Applications of Radial Basis Neural Networks for Area Forest

This paper proposes a new method using radial basis neural networks in order to find the classification and the recognition of trees species for forest inventories. This method computes the wood volume using a set of data easily obtained. The results that are obtained improve the used classic and statistical models.

Distances between Predicates in By-Analogy Reasoning Systems

The purpose is to develop expert systems where by-analogy reasoning is used. Knowledge “closeness” problems are known to frequently emerge in such systems if knowledge is represented by different production rules. To determine a degree of closeness for production rules a distance between predicates is introduced. Different types of distances between two predicate value distribution functions are considered when predicates are “true”. Asymptotic features and interrelations of distances are studied. Predicate value distribution functions are found by empirical distribution functions, and a procedure is proposed for this purpose. An adequacy of obtained distribution functions is tested on the basis of the statistical 2 χ –criterion and a testing mechanism is discussed. A theorem, by which a simple procedure of measurement of Euclidean distances between distribution function parameters is substituted for a predicate closeness determination one, is proved for parametric distribution function families. The proposed distance measurement apparatus may be applied in expert systems when reasoning is created by analogy.

Обобщенные Интервальные Оценки в Сценарном Анализе

Показано, что метод обобщенных интервальных оценок (ОИО), первоначально предназначавшийся для выявления и формализованного представления экспертных знаний об известных с неопределенностью количественных исходных данных моделей интеллектуальных систем поддержки экспертных решений (СПЭР), можно рассматривать как развитие сценарного подхода в теории принятия решений. Предложены процедуры исследования методом ОИО задач с зависимыми параметрами, таких как задача прогнозирования объемов извлекаемых запасов месторождений в зависимости от уровней цены на углеводороды. Установлены аналитические соотношения для функций распределения вероятностей обобщенных равномерных распределений, используемых в сценарном анализе и анализе результирующих показателей моделей включенных в базу моделей СПЭР.

Trained Neural Network Characterizing Variables for Predicting Organic Retention by Nanofiltration Membranes

Many organic compounds cause an irreversible damage to human health and the ecosystem and are present in water resources. Among these hazard substances, phenolic compounds play an important role on the actual contamination. Utilization of membrane technology is increasing exponentially in drinking water production and waste water treatment. The removal of organic compounds by nanofiltration membranes is characterized not only by molecular sieving effects but also by membrane-solute interactions. Influence of the sieving parameters (molecular weight and molecular diameter) and the physicochemical interactions (dissociation constant and molecular hydrophobicity) on the membrane rejection of the organic solutes were studied. The molecular hydrophobicity is expressed as logarithm of octanol-water partition coefficient. This paper proposes a method used that can be used for symbolic knowledge extraction from a trained neural network, once they have been trained with the desired performance and is based on detect the more important variables in problems where exist multicolineality among the input variables.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Fuzzy Membership Functions in a Fuzzy Decision Making Problem

Authors analyses questions of the subjective uncertainty and inexactness situations in the moment of using expert information and another questions which are connected with expert information uncertainty by fuzzy sets with rough membership functions in this article. You can find information about integral problems of individual expert marks and about connection among total marks “degree of inexactness” with sensibility of measurement scale. A lot of different situation which are connected with distribution of the function accessory significance and orientation of the concrete take to task decision making are analyses here.

Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers

For metal and metal halide vapor lasers excited by high frequency pulsed discharge, the thermal effect mainly caused by the radial temperature distribution is of considerable importance for stable laser operation and improvement of laser output characteristics. A short survey of the obtained analytical and numerical-analytical mathematical models of the temperature profile in a high-powered He-SrBr2 laser is presented. The models are described by the steady-state heat conduction equation with mixed type nonlinear boundary conditions for the arbitrary form of the volume power density. A complete model of radial heat flow between the two tubes is established for precise calculating the inner wall temperature. The models are applied for simulating temperature profiles for newly designed laser. The author’s software prototype LasSim is used for carrying out the mathematical models and simulations.

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size

2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.