Identification of Forces in Vibrating Plates by Pointwise and Line Observations: Uniqueness and Stability

1995 ◽  
Author(s):  
Masahiro Yamamoto
Keyword(s):  
Finite Time ◽  
Large Time ◽  
Single Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Line Parallel ◽  
Vibrating Plates ◽  
External Forces ◽  
Spatially Varying

Abstract We consider determination of spatially varying external forces in a rectangle vibrating plate from displacement observed along a line parallel to a side of the plate over a finite time interval. For a suitable choice of the line and a sufficient large time interval, we prove the uniqueness of external forces and estimate them by appropriate norm of displacement. Moreover we discuss determination of external forces from displacement observed at a single point over a time interval.

scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance

2019 ◽  
Vol 27 (1) ◽  
pp. 133-149 ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Wave Equation ◽  
Time Reversal ◽  
Finite Time ◽  
Single Point ◽  
Arbitrary Point ◽  
Time Interval ◽  
Finite Time Interval ◽  
Reversal Invariance ◽  
Enclosure Method ◽  
Space Wave

Abstract The wave equation is time-reversal invariant. The enclosure method, using a Neumann data generated by this invariance, is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a finite time interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.

scholarly journals The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Masaru Ikehata
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Finite Time ◽  
Single Point ◽  
Obstacle Problems ◽  
Time Interval ◽  
Finite Time Interval ◽  
Partial Differential ◽  
Response Operator ◽  
Enclosure Method

AbstractA final and maybe the simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

scholarly journals Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Stochastic Boundedness ◽  
Partly Unknown Transition Probabilities ◽  
Finite Time Boundedness

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

Sign in / Sign up

Export Citation Format

Share Document