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The purpose of this paper is to use α‐dense curves for solving Boolean equations, 0‐1 integer programming problems such as the shortest path problem or the knapsack problem.

The paper's aim is to present the applications in Boolean algebra and 0‐1 integer programming of a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. The α‐dense curves generalize the space filling curves (Peanocurves,…) and fractal curves. The main idea consists in expressing n variables by means of a single one.

Apply the method to Boolean algebra and 0‐1 integer programming.

The paper presents a new method based on α‐dense curves for solving Boolean equations and 0‐1 integer programming problems.

Vulnerability analysis provides an assessment of the likelihood of system failure in a man‐made hostile environment, involving sabotage, security compromise and combat damage. The fault‐tree approach proved most useful as many obscure but significant failure modes surfaced as a result of the step‐by‐step logic involved. Analysis tools were applied to the problems of nuclear reactor sabotage, space shuttle and combat system vulnerability. An increased qualitative understanding of system vulnerabilities, the effectiveness of counter‐measures and the ranking of scenarios by their attractiveness to saboteurs or other adversaries were the chief results of the work.

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.

Discusses the relationship between computer proof and human proof. These issues are discussed both in general and specifically regarding the recent solution of the Robbins problem via a proof generated by computer. The Robbins problem was a long‐standing open problem about axioms for Boolean algebra. One point of this paper is to show that the proof of the Robbins conjecture, generated by a computer, can be filled in and understood by human beings. We accomplish this aim in the present paper by presenting a notational reformulation of Boolean algebra and the Robbins problem. The notational/linguistic issue developed here is of cybernetic, linguistic and semiotic interest. It is our contention that mathematics can behave non‐trivially under change of notation. Change of notation can be as significant as change of language. In the present case the change of language afforded by an appropriate change of notation makes a mathematical domain accessible to human beings that has heretofore been only accessible to computers.

Provides a background on the concepts and development of data mining and data warehousing that need to be known by students and educators. Then discusses the applications of data mining for the construction of graphical mappings of the sensory space as a two‐dimensional neural network grid as well as the traveling salesman problem (TSP) and simulated annealing. Data mining is also used as a tool for the construction of computer graphics as solutions to the TSP and also for the activation of an output neuron for a three‐layer feed‐forward network that is trained using a Boolean function. Conclusions and future directions of the research are also discussed.

Graph products are extensively used in the analysis and design of regular structures. It is often thought that these products are only applicable to regular graphs. The main aim of this paper is develop new products which are applicable to regular as well and non‐regular structural models.

New graph products are defined with specified domains. In these products the logical operations of the graph products are only performable in specified domains, and therefore these products can produce configurations which do not need to be regular.

New graph products are defined and a general theorem is proved for the formation of their adjacency matrices.

The presented graph products overcome the difficulty of employing graph products in structural mechanics, and in particular in space structures. The general theorem of this paper can efficiently be used in the formation of adjacency matrices of the structural models.

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 purpose of this paper is to introduce a novel approach of designing, specifying, and describing the behavior of software systems in a way that helps to predict their reliability from the reliability of the components and their interactions.

Design imperatives and relevant mathematical documentation techniques for improved reliability predictability of software systems are identified.

The design approach, which is named design for reliability predictability (DRP), integrates design for change, precise behavioral documentation and structure based reliability prediction to achieve improved reliability predictability of software systems. The specification and documentation approach builds upon precise behavioral specification of interfaces using the trace function method (TFM) and introduces a number of structure functions or connection documents. These functions capture both the static and dynamic behavior of component‐based software systems and are used as a basis for a novel document driven structure based reliability predication model.

Decades of research effort have been spent in software design, mathematical/formal specification and description and reliability prediction of software systems. However, there has been little convergence among these three areas. This paper brings a new direction where the three research areas are unified to create a new design paradigm.

The purpose of this paper is to enhance the method developed by previous researchers. In addition to using the combined interference matrix, the combined connection matrix and the combined contact matrix of product components, the disassembly sequence matrix and the combined instability matrix with platform to evaluate instability of sub‐assemblies are built, and effects of changes of sub‐assembly disassembly directions or tools and the effect of gravity are considered to obtain the best disassembly sequence for a product with many components. A computer program is generated and results of two cases are compared with those of the available studies.

The methodology includes the combined interference matrix, the combined contact matrix and the combined connection matrix of components for a product. The combined instability matrix of sub‐assemblies, changes of sub‐assembly disassembly direction or tools, and the effect of gravity during operation are considered. The binary number system is used to simplify relations among components of a product.

This methodology enhances the existing method and software is generated. Results of two cases are compared and show the same optimum disassembly processes as those obtained from other researchers.

All matrices are defined by the directions of x, y and z with three axes perpendicular to each other. The computer program generated cannot be used for a product with components that must be disassembled in the directions different from the axes.

Two cases are used to investigate feasibility of the proposed methodology with the computer program generated. The first one is an electric drill, and the second one is a flash lighter.

The methodology described in this paper is feasible for study of disassembly processes of products. The software generated can be used to obtain the optimum disassembly process of products.

This paper presents an efficient algorithm for solving general constrained optimization problems that arise in operational research (OR).

An unified approach is accomplished by converting the constrained optimization problem into an unconstrained one and by using Alienor method coupled to the new optimization preserving operator^* (OPO^*) technique for the resolution.

A new algorithm for solving general constrained optimization problems with continuous objective function contributes to research in this area and in particular, to applications to OR.

Some improvements could probably be obtained at calculation time. We will in future work, develop an adaption of these methods and techniques to optimization problems with mixed variables or with integer and Boolean variables.

The new algorithm can be advantageously compared with other methods such as generalized reduced gradient. Small‐sized numerical examples are given.

A new algorithm is given which guarantees a global optimal solution is easily obtained in all cases.