Nonlinear approximationtheoretic methods of numerical table data compression
| Project/Area Number |
22540151
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
AKASHI Shigeo 東京理科大学, 理工学部情報科学科, 教授 (30202518)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | 情報数理 / Hilbertの第13問題 / ε-エントロピー / 多変数関数 / Collatz予想 / Lee-Yorkの定理 / アトラクター / データ圧縮 / Goedel数 / Hilberの第13問題 / 数値表データ / 数値群データ / 形状認識 / Hilbertの13問題 / Arzela^Ascoliの定理 / 同程度連続性 / ソボレフノルム / フレシュ距離 / 多変数関数の重ね合わせ表現 |
|---|
| Research Abstract |
The main research results obtained in the research period which began in 2010 and ended in 2012 are the following:
(1). A version of Hilbert’s 13thproblem for infinitely differentiable functions, which remained to be open, has been solved constructively.
(2). Embedding of Collatz mapping into a certain one-dimensional compact dynamical system has enabled us to apply the theory of topological dynamics to its famous conjecture
|
Report
(4 results)
Research Products
(30 results)
