l-stable Functions and Constrained Optimization

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5].

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

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.

A Recession Notion for a Class of Monotone Bivariate Functions

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.

A Multicriteria Decision Support System MultiDecision-1

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making."

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Оптимизация на учителския състав в училище

Silvia Baeva - In the Ministry of Education and Science’s system it has been talked about optimization of the school network; this optimization can be carried out in different directions and be supported by laws. An important aspect in the optimization of the school network is to reduce costs and increase overall efficiency in each school. We will formulate this aspect as a problem of the multicriteria decisions making and by appropriate numbers of methods and criteria it can be transformed to the problem of unicriterion optimization. This problem is separated into two stages: 1-th stage – determining the minimum number of classes in a school under certain statutory provisions for the size of each of them; 2-th stage – the appointment of a minimum number of teachers and achievement of maximal effectiveness of teaching and acquiring of knowledge and skills by students according to certain statutory provisions for teachers’ annual norms of subjects and number of hours in a particular subject area and the salaries of teachers. The achievement of maximum overall efficiency is a priority in all schools.

Multiresponse Robust Engineering: Case with Errors in Factor Levels

2000 Mathematics Subject Classification: 62J05, 62J10, 62F35, 62H12, 62P30.

Application of Statistical Experimental Design in Food Sciences

The development of new, health supporting food of high quality and the optimization of food technological processes today require the application of statistical methods of experimental design. The principles and steps of statistical planning and evaluation of experiments will be explained. By example of the development of a gluten-free rusk (zwieback), which is enriched by roughage compounds the application of a simplex-centroid mixture design will be shown. The results will be illustrated by different graphics.

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.