Fixed Point Theorems of Kannan Type for Cyclical Contractive Conditions

The main aim of this paper is to obtain fixed point theorems for Kannan and Zamfirescu operators in the presence of cyclical contractive condition. A method for approximation of the fixed points is also provided, for which both a priori and a posteriori error estimates are given. Our results generalize, unify and extend several important fixed points theorems in literature. In order to illustrate the efficiency of our generalizations five significant examples are also given.

Null Condition for Semilinear Wave Equation with Variable Coefficients

∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”

Active Monitoring and Decision Making Problem

Active monitoring and problem of non-stable of sound signal parameters in the regime of piling up response signal of environment is under consideration. Math model of testing object by set of weak stationary dynamic actions is offered. The response of structures to the set of signals is under processing for getting important information about object condition in high frequency band. Making decision procedure by using researcher’s heuristic and aprioristic knowledge is discussed as well. As an example the result of numerical solution is given.

Signal Processing under Active Monitoring

This paper describes a method of signal preprocessing under active monitoring. Suppose we want to solve the inverse problem of getting the response of a medium to one powerful signal, which is equivalent to obtaining the transmission function of the medium, but do not have an opportunity to conduct such an experiment (it might be too expensive or harmful for the environment). Practically the problem can be reduced to obtaining the transmission function of the medium. In this case we can conduct a series of experiments of relatively low power and superpose the response signals. However, this method is conjugated with considerable loss of information (especially in the high frequency domain) due to fluctuations of the phase, the frequency and the starting time of each individual experiment. The preprocessing technique presented in this paper allows us to substantially restore the response of the medium and consequently to find a better estimate for the transmission function. This technique is based on expanding the initial signal into the system of orthogonal functions.

Model of Active Structural Monitoring and Decision-making for Dynamic Identification of Buildings, Monuments and Engineering Facilities

Structural monitoring and dynamic identification of the manmade and natural hazard objects is under consideration. Math model of testing object by set of weak stationary dynamic actions is offered. The response of structures to the set of signals is under processing for getting important information about object condition in high frequency band. Making decision procedure into active monitoring system is discussed as well. As an example the monitoring outcome of pillar-type monument is given.

Intelligent Computations for Flood Monitoring

Floods represent the most devastating natural hazards in the world, affecting more people and causing more property damage than any other natural phenomena. One of the important problems associated with flood monitoring is flood extent extraction from satellite imagery, since it is impractical to acquire the flood area through field observations. This paper presents a method to flood extent extraction from synthetic-aperture radar (SAR) images that is based on intelligent computations. In particular, we apply artificial neural networks, self-organizing Kohonen’s maps (SOMs), for SAR image segmentation and classification. We tested our approach to process data from three different satellite sensors: ERS-2/SAR (during flooding on Tisza river, Ukraine and Hungary, 2001), ENVISAT/ASAR WSM (Wide Swath Mode) and RADARSAT-1 (during flooding on Huaihe river, China, 2007). Obtained results showed the efficiency of our approach.

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

ACM Computing Classification System (1998): E.4.

Method of Averaging for Impulsive Differential Inclusions

AMS subject classification: Primary 49N25, Secondary 49J24, 49J25.

Optimum Chemical Balance Weighing Design under Certain Condition

2000 Mathematics Subject Classification: 62K05, 05B05.