The paper refers to a pair of conjugate systems (master and slave systems) associated by the condition that the evolution of the first is function on its current state and on a…
Abstract
Purpose
The paper refers to a pair of conjugate systems (master and slave systems) associated by the condition that the evolution of the first is function on its current state and on a future state of the second system, while the evolution of the second system depends on its current state and on a past state of the first system also. The purpose of this paper is to solve particular cases of differential systems of equations which express the behaviour of conjugate systems, in order to see what kind of symmetry or harmony is established in the common evolution of the two systems.
Design/methodology/approach
Becoming with the Dubois' definition of conjugate retardation and anticipation variables and his mixed advanced‐retarded differential equations, the paper considers some cases: first case when information about future and past is kept constant, without and with an impulse from the side of the master system, then when information about future and respective past is a variable.
Findings
In the case with variable information about future and past, and for a constant shift time, there are found exponential solutions; it has been ascertained that the two trajectories present a symmetry expressed by their proportionality all the time. A definition of symmetry by anticipation and retardation is given. It is also found that a system with uniform linear development cannot be in a symmetry by anticipation and retardation with any other system.
Practical implications
In the paper, the practical implications are linked by the relationship between man and his environment and how to consider the data delivered by forecast.
Originality/value
The calculus and its results, the notion of symmetry by anticipation and retardation, examples and conclusions, all are original contributions.
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Keywords
Eufrosina Otlacan and Romulus‐Petru Otlacan
To explain the objectivity of the globalisation process by using the mathematical theory of topological structures.
Abstract
Purpose
To explain the objectivity of the globalisation process by using the mathematical theory of topological structures.
Design/methodology/approach
After a brief presentation of the history and features of the globalisation phenomena, there are presented the basic notions of the mathematical concept of topology. Besides geometrical distance and geometrical topology, the authors define informational distance and informational topology. An informational neighbourhood of a person P is the informational medium that he/she masters, a set of persons with whom P communicates in a well‐determined interval of time. There is presented a hierarchy of informational topologies which structured human life on Earth. Nowadays, the world benefits from the finest topology, the topology of communication by the internet (TCI).
Findings
The possibility to conceive the globalisation process as a multidimensional vector function defined on the set of the world population. The projections of this vector function on the subsystems of human life refer to the political, economic, military, cultural or religious life. The continuity of this function in the TCI sense expresses the possibility for the globalisation phenomenon to be controlled.
Practical implications
The very understanding of the objectivity of the globalisation process and an important conclusion: the control of the situation only on a compact geographic area cannot ensure the stability of this area; it must have control over a neighbourhood of the informational topology. This means possessing informational instruments so as to be able to manage the economic, political and social activity and to avoid catastrophe.
Originality/value
Concept of mathematical topological structure applied to a complex social phenomenon.
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Keywords
The paper accepts the “functional paradigm” in the formative process of the image of an object. It holds that the used formulae must be mathematically demonstrated. As for many…
Abstract
The paper accepts the “functional paradigm” in the formative process of the image of an object. It holds that the used formulae must be mathematically demonstrated. As for many systems with memory, the frequently met formula is a defined integral. Its inferior limit is considered “the initial instant”. In this paper we show that: (1) The integral representation formula, that gives the image η (t) as a functional on the history ξ =ξ (τ),τ≤q t, of the evolutions both of the observed object and the observer, is only an approximate one. There exists the possibility to appreciate the order of size of the error. (2) The inferior limit of the integral may be mathematically determined and its choice requires some discussions. (3) A more precise formula of η (t) contains also a double integral upon a quadratic form of ξ(τ). The mathematical model is based on the differential calculus on the linear topological locally convex spaces.