Part I Society, economics and science.- Scientific structures and systems.- Complex structure and system of science.- Nonlinear dynamics of scientific entities.- Science is so important.- On the connection between science and technology.- Several features of technological progress.- Science as important component of the economic growth of a country: global point of view.- Role of technology for the growth of a GDP of a country.- Role of science for development of technology.- Factors for growth of science.- Science as important component of economic growth of a country: local point of view.- Why the size of the scientific community is important?.- The effective solutions of the scientific problems depend on the size of the scientific community.- Increasing complexity of problems requires increase of the size of group of scientists that has to solve them.- Science structures are dissipative. Three levels of the structure of science.- Science as open system.- Financial, material, and human resource flows keep science in an organized state.- Levels and characteristic features of science structures.- Role of instability for evolution of science.- Model of science as a part of global model of a social system.- Two scenarios based on the model of science as a part of the social system.- Scientific competition among the nations. Extended academic diamond.- Several concluding remarks.- References.- Quality and quantity in the study of science, research work and research productivity. The role of mathematics.- Remarks about publications and other aspects of evaluation of performance in science.- Quality management systems. Processes and process indicators.- Performance measurement systems.- Analysis of key processes.- Analysis of the needs of the organization and its stakeholders.- Plan of the system and plan for implementation of the system.- An example of quality management model: EFQM.- Latent variables and their operational definition by means of groups of indicators.- Measurements, qualitative analysis, quantitative analysis.- Scales and 2 kinds of measurements.- Qualitative analysis and measurement.- Differences in statistical characteristics of processes in Nature and society.- About the non-Gaussian nature of processes in society and science.- Well, many distributions in social sciences are non-Gaussian.What follows from this?.- Several notes on scientometrics.- Examples of quantities that can be analyzed in the process of study of science dynamics.- Inequality of scientific achievements.- Knowledge landscapes.- Scientific productivity and its evaluation.- Role of science structure and system for scientific productivity.- Age effects in scientific productivity.- Notes on statistical analysis of scientific productivity.- Other factors that affect scientific productivity.- Complexity of scientific productivity.- Method of expert evaluation.- Scientific publications as a characteristic of scientific productivity.- Notes on scientce indicators and inequality.- Examples of evaluation and assessment of research work.- How to perform a complex evaluation of a researcher.- How to assess basic research.- An example of institute evaluation system: The SEP system of Netherlands.- Second example of institutes evaluation system: AERES (France).- Example for system of indicators for evaluation of national research policy: OECD indicators.- On mathematics and quantification of research performance.- English-Czerwon method for quantification of performance of research units.- Scientific performance from the point of view of information production processes.- Additional notes on application of mathematics for quantifications of scientific achievements.- Part II Indicators and indexes of scientific productivity.- Scientific productivity of individual researchers.- Introduction remarks.- Money cuts and "value for money". Peer review and evaluation by a sets of indicators and indices.- Indicators and indexes.- The h-index of Hirsch.- Advantages and disadvantage of the h-index. Use the h-index carefully.- Normalized h-index.- Tapered h-index.- Temporally bounded h-index. Age dependent h-index.- The problem of multiple authorship. h-index of Hirsch and gh-index of Galam.- m-index.- The g-index of Egghe.- The in-index.- The p-index.- IQp-index.- A-index and R-index.- Additional indexes.- h-like indexes and indexes complementary to the Hirsch.- Index.- Indexes based on normalization mechanisms.- PI-indexes.- Indexes for personal success of a researcher.- Indexes for characterization of scientific networks.- References.- Indexes for characteristics of research productivity in a group of researchers.- Indexes based on simple statistical concepts.- A simple index of quality of scientific output based on the publications in major journals.- MII-index.- Shutz coefficient of inequality.- Wilcox deviation from the mode (from the maximum percentage).- Nagel's index of equality.- Coefficient of variation.- Gini's mean relative difference.- Gini's coefficient of inequality.- Herfindahl-Hirschmann index of concentration.- Horvath's index of concentration.- RTS-index of concentration.- Diversity index of Lieberson.- Index of imbalance of Taagepera.- RT-index of fragmentation.- Indexes based on the concept of entropy.- Theil's index of entropy.- Redundancy index of Theil.- Negative entropy index.- Expected information content of Theil.- The Lorenz curve and associated indicators.- Lorenz curve.- The index of Gini from the point of view of the Lorenz curve.- Index of Kuznets.- Pareto diagram (Pareto chart).- Indexes for the case of stratified data.- References.- Comparison of research productivities of groups of researchers.- Indexes of dissimilarity and diversity.- Index of dissimilarity.- Index of diversity of Lieberson.- Indexes of difference and advantage.- Other indexes.- Index of net difference of Lieberson.- Index of average relative advantage.- Index of inequity of Coulter.- Proportionality index of Nagel.- RELEV method for assessment of scientific research performance within public institutes.- Comparison among scientific communities in different countries.- Efficiency of scientific production based on papers and patents.- Additional characteristics of scientific productivity of a nation.- Scientific elites.- Several characteristics of a scientific elite.- Several words about studied groups of institutes.- Size of elite.- Sizes of superelite, hyperelite, etc.- Strength of elite.- Remarks about some characteristics of the scientific elites of the two groups of institutes.- References.- Part III Basic laws and selected models.- Frequency and the rank approaches to scientific productivity.- Measurement of scientific productivity by publications.- Frequency approach and rank approach: general remarks.- Differential and integral form of the frequency and rank distributions.- Why frequency distributions are dominant in the natural sciences and rank distributions are frequently used in the social sciences?.- Status of Zipf distribution in the world of non-Gaussian distributions.- Importance of the stable non-Gaussian distributions for the organization of science.- Non-Gaussian distributions. Characteristic features.- Stable non-Gaussian distributions.- Frequently used stable non-Gaussian distributions.- Frequency approach. Law of Lotka for scientific publications.- Presence of extremely productive scientists: imax ¿¥.- imax: finite - the most productive scientists have finite productivity. Scientific elite according to Price.- The exponent a: measure of inequality.- The continuous limit: from law of Lotka to the distribution of Pareto.- The shortcomings of Pareto distribution and overcoming them by Pareto II distribution.- Rank approach.- Law of Zipf.- Zipf-Mandelbrot law.- Law of Bradford for scientific journals.- Distributions connected to citation analysis.- Citation analysis.- Modeling citation behavior in journals.- Quantities connected to the age of citation.- Growth dynamics of citations.- References.- Selected models for evolution of research organizations and scientific productivity.- Variation approach to scientific productivity.- A hint for a possible applicability of an variation approach.- Variation principle of Boltzmann and distribution of research productivity in the equilibrium state of the scientific system.- "Temperature".- Scientific productivity,Yule distribution and the random branching process.- Definition, initial conditions, and differential equations for the process.- How Yule process arises.- Properties of the scientific productivity according to the model.- Modeling production/citation process.- Model of h-index based on Paretian distributions.- Model of h-index based on Poisson distribution.- Matthew effect in science.- Deterministic models.- Logistic curve and its generalizations.- Aging of scientific information and importance of fundamental research.- Price model of knowledge growth. Cycles of growth of knowledge.- SI (susceptibles-infectives) discrete model of the change in the number of publications for a scientific field.- Goffman-Newill continuous model for the dynamics of populations of scientists and papers.- Continuous model of competition between systems of ideas.- Stochastic models.- Aging of scientific information as a death stochastic process.- Aging of scientific literature as nonhomogeneous birth process.- Stochastic model of scientific productivity.- Reproduction-transport equation model of the evolution of scientific subfields.- References.- Several concluding remarks.- Importance of science for society.- General characteristics of science structures and systems.- Quality management systems and performance measurement systems.

This book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to understand the nonlinear science dynamics and to be able to develop or construct systems for appropriate evaluation of research productivity and management of research groups and organizations. The dynamics of science structures and systems is complex, and the evaluation of research productivity requires a combination of qualitative and quantitative methods and measures. The book has three parts. The first part is devoted to mathematical models describing the importance of science for economic growth and systems for the evaluation of research organizations of different size. The second part contains descriptions and discussions  of numerous indexes for the evaluation of the productivity of researchers and groups of researchers of different size (up to the comparison of research productivities of research communities of nations). Part three contains discussions of non-Gaussian laws connected to scientific productivity and presents various deterministic and stochastic models of science dynamics and research productivity. The book shows that many famous fat tail distributions as well as many deterministic and stochastic models and processes, which are  well known from physics, theory of extreme events or population dynamics, occur also in the description of dynamics of scientific systems and in the description of the characteristics of research productivity. This is not a surprise as scientific systems are nonlinear, open and dissipative.