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The need to enhance query performance in databases within the contemporary information environment is crucial for ensuring efficient operations across various domains. This paper is dedicated to an analysis of database indexing techniques aimed at understanding their impact on query performance and efficiency. It meticulously examines various types of indexes, including B-trees, hash tables, and textual indexes, analyzing their advantages and limitations.

The user activity for finding informative meaningful objects needed to solve the problem is considered. To formalize this activity, set theory is used. The mathematical models of formulation of request, analysis of the issued documents and selection of information objects for the solution to the user problem are presented. In addition, mathematical models of intellectual activitiesof user and cognitive processes are developed. The experimental results of the search engines such as Google, Yandex, META, Rambler, Yahoo are given.

Using the analogue neural circuit of maximal value signals from signal set identification is proposed for information retrieval in data sets. The circuit is fast, it has simple structure and can be implemented in a modern hardware. A resolution of the circuit is theoretically infinite and it is not dependent on a value of its parameter. An average time necessary for trajectory convergence of the circuit state variable to a steady state is not dependent on a dimension of input data.

The article considered the information systems used in the libraries to improve their work processes. The basic sources of information for digital libraries were given. The paper analyzed the basic requirements for digital libraries about the presentation of information. Also, the major formats were considered in this article, which are currently used by digital libraries to provide relevant information to users.