Painlevé is theorem on automorphic functions

It is proved that a certain type of third order algebraic differential equations defined over ℂ which are satisfied by Schwarz triangle functions, cannot be reduced to first order.     

Theoretical study of resonant tunneling in rectangular double-, triple-, quadruple-, and quintuple-barrier structures

The transmission coefficient and the resonance condition in the one-dimensional rectangular double-, triple-, quadruple-, and quintuple-barrier structures are derived theoretically under the assumption of the constant tunneling effective mass. It is found that the resonance energies are different from the eigenvalues in the quantum well due to coupling between wells in the multiple-barrier (much more than triple-barrier) structures. It is confirmed that the transmission spectrum is a Lorentzian near to energies of resonance.     

Prediction of sinkage and motion resistance of a tracked vehicle using plate penetration test

The relationship between contact pressure and sinkage must be represented by a mathematical model to estimate the sinkage and the motion resistance due to a vehicle. In this study an approximate and simple pressure-sinkage model is proposed. This model takes into account the effect of the size of the penetration plate on soil response, and includes two soil values that can be obtained by a single plate penetration test. It is submitted that the sinkage and the motion resistance of a tracked vehicle can be estimated by means of the proposed model.     

Versatile In Situ Generated N‐Boc‐Imines: Application to Phase‐Transfer‐Catalyzed Asymmetric Mannich‐Type Reactions

The efficient construction of nitrogen‐containing organic compounds is a major challenge in chemical synthesis. Imines are one of the most important classes of electrophiles for this transformation. However, both the available imines and applicable nucleophiles for them are quite limited given the existing preparative methods. Described herein are imine precursors which generate reactive imines with a wide variety of substituents under mild basic conditions. This approach enables the construction of various nitrogen‐containing molecules which cannot be accessed by the traditional approach. The utility of the novel imine precursor was demonstrated in the asymmetric Mannich‐type reaction under phase‐transfer conditions.     

Phase structure change and ER effect in liquid crystalline polymer/dimethylsiloxane blends

The mechanism of the electrorheological (ER) effect in two types of liquid crystalline polymer (LCP)/dimethylsiloxane (DMS) blends was investigated by rheological measurements and by structure observation under electric field and shear flow. The results show that the phase structures of these immiscible blends can be categorized into slipping (low viscosity) and non-slipping (high viscosity) states. In the non-slipping state, higher viscosity LCP domains connect the electrodes. In the slipping state, on the other hand, LCP domains do not connect the electrodes and the shear is mainly confined in the lower viscosity DMS domains. The ER effect (electrically induced viscosity increase) originates from the electrically induced slipping to non-slipping transition. In one of the blends, the ER effect occurs only at high shear rate, since this blend is in non-slipping state even under no field if the shear rate is low. Received: 29 April 1997 Accepted: 3 November 1997