1998 Fiscal Year Final Research Report Summary
applicatin of the recursive function theory to problems of computational quantity
| Project/Area Number |
09640257
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
SATOH Junya Graduate School of Human Informatics, Nagoya University Associate Professor, 大学院・人間情報学研究科, 助教授 (20235352)
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| Co-Investigator(Kenkyū-buntansha) |
YASUMOTO Masahiro Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (10144114)
MATSUBARA Yo School of Informatics and Sciences, Associate Professor, 情報文化部, 助教授 (30242788)
IHARA Shunsuke School of Informatics and Sciences, Professor, 情報文化部, 教授 (00023200)
OZAWA Masanao School of Informatics and Sciences, Professor, 情報文化部, 教授 (40126313)
MITSUI Taketomo Graduate School of Human Informatics, Professor, 大学院・人間情報学研究科, 教授 (50027380)
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| Project Period (FY) |
1997 – 1998
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| Keywords | recursive function / computational quantity / polynomial-time |
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| Research Abstract |
(1)We extend a well-known formula for sums of products of two Bernoulli numbers to that of Garlitz's q-Bernoulli numbers.
(2)We give a Kaneko's type of recurrence formula for the q-Bernoulli numbers attached to formal group.
(3)A linearized implicit finite difference method for the KdV is proposed and straightforwardly extended to the KP equation. We investigate the order of accuracy of the method and prove the method to be unconditionally lineary stable.
(4)Thehalt scheme for quantum Turing machine, originally proposed by Deutsch, is reformulated precisely and is proven to work without spoiling the computation.
(5)We consider continuous-time Gaussian channels with feedback and investigate problems on the mutual information and the channel capacity. While, in most of the previous works, some conditions are imposed on the Gaussian noise, in this paper we do not require any special conditions on the Gaussian noise. We derive a formula for the mutual information transmitted over the Gaussian channel with feedback. Then we show that the capacity of the channel is achieved in linear schemes, more precisely, achieved by sending a Gaussian message with the aid of linear feedback. We also show some inequalities concerning the capacity of the channel.
(6)We present a simple condition for an ideal to be nowhere precipitous. Through this condition we show nowhere precipitousness of fundamental ideals on P_<kappa>lambda paticular the non-stationary ideal NS_<kappa>lambda under cardinal arithmetic assumptions.
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