| Project/Area Number |
11640160
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | SHINSHU UNIVERSITY |
|---|
Principal Investigator |
KAWABE Jun Shinshu University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (50186136)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KIMURA Morishige Shinshu University, Faculty of Engineering, Professor, 工学部, 教授 (00026345)
SAKAI Yuji Shinshu University, Faculty of Engineering, Professor, 工学部, 教授 (80021004)
OKUYAMA Yasuo Shinshu University, Faculty of Engineering, Professor, 工学部, 教授 (70020980)
TAKANO Kazuhiko Shinshu University, Faculty of Engineering, Lecturer, 工学部, 講師 (80252063)
YAMASAKI Motohiro Shinshu University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30021017)
|
|---|
| Project Period (FY) |
1999 – 2000
|
| Project Status |
Completed (Fiscal Year 2000)
|
| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
|
|---|
| Keywords | weak convergence / injective tensor integral / fuzzy optimization / Fourier coefficients / nonlinear regulator / controller time-delay / martingale-like sequence / Riemannian submersion / weak convergence of vector measures / fuzzy set / generalized Norlund summability / Bochner curvature tensor / majorization / Raccati difference equation / stochastic differential equation |
|---|
| Research Abstract |
We have studied weak convergence of vector measures with values in Banach spaces and nuclear spaces, and have applied it to several interesting problems in real analysis, probability theory, control theory, differential geometry and so on. Some of our important results are as follows :
1. By an essential use of Bartle's bilinear integration theory, it is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures.
2. The weak compactness of a set of control inputs is shown in the case that they are given by the gravity calculation of time dependent fuzzy membership functions. As an application, the existence of optimal solution is discussed in a fuzzy control for an open-loop system.
3. We obtain a convergence theorem of compound probability measures on a uniform space for a net of uniformly equicontinuous transition probabilities. This result applies to Gaussian transition probabilities on a Hilbert spaces.
4. We obtain a general theorem for the method (N,p_n, q_n)(C, 1) summability of the sequence {nB_n (x)}, which contains some theorems due to S.P.Khare, V.K.Tripathi and A.N.Singh and et al.
5. It is shown that some central manifold exists in a neighborhood of a point of equilibrium.
6. It is shown that a set of fuzzy membership functions in the NBV space is compact with respect to the weak^* topology. This result applies to the existence of fuzzy optimal control.
7. A relation between two convergence theorems of maritingale in the limit, i.e., L^1-boundedness and integrability of stopped processes is studied.
8. We define another almost complex structure (resp.almost contact structure) and an indefinite Kahlerian (resp. Sasakian) manifold with affine connection.
|
