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System identification from multiple-trial data corrupted by non-repeating periodic disturbances

Minh Phan;  Richard Longman;  Soo Lee;  Jae-Won Lee — 2003

International Journal of Applied Mathematics and Computer Science

Iterative learning and repetitive control aim to eliminate the effect of unwanted disturbances over repeated trials or cycles. The disturbance-free system model, if known, can be used in a model-based iterative learning or repetitive control system to eliminate the unwanted disturbances. In the case of periodic disturbances, although the unknown disturbance frequencies may be the same from trial to trial, the disturbance amplitudes, phases, and biases do not necessarily repeat. Furthermore, the...

Spherical harmonics on Grassmannians

Roger Howe;  Soo Teck Lee — 2010

Colloquium Mathematicae

We propose a generalization of the theory of spherical harmonics to the context of symmetric subgroups of reductive groups acting on flag manifolds. We give some sample results for the case of the orthogonal group acting on Grassmann manifolds, especially the case of 2-planes.

Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang;  Yu-Qing Chen;  Yeol Je Cho;  Byung-Soo Lee — 1998

Commentationes Mathematicae Universitatis Carolinae

Let P be a cone in a Hilbert space H , A : P → 2 P be an accretive mapping (equivalently, - A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type - A + T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in L 2 ( Ω ) .

Coincidence point theorems in certain topological spaces

Jong Soo Jung;  Yeol Je Cho;  Shin Min Kang;  Yong Kab Choi;  Byung Soo Lee — 1999

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in F-type topological space. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

Random fixed point theorems for a certain class of mappings in Banach spaces

Jong Soo Jung;  Yeol Je Cho;  Shin Min Kang;  Byung-Soo Lee;  Balwant Singh Thakur — 2000

Czechoslovak Mathematical Journal

Let ( Ω , Σ ) be a measurable space and C a nonempty bounded closed convex separable subset of p -uniformly convex Banach space E for some p > 1 . We prove random fixed point theorems for a class of mappings T Ω × C → C satisfying: for each x , y ∈ C , ω ∈ Ω and integer n ≥ 1 , ∥ T n ( ω , x ) - T n ( ω , y ) ∥ ≤ a ( ω ) · ∥ x - y ∥ + b ( ω ) { ∥ x - T n ( ω , x ) ∥ + ∥ y - T n ( ω , y ) ∥ } + c ( ω ) { ∥ x - T n ( ω , y ) ∥ + ∥ y - T n ( ω , x ) ∥ } , where a , b , c Ω → [ 0 , ∞ ) are functions satisfying certain conditions and T n ( ω , x ) is the value at x of the n -th iterate of the mapping T ( ω , · ) . Further we establish for these mappings some random fixed point theorems in a Hilbert space, in L p spaces, in Hardy spaces H p and in Sobolev spaces H k , p ...

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