Dynamic stability of a slender beam under horizontal–vertical excitations

The dynamic stability of a vertically standing cantilevered beam simultaneously excited in both horizontal and vertical directions at its base is studied theoretically. The beam is assumed to be an inextensible Euler–Bernoulli beam. The governing equation of motion is derived using Hamilton's principle and has a nonlinear elastic term and a nonlinear inertia term. A forced horizontal external term is added to the parametrically excited system. Applying Galerkin's method for the first bending mode, the forced Mathieu–Duffing equation is derived. The frequency response is obtained by the harmonic balance method, and its stability is investigated using the phase plane method. Excitation frequencies in the horizontal and vertical directions are taken as 1:2, from which we can investigate the influence of the forced response under horizontal excitation on the parametric instability region under vertical excitation. Three criteria for the instability boundary are proposed. The influences of nonlinearities and damping of the beam on the frequency response and parametric instability region are also investigated. The present analytical results for instability boundaries are compared with those of experiments carried out by one of the authors.     

Electrochemically active cross-linking reaction for fluorescent labeling of aliphatic alkenes

Although cross-linking reactions serve as a valuable tool for the integration of two or more functionalities or properties, the application of electrochemical synthesis to cross-linking reactions is restricted due to the difficulty of mass transfer. Thus, the primary purpose of this research is to explore electrochemical cross-linking systems to construct a fluorescent probe, triggered by the formation of a covalent linkage. The second purpose is to apply the probe to insoluble targets. Towards these goals, a combination of electrochemically active phenol derivatives and aliphatic alkenes were employed to form polycyclic compounds. Several of the dihydrobenzofuran derivatives formed through [3+2] cyclization reactions exhibited fluorescence. Furthermore, this approach allowed the effective modification of alkene-modified silica gel with electrochemically active species, which enables the construction of fluorescent probes that are triggered by C-C bond formation.     

Copper-catalyzed aerobic spirocyclization of biaryl-N-H-imines via 1,4-aminooxygenation of benzene rings

A synthetic method of azaspirocyclohexadienones has been developed through copper-catalyzed aerobic spirocyclization of biaryl-N-H-imines prepared by the reaction of biarylcarbonitriles and Grignard reagents.     

Formal [4 + 1]- and [5 + 1]-annulation by an S(N)2-conjugate addition sequence: stereoselective synthesis of highly substituted carbocycles

K(2)CO(3)-mediated reactions of 6-bromo-2-hexenoates and 7-bromo-2-heptenoate with active methylene compounds deliver highly substituted cyclopentane and cyclohexane derivatives, respectively via a sequence of S(N)2-conjugate addition reactions (formal [4 + 1]- and [5 + 1]-annulation) in a diastereoselective manner.     

The structure of liquid SnTe under pressure

We investigated the structure of liquid SnTe at high pressures up to 8.2 GPa by energy-dispersive x-ray diffraction. On melting at low pressures, the crystalline B1 structure changed into not B1-like but distorted-B1-like local structure. We also found that the structure changes at around 1.6-3.3 GPa. At high pressures, the bond angle and coordination number approached those for B2-based structure, but still showed clear deviations from B2-like local structure.     

A concise synthesis of a very late antigen-4 antagonist trans-4-[1-[[2,5-dichloro-4-(1-methyl-3-indolylcarboxyamide)phenyl]acetyl]-(4S)-methoxy-(2S)-pyrrolidinylmethoxy]cyclohexanecarboxylic acid via reductive etherification

This contribution describes a concise synthesis to ethyl trans-[(4S)-methoxy-(2S)-pyrrolidinylmethoxy]cyclohexanecarboxylate (2b) as a key intermediate of very late antigen-4 (VLA-4) antagonist trans-4-[1-[[2,5-dichloro-4-(1-methyl-3-indolylcarboxyamide)phenyl]acetyl]-(4S)-methoxy-(2S)-pyrrolidinylmethoxy]cyclohexanecarboxylic acid (1). The synthesis employs a reductive etherification as a key reaction using (2S,4S)-1-benzyloxycarbonyl-4-methoxypyrrolidine-2-carboxyaldehyde (12) and trans-4-triethylsilyloxycyclohexanecarboxilic acid ethyl ester (13b). This synthesis provides 2b in 6 steps with 38% overall yield from commercially available starting material.     

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

Calculation of amino acid hydrophilicity indices for retention of peptides on amide, diol and silica columns in normal-phase liquid chromatography

Summary A set of hydrophilicity parameters in a normal-phase liquid chromatography of peptides is presented in order to clarify the contribution of individual amino acid residues to peptide retention and to predict retention times. The retention of 100 peptides was studied using normal-phase liquid chromatography on amide, diol and silica columns. An acetonitrile-water mixed solution containing 0.2% trifluoroacetic acid +0.2% triethylamine was used as the mobile phase in a linear gradient elution system. The contribution of each residue upon retention was calculated by linear multiple regression analysis. This paper described the contribution values as “hydrophilicity retention coefficients”. Using these hydrophilicity retention coefficients, retention times could be predicted for peptides of known amino acid content and sequence. A set of hydrophilicity retention coefficients on each column was successfully explained by contributions to the degree of retention.     

Stereo-controlled anti-hydromagnesiation of aryl alkynes by magnesium hydrides

A concise protocol for anti-hydromagnesiation of aryl alkynes was established using 1 : 1 molar combination of sodium hydride (NaH) and magnesium iodide (MgI₂) without the aid of any transition metal catalysts. The resulting alkenylmagnesium intermediates could be trapped with a series of electrophiles, thus providing facile accesses to stereochemically well-defined functionalized alkenes. Mechanistic studies by experimental and theoretical approaches imply that polar hydride addition from magnesium hydride (MgH₂) is responsible for the process.

Anti-hydromagnesiation of aryl alkynes was facilitated solely by magnesium hydride. The resulting alkenylmagnesium intermediates were functionalized with various electrophiles to afford stereochemically defined tri-substituted alkenes.