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91.
T. Komatsu 《Lithuanian Mathematical Journal》2006,46(4):417-431
The tanh-type, tan-type, and e-type Hurwitz continued fractions have been generalized by the author. In this paper, we study a generalized form
of e2-type Hurwitz continued fractions by using confluent hypergeometric functions. We also obtain a similar type of Tasoev continued
fractions.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 513–531, October–December, 2006. 相似文献
92.
R.V.S.S.N Ravikumar R Komatsu A.V Chandrasekhar Y.P Reddy 《Journal of Physics and Chemistry of Solids》2003,64(2):261-264
Electron paramagnetic resonance and optical investigations of copper and chromium doped LiRbB4O7 glasses are carried out. From the results and discussions, it is predicted that both the transition metal ions exhibit octahedral environment. In the case of Cr3+, the site symmetry is near octahedral, whereas in the case of Cu2+, it is tetragonally distorted octahedral environment. Crystal field, spin-Hamiltonian and bonding parameters are evaluated. The bonding parameters are suggesting ionic. 相似文献
93.
94.
95.
96.
Takao Komatsu 《Monatshefte für Mathematik》2005,27(2):47-60
The continued fractions studied by Tasoev are not widely known although their characteristics are very similar to those of Hurwitz continued fractions. Recently, the author found several general forms of Tasoev continued fractions, and by applying this method he also obtained some more general forms of Hurwitz continued fractions belonging to so called tanh-type and tan-type. In this paper, we constitute a new class of general forms of Hurwitz continued fractions of e-type. The known continued fraction expansions of e1/a (a 1), ae1/a and (1/a)e1/a are included as special cases. The corresponding Tasoev continued fractions are also derived. 相似文献
97.
Takao Komatsu 《Monatshefte für Mathematik》2005,145(1):47-60
The continued fractions studied by Tasoev are not widely known although their characteristics are very similar to those of Hurwitz continued fractions. Recently, the author found several general forms of Tasoev continued fractions, and by applying this method he also obtained some more general forms of Hurwitz continued fractions belonging to so called tanh-type and tan-type. In this paper, we constitute a new class of general forms of Hurwitz continued fractions of e-type. The known continued fraction expansions of e1/a (a 1), ae1/a and (1/a)e1/a are included as special cases. The corresponding Tasoev continued fractions are also derived. 相似文献
98.
99.
Kotaro Komatsu 《The Journal of Mathematical Behavior》2010,29(1):1-10
The purpose of this study is to explore how primary school students reexamine their conjectures and proofs when they confront counter-examples to the conjectures they have proved. In the case study, a pair of Japanese fifth graders thought that they had proved their primitive conjecture with manipulative objects (that is, they constructed an action proof), and then the author presented a counter-example to them. Confronting the counter-example functioned as a driving force for them to refine their conjectures and proofs. They understood the reason why their conjecture was false through their analysis of its proof and therefore could modify their primitive conjecture. They also identified the part of the proof which was applicable to the counter-example. This identification and their action proof were essential for their invention of a more comprehensive conjecture. 相似文献
100.
[Structure: see text] tert-Butyl hypoiodite (t-BuOI) was found to be a powerful reagent for the cyclization of N-alkenylamides leading to a variety of N-heterocycles under extremely mild conditions. When N-alkenylsulfonamides were employed in the reaction, three- to six-membered saturated N-heterocycles were obtained in good to excellent yields with complete stereoselectivity. The method was applicable to the cyclization of alkenylbenzamide derivatives to afford N-, O- or N-, S-heterocycles. 相似文献