area reduction. The finite element analysis takes into account active crystallographic slip and orientation effects during the drawing process. Regions at the interface of die–wire exhibited complex textures, which was widely seen in the multiple step drawing pattern.     

Crystal and Molecular Structure Studies of 1′-Benzyl-8-(4-fluorobenzyl)-8-azaspiro[bicyclo-[3.2.1]octane-3,4′-imidazolodine]-2′,5′-dione

Abstract  

The title compound, C₂₃H₂₃FN₃O₂ has been synthesized and the structure was investigated by X-ray diffraction studies. The compound crystallizes in the triclinic crystal class in the space group P[`1]P\overline{1} with cell parameters a = 9.345(2) ?, b = 10.940(3) ?, c = 11.986(4) ?, α = 72.349(6)°, β = 68.106(18)°, γ = 66.867(5)°, Z = 2 and V = 1027.8(5) ?³. The hydantoin ring adopts a planar conformation and is affected by the π conjugation. The pyrrolidine and piperidine rings in the bicyclo octane moiety adopt envelope and chair conformations respectively. The structure exhibits both inter and intramolecular hydrogen bonds of the type N–H···O, C–H···O and C–H···N. One of the oxygen atoms attached to the hydantoin ring simultaneously accepts two hydrogen bonds to form a three centered hydrogen bonding pattern.     

Enantioselective synthesis of cyclopropyl δ-lactonealdehydes and dodecyl-5-ene-1-yne-3-ol: advanced intermediates of solandelactone A and B

A stereocontrolled synthesis of cyclopropyl δ-lactonealdehydes and dodecyl-5-ene-1-yne-3-ol is accomplished with predictable absolute stereochemistry via organocatalytic and catalytic asymmetric transfer hydrogenation reactions. The salient feature of this protocol is the genesis of chirality through an organocatalytic reaction and utilized for installing a critical bifunctional trans-cyclopropane motif, which is a key segment of every representative member of the oxylipin class of natural products such as solandelactone A and B.