An application of the Kantorovich theoremto nonlinear finite element analysis

Summary. Finite element solutions of strongly nonlinear elliptic boundary value problems are considered. In this paper, using the Kantorovich theorem, we show that, if the Fréchet derivative of the nonlinear operator defined by the boundary value problem is an isomorphism at an exact solution, then there exists a locally unique finite element solution near the exact solution. Moreover, several a priori error estimates are obtained. Received March 2, 1998 / Published online September 7, 1999     

Consideration for Affects of an XOR in a Random Number Generator Using Ring Oscillators

A cloud service to offer entropy has been paid much attention to. As one of the entropy sources, a physical random number generator is used as a true random number generator, relying on its irreproducibility. This paper focuses on a physical random number generator using a field-programmable gate array as an entropy source by employing ring oscillator circuits as a representative true random number generator. This paper investigates the effects of an XOR gate in the oscillation circuit by observing the output signal period. It aims to reveal the relationship between inputs and the output through the XOR gate in the target generator. The authors conduct two experiments to consider the relevance. It is confirmed that combining two ring oscillators with an XOR gate increases the complexity of the output cycle. In addition, verification using state transitions showed that the probability of the state transitions was evenly distributed by increasing the number of ring oscillator circuits.     

Effect of impingement angle on the outcome of single water drop impact onto a plane water surface

Experiments of single water drop impact onto a plane water surface were carried out to investigate the effect of impingement angle on the total mass of secondary drops produced during the collision. When the impingement angle (the angle between the velocity vector of primary drop and the normal vector to water surface) was less than 50°, an increase in the impingement angle led to a remarkable increase in the total mass of secondary drops; this could be attributed to a significant increase in the secondary drop size. However, no secondary drop was observed within the experimental ranges tested when the impingement angle exceeded 70°.     

On the robust thermodynamical structures against arbitrary entropy form and energy mean value

We discuss how the thermodynamical Legendre transform structure can be retained not only for the arbitrary entropic form but also for the arbitrary form of the energy constraints by following the discussion of Plastino and Plastino. The thermodynamic relation between the expectation values and the conjugate Lagrange multipliers are seen to be universal. Furthermore, Gibbs' fundamental equation is shown to be unaffected by the choice of the entropy and the definition of the mean values due to the robustness of the Legendre transform structure. Received 28 April 2000 and Received in final form 29 July 2000     

Total Synthesis of 6-Deoxydihydrokalafungin,a Key Biosynthetic Precursor of Actinorhodin,and Its Epimer

In this article, we report the total synthesis of 6-deoxydihydrokalafungin (DDHK), a key biosynthetic intermediate of a dimeric benzoisochromanequinone antibiotic, actinorhodin (ACT), and its epimer, epi-DDHK. Tricyclic hemiacetal with 3-siloxyethyl group was subjected to Et₃SiH reduction to establish the 1,3-cis stereochemistry in the benzoisochromane, and a subsequent oxidation/deprotection sequence then afforded epi-DDHK. A bicyclic acetal was subjected to AlH₃ reduction to deliver the desired 1,3-trans isomer in an approximately 3:1 ratio, which was subjected to a similar sequence to that used for the 1,3-cis isomer that successfully afforded DDHK. A semisynthetic approach from (S)-DNPA, an isolable biosynthetic precursor of ACT, was also examined to afford DDHK and its epimer, which are identical to the synthetic products.     

Total Synthesis of Decahydroquinoline Poison Frog Alkaloids ent-cis-195A and cis-211A

The total synthesis of two decahydroquinoline poison frog alkaloids ent-cis-195A and cis-211A were achieved in 16 steps (38% overall yield) and 19 steps (31% overall yield), respectively, starting from known compound 1. Both alkaloids were synthesized from the common key intermediate 11 in a divergent fashion, and the absolute stereochemistry of natural cis-211A was determined to be 2R, 4aR, 5R, 6S, and 8aS. Interestingly, the absolute configuration of the parent decahydroquinoline nuclei of cis-211A was the mirror image of that of cis-195A, although both alkaloids were isolated from the same poison frog species, Oophaga (Dendrobates) pumilio, from Panama.