Dynamic stability of spinning pretwisted beams subjected to axial random forces

This paper studies the dynamic stability of a pretwisted cantilever beam spinning along its longitudinal axis and subjected to an axial random force at the free end. The axial force is assumed as the sum of a constant force and a random process with a zero mean. Due to this axial force, the beam may experience parametric random instability. In this work, the finite element method is first applied to yield discretized system equations. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the mean-square stability criterion is utilized to determine the stability condition of the system. Numerical results show that the stability boundary of the system converges as the first three modes are taken into calculation. Before the convergence is reached, the stability condition predicted is not conservative enough.     

-isomorphisms, Jordan isomorphisms, and numerical range preserving maps

Let or , where is the algebra of a bounded linear operator acting on the Hilbert space , and is the set of self-adjoint operators in . Denote the numerical range of by It is shown that a surjective map satisfies

if and only if there is a unitary operator such that has the form

where is the transpose of with respect to a fixed orthonormal basis. In other words, the map or is a -isomorphism on and a Jordan isomorphism on . Moreover, if has finite dimension, then the surjective assumption on can be removed.

     

Synthesis, characterization, and structures of oxovanadium(V) complexes of Schiff bases of beta-amino alcohols as tunable catalysts for the asymmetric oxidation of organic sulfides and asymmetric alkynylation of aldehydes

Oxovanadium(V) complexes and with general formula VO(L3*)(OR5) were prepared in quantitative yields in alcohol (R5OH) from reactions of VO(O-i-Pr)3 and tridentate Schiff bases of beta-amino alcohols having one or two stereogenic centers, (HO)C*(R1)(R2)C*H(R3)N[double bond, length as m-dash]CH(2-OH-3,5-R4(2)-C6H2) (H2L3*). The alkoxy OR5 ligand exchanges readily with the alcoholic molecule in the solvent. Crystal structures of and were determined to be five-coordinate square pyramidal monomers. However, 1H NMR spectra of the complexes reveal two sets of signals, indicating the presence of two isomers in solution. The two isomers are suggested to be the endo/exo pair or the monomer/dimer pair. Asymmetric oxidations of methyl phenyl sulfide catalyzed by catalyst precursors were demonstrated to afford the chiral sulfoxide in yields and ee values similar to those obtained from the in situ-formed catalytic systems of VO(acac)2 and corresponding Schiff base ligands. Complexes and are also good catalysts for asymmetric alkynyl additions to aldehydes. Structural differences between the oxovanadium complexes, for inducing high stereoselectivities in the asymmetric oxidation of organic sulfides and the asymmetric alkynyl addition to aldehydes, are rationalized.     

AlAr3(THF): highly efficient reagents for cross-couplings with aryl bromides and chlorides catalyzed by the economic palladium complex of PCy3

Novel and highly efficient cross couplings of aryl bromides and chlorides with AlAr3(THF) (Ar = Ph, 2,4,6-Me3C6H2, 2-naphthyl or 4-Me3SiC6H4) catalyzed by the economic palladium catalyst of PCy3 are reported without the use of a base and under mild reaction conditions at room temperature or temperatures < or = 60 degrees C even for couplings of bulky aryl halides and the Al(2,4,6-Me3C6H2)3(THF) reagent.     

半无限空心截锥的特征值与端部效应

本文通过Birkhoff-Morgan关于单参数连续群不变性理论建立了空心半无限截锥的特征值方程,由此可以得到不同锥角下空心锥体的特征值,利用最小二乘法,本文得到了应力展开式中的各特征值系数,并由此得到问题的解。     

Synthesis,characterization, and structures of arylaluminum reagents and asymmetric arylation of aldehydes catalyzed by a titanium complex of an N-sulfonylated amino alcohol

A series of phenylaluminum reagents AlPh_xEt_3?x(L) (x = 1–3) containing adduct ligand L [Et₂O, THF, OPPh₃, or 4-dimethylaminopyridine (DMAP)] were synthesized and characterized. NMR studies showed that AlPh_xEt_3?x(L) (x = 1 or 2) exists as an equilibrium mixture of 3–4 species in solution. Solid-state structures of the phenylaluminum reagents reveal a distorted tetrahedral geometry. Asymmetric additions of phenylaluminum to 2-chlorobenzaldehyde were examined employing a titanium(IV) complex [TiL¹(OPrⁱ)₂]₂ 10 (H₂L¹ = (1R,2S)-2-(p-tolylsulfonylamino)-1,3-diphenyl-1-propanol) as a catalyst precursor. It was found that the adduct ligand L had a strong influence on the reactivity and the enantioselectivity in asymmetric phenyl additions to aldehydes. The phenylaluminum reagents with OPPh₃ or DMAP were unreactive toward aldehydes, and AlPh₃(THF) was found to be superior to AlPh₃(OEt₂) or AlPhEt₂(THF). Asymmetric aryl additions of AlAr₃(THF) to aldehydes employing a loading of 5 mol % titanium(IV) complex 10 with a strategy of a slow addition of the aldehydes over 20 min were conducted, and the reactions produced optically active secondary alcohols in high yields with excellent enantioselectivities of up to 94% ee.     

Mathematical model for formation decontamination by pumping with well bore mixing

This work presents a novel mathematical model to evaluate the effect of pumped well bore mixing volume on formation decontamination. The model equation is solved by the Laplace transform finite difference method. The developed model is applied to assess the effect of well bore mixing volume on contaminant remediation. The simulated results indicated that the well bore volume effect is pronounced for initial plumes with a small maximum contaminated radius, and in media such as bedrock formation where aquifer porosity and longitudinal dispersivity are small. In such systems, the pumped well bore mixing effect reduces the early contaminant concentrations, shifts the peak breakthrough curves to the right and spreading the breakthrough curve, and thus increases the decontamination time. If such a system does not account for pumped well mixing bore effect, estimates of decontamination time required to the regulatory level will be inaccurate.     

Ground state and excited state properties of ethylene isomers studied by a combined Feynman path integral-ab initio approach

Ground state and excited state properties of ethylene, C₂H₄, and several ethylene isomers have been studied by Feynman path integral Monte Carlo (PIMC) simulations. The PIMC treatment of the atomic nuclei has been combined with different electronic Hamiltonians in order to analyse the influence of the nuclear degrees of freedom on electronic quantities. Electronic expectation values at the minimum of the potential energy surface (PES) have been compared with PIMC based ensemble averaged values. Ensemble averaged quantities have been derived by Hamiltonians of the ab initio type and a tight-binding (TB) one-electron model. The combined influence of anharmonicities in the interatomic potential and the quantum fluctuations of the atomic nuclei lead to ensemble averaged bondlengths r _g which are significantly larger than the parameters r _e, at the minimum of the PES. The implications of this bond length elongation for the electronic properties of ethylene are discussed. The occupied canonical molecular orbitals (CMOs) of ethylene are destabilized under the influence of the nuclear degrees of freedom while virtual CMOs are stabilized. These shifts of one-electron energies suggest a comparison of electronic excitation energies at the minimum of the PES with PIMC based ensemble averages. The quantum fluctuations of the nuclei cause a strong redistribution in the intensities of electronic transitions. Transitions, which are dipole allowed in the planar D_2h geometry of ethylene, lose intensity under the influence of nuclear quantum effects, and vice versa for electronic excitations that are dipole forbidden under D_2h symmetry. This ‘vibrational borrowing’ is enhanced with decreasing atomic masses. The Feynman centroid density has been used to calculate the anharmonic vibrational wavenumbers of C₂H₄ and C₂D₄. The results of the present PIMC simulations have been employed to emphasize general problems of electronic structure calculations based on a single nuclear configuration (i.e. the configuration at the minimum of the PES).