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The purpose of this paper is to provide the general method for the solution of the Boolean function's primary function, and its application in encryption systems.

In the Boolean function theory, there is always a lack in the general method for the solution of primary function. This paper uses a very useful tool – e‐derivative, and by the help of this tool, obtains some very useful theorems.

The paper not only finds the method of solving the primary function of the Boolean function but also provides its application in encryption systems.

The Boolean function's primary function is also very useful in the detection of circuitry, not introduced in this paper.

This paper is very useful for information security.

The paper solves the initial‐value problem of the Boolean function's primary function, and constructs some Boolean functions with many cryptographical characters which are very useful in encryption systems.

The purpose of this paper is to develop a new mathematical method for the reliability analysis and evaluation of multi-state system (MSS) reliability that agrees with specifics of such system. It is possible based on the application of multiple-valued logic (MVL) that is a natural extension of Boolean algebra used in reliability analysis.

Similar to Boolean algebra, MVL is used for the constriction of the structure function of the investigated system. The interpretation of the structure function of the MSS in terms of MVL allows using mathematical methods and approaches of this logic for the analysis of the structure function.

The logical differential calculus is one of mathematical approaches in MVL. The authors develop new method for MSS reliability analysis based on logical differential calculus, in particular direct partial logical derivatives, for the investigation of critical system states (CSSs). The proposed method allows providing the qualitative and quantitative analyses of MSS: the CSS can be defined for all possible changes of any system component or group of components, and probabilities of this state can also be calculated.

The proposed method permits representing the MSS in the form of a structure function that is interpreted as MVL function and provides the system analyses without special transformation into Boolean interpretation and with acceptable computational complexity.

Modified reconstructability analysis (MRA), a novel decomposition technique within the framework of set‐theoretic (crisp possibilistic) reconstructability analysis, is applied to three‐variable NPN‐classified Boolean functions. MRA is superior to conventional reconstructability analysis, i.e. it decomposes more NPN functions. MRA is compared to Ashenhurst‐Curtis (AC) decomposition using two different complexity measures: log‐functionality, a measure suitable for machine learning, and the count of the total number of two‐input gates, a measure suitable for circuit design. MRA is superior to AC using the first of these measures, and is comparable to, but different from AC, using the second.

This paper aims to show how a sociological description – a swarm analysis of the Nazi dictatorship – initially made with the means borrowed from George Spencer-Brown’s Calculus of Indications, can be transformed into a digital circuit and with which methods and tools of digital mathematics this digital circuit can be analyzed and described in its behavior. Thus, the paper also aims to contribute to a better understanding of Chapter 11 of “Laws of Form.”

The analysis uses methods of automata theory for finite, deterministic automata. Basic set operations of digital mathematics and special set operations of the Boolean Differential Calculus are used to calculate digital circuits. The software used is based on ternary logic, in which the binary Boolean logic of the elements {0, 1} is extended by the third element “Don’t care” to {0, 1, −}.

The paper confirms the method of transforming a form into a digital circuit derived from the comparative functional and structural analysis of the Modulator from Chapter 11 of “Laws of Form” and defines general rules for this transformation. It is shown how the indeterminacy of re-entrant forms can be resolved in the medium of time using the methods of automata theory. On this basis, a refined definition of the degree of a form is presented.

The paper shows the potential of interdisciplinary approaches between sociology and information technology and provides methods and tools of digital mathematics such as ternary logic, Boolean Differential Calculus and automata theory for application in sociology.

The set of fuzzy threshold functions is defined to be a fuzzy set over the set of functions. All threshold functions have full memberships in this fuzzy set. Defines and investigates a distance measure between a non‐linearly separable function and the set of all threshold functions. Defines an explicit expression for the membership function of a fuzzy threshold function through the use of this distance measure and finds three upper bounds for this measure. Presents a general method to compute the distance, an algorithm to generate the representation automatically, and a procedure to determine the proper weights and thresholds automatically. Presents the relationships among threshold gate networks, artificial neural networks and fuzzy neural networks. The results may have useful applications in logic design, pattern recognition, fuzzy logic, multi‐objective fuzzy optimization and related areas.

A binary decision diagram (BDD) is a representation of Boolean functions that uses the notion of two‐way branching. It has long been used in the synthesis, simulation and testing of Boolean circuits, and has recently been adopted to solve fault tree models for both quantitative and qualitative reliability analyses. In this paper, the concept of binary decision diagram is first introduced. Then, a new method is proposed to analyze the reliability of fault tolerant systems using binary decision diagrams. Traditionally, such analyses are tackled by using fault trees based on cutsets. For complex models, an algorithm based on binary decision diagrams can shorten solution time dramatically. Experimental results are also presented to demonstrate the practicality and benefits of applying the proposed method in reliability analysis.

A general description of a continuous (‐valued) logic is given, basic operations of the logic are defined, and some problems and particulars of their solutions are discussed. First, we define algebra of continuous logic and enumerate its basic unary, binary and ternary functions. All laws of continuous logic are compared with laws of discrete binary logic. We discuss how to enumerate all functions of continuous logic with specified number of variables and how to represent the functions in a standard form. Procedures of minimization of continuous logical functions and their decomposition into the functions with less clarity are exploited. The procedures are compared with their counterparts from binary logic. We also tackle problems of analysis and synthesis of continuous logical functions, and show that the problem of synthesis may not have a solution. Basics of differential and integral calculus are applied to continuous valued logic. We demonstrate that any continuous logical function has the points where a derivative does not exist. At the end of the paper we briefly discuss an incompleteness problem of continuous logic, application of continuous logic in mathematics, engineering and economy, give examples, draw a perspective of further development and supply extensive bibliography of Russian works in the field.

In addition to the prediction of effective elastic properties of random media, the statistical variations of these properties for finite size specimens are of practical interest. From finite element method calculations on simulated 2D random media, size effects are studied and modelled. They enable us to draw practical conclusions for finite element applications to elastic random media.

Research on context‐aware systems design has received significant attention lately. One of the research directions on context‐aware systems is towards context‐aware frameworks adapted to domain‐specific requirements, aiming to improve their applicability in a variety of applications, which share common requirements. The purpose of this paper is to present the design of a domain‐specific context‐aware platform supporting context acquisition, presentation and rule‐based control.

The proposed platform uses a formal context model, based on ontologies description, aiming to provide a common representation of contextual information, facilitating thus integration and reusability in application domains, which embrace a common set of requirements. A context‐aware system has been built upon a well defined data model, which inherits a list of offered functionalities and/or services at the acquisition, presentation and reasoning level. The presented platform entails an event‐driven context‐based inference mechanism aiming to enable automated reasoning.

The proposed platform has been applied in two different case studies, aiming to provide a proof of concept towards the applicability of the proposed framework in different application areas through the offered integration and adaptation mechanisms. Evaluation results, in the frame of these case studies, show the ease of using the platform and its acceptable performance in practice.

As context‐aware applications within specific domains share common requirements, it becomes mandatory to offer solutions, like the proposed in this paper, which can be easily adapted to application semantics and can be reused with different levels of abstractions in order to meet specific requirements. The present paper proposes a domain‐specific platform, which applies on a variety of application types with a common set of requirements.

This paper aims to design an expert system that gets data from researchers and determines their maturity level. This system can be used for determining researchers’ support programs as well as a tool for researchers in research-based organizations.

This study focuses on designing the inference engine as a component of an expert system. To do so, rough set theory is used to design rule models. Various complete, discretizing and reduction algorithms are used in this paper, and different models were run.

The proposed inference engine has the validity of 99.8 per cent, and the most important attributes to determine the maturity level of researchers in this model are “commitment to research” and “attention to research plan timeline”.

To accurately determine researchers’ maturity model, solely referring to documents and self-reports may reduce the validation. More validation could be reached through using assessment centers for determining capabilities of samples and observations in each maturity level.

The assessment system for the professional maturity of researchers is an appropriate tool for funders to support researchers. This system helps the funders to rank, validate and direct researchers. Furthermore, it is a valid criterion for researchers to evaluate and improve their abilities. There is not any expert system to assess the researches in literature, and all models, frameworks and software are conceptual or self-assessment.