A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

A Stochastic Approach for Finding of Semantically Related Words

2000 Mathematics Subject Classification: 62P99, 68T50

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

Analysis and Optimization of Synthetic Aperture Ultrasound Imaging Using the Effective Aperture Approach

An effective aperture approach is used as a tool for analysis and parameter optimization of mostly known ultrasound imaging systems - phased array systems, compounding systems and synthetic aperture imaging systems. Both characteristics of an imaging system, the effective aperture function and the corresponding two-way radiation pattern, provide information about two of the most important parameters of images produced by an ultrasound system - lateral resolution and contrast. Therefore, in the design, optimization of the effective aperture function leads to optimal choice of such parameters of an imaging systems that influence on lateral resolution and contrast of images produced by this imaging system. It is shown that the effective aperture approach can be used for optimization of a sparse synthetic transmit aperture (STA) imaging system. A new two-stage algorithm is proposed for optimization of both the positions of the transmitted elements and the weights of the receive elements. The proposed system employs a 64-element array with only four active elements used during transmit. The numerical results show that Hamming apodization gives the best compromise between the contrast of images and the lateral resolution.

Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

An Approach to Wealth Modelling

2000 Mathematics Subject Classification: 60G48, 60G20, 60G15, 60G17. JEL Classification: G10

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.

Probabilistic Approach to Design of Large Antenna Arrays

2000 Mathematics Subject Classification: 78A50