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The purpose of this paper is to describe a general method for solving all problems arising in industrial processes and more generally in operational research.

The paper's aim is to present a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. This technique allows to solve all problems of operational research in a simple way. For instance, industrial problems leading to optimization or optimal control problems can be easily and precisely solved by this very general technique. The main idea consists in expressing n variables by means of a single one.

This new method, based on “alpha‐dense curves” allows to express n variables in function of a single variable. One of the most important applications is related to global optimization. Multivariable optimization problems can be quickly and easily solved, even for great numbers of variables and for integer or boolean variables. Every problem (linear or nonlinear) coming from operational research or from industry becomes simple to solve in a very short time on micro‐calculators.

This method is deduced from the original works of Yves Cherruault et al. of MEDIMAT laboratory. The reducing transformations were initiated at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. Then they were generalized by the notion of α‐dense curves. A lot of applications were derived covering entirely the operational research and a part of functional analysis.

Aims to study direct identification of general linear compartmental systems by means of (n−2) compartmental measures. This is based on two main results.

The first result presented is related to the existence and uniqueness of identification exchange parameters in linear compartmental systems by using a direct method with less restrictive assumptions. A second result given, permits us to show that (n−2) observations are sufficient to identify the compartmental systems.

This research study describes a method which shows that in an open linear compartmental systems there exists an energy dissipation from compartmental 1 to the systems exterior. An explicit relationship between the dissipated energy and the exchange parameters was established. The results are probably perfectible and are optimal for n=3, where only an observable compartment is needed.

The identification of exchange parameters is easily obtained by using the matrix of the elementary masses and by solving a linear algebraic system. Among the open problems in compartmental analysis is the problem of minimizing the observable compartments which is studied in this paper.

The study is based on the original work of Yves Cherruault who has already presented methods for proving that a bicompartmental systems is uniquely identified. He has generalised his method for n‐compartments.

The purpose of this paper is to present an efficient algorithm to solve multi‐objective linear programming (MOLP) problem.

This new approach consists to convert the constrained multicriteria problem into an unconstrained global optimization problem. Then, the Alienor method coupled to the optimization preserving operators* (OPO*) technique is used to solve the transformed problem.

A determinist algorithm for solving general MOLP problem contributes to research in the decision‐makers area.

Some improvements could probably be obtained. In future work, other scalarized functions will be used and this algorithm's complexity will be studied.

The new algorithm can be advantageously compared with other methods To illustrate this new approach, an example is studied.

A new algorithm is given which guarantees all efficient solutions are easily obtained in most cases.

Gives a new method for defining and calculating multiple integrals. More precisely proposes that it is possible to define a multiple integral by means of a simple integral. This can be performed by using α‐dense curves in Rⁿ, already introduced for global optimization using the ALIENOR method.

The purpose of this paper is to use α‐dense curves for solving some Diophantine equations, such as Pythagorean triples, Linear Diophantine equations, the Pell Fermat equation, the Mordell equation for positive values.

The paper's aim is to present the applications in Number Theory 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. This technique can be used for solving all problems of operational research in a simple way. The main idea consists in expressing n variables by means of a single one.

Apply the method to Number Theory. One of the most important applications is related to global optimization. Multivariable optimization problems coming from operational research or from industry can be quickly and easily solved.

The paper presents a new method based on α‐dense curves for solving Diophantine equations.