In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.

introduction the chemical characteristic of groundwater as a major source of water supply for human life is an important factor in determining the usage of it for agriculture, industry and drinking. useful techniques and different methods of studying the chemical composition of groundwater such as correlation coefficient, descriptive statistics, factor analysis and cluster analysis provide an u...

Evaluating pairwise comparisons breaks down complex decision problems into tractable ones. Pairwise comparison matrices (PCMs) are regularly used to solve multiple-criteria decision-making (MCDM) problems using Saaty’s analytic hierarchy process (AHP) framework. There are two significant drawbacks of using PCMs. First, humans evaluate PCM in an inconsistent manner. Second, PCMs of large problem...

We discuss a possibility of visual data global analysis with respect to the aesthetic (harmonious) criteria. We explain our approach that is mathematical based and expressed by the Hereditary Entropy Thesis. We give some computational evidence which outlines aims and indicates meaning of this project.

A new method for determining the optimal parameters for Nearest Neighbor Deblurring algorithm is presented. The maximum entropy in image frequency domain is used as the optimization criteria. The proposed method allows finding optimal parameters from three images: the image in focus and two images at adjacent levels. An automatic parameter setup procedure can be built on the basis of proposed m...

A strong discrepancy of criteria appears in texts on Statistical Mechanics when associating the partition function of simple magnetic systems with thermodynamical potentials. The aim of this work is to provide an adequate description, starting from the maximization of entropy. Finally, a discussion about some thermodynamic properties is given. r 2002 Elsevier Science B.V. All rights reserved.

We apply polarities, axiallities and the notion of entropy to the task of identifying marketable items and the customers that should be approached in a marketing campaign. An algorithm that computes the criteria for identifying marketable items and the corresponding experimental work is also included.

The maximum entropy method has been applied to investigate the oscillating structure in the pp− and pp−elastic scattering differential cross-section at high energy and small momentum transfer. Oscillations satisfying quite realistic reliability criteria have been found. e-mail address: [email protected] e-mail address: [email protected] e-mail address: [email protected]

The present study carefully examined entropy generation during wustite pellet reduction to sponge iron. The finite volume method was used to solve the governing equations. The grain model was used to simulate the reaction rate. The reactant gases including carbon monoxide and hydrogen were converted to water and carbon dioxide after wustite reduction. Entropy is generated by heat transfer, mass...