فهرست مطالب uosef mohammadi

Crime control and security are among the essential needs of development in any society. One of the frequently used theories of criminology that its birth was in the 1990s is postmodern or eclectic criminology. Postmodern criminology through combining different scientific theories, including mathematics tries to do a comprehensive analysis of crime. Nowadays, mathematical models are used to study the dynamic behavior of many phenomena and processes in engineering sciences, basic sciences and humanities. Mathematical modeling is one of the important tools of scientists in controlling and predicting the future of various dynamic phenomena. In the field of law and especially in criminology, these models are very useful for evaluating crime control strategies. In this article, using a new mathematical model, we deal with mass dynamic modeling and its analysis.

‎In the context of observers‎, ‎any mathematical model according to the viewpoint of an observer is called a relative model‎. ‎The purpose of the present paper is to study the relative model of logical entropy‎. ‎Given an observer ‎, ‎we define the relative logical entropy and relative conditional logical entropy of a sub- -algebra having finitely many atoms on the relative probability ‎‎ measure space and prove the ergodic properties of these measures‎. ‎Finally‎, ‎it is shown that the relative logical entropy is invariant under‎ ‎the relation of equivalence modulo zero.

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer Θ. The relative entropy of a sub-σΘ-algebra having finite atoms is defined and then the ergodic properties of relative semi-dynamical systems are investigated. Also, a relative version of Kolmogorov-Sinai theorem is given. Finally, it is proved that the relative entropy of a relative Θ-measure preserving transformations with respect to a relative sub-σΘ -algebra having finite atoms is affine.

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is complete.

In this paper, a new invariant called {\it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {\it conditional logical entropy} is defined and then some of its properties are studied. The invariance of the {\it logic entropy} of a system under isomorphism is proved. At the end, the notion of an m-generator of a dynamical system is introduced and a version of the Kolmogorov-Sinai theorem is given.

In this paper by use of mathematical modeling of an observer [14, 15] the notion of relative information functional for relative dynamical systems on compact metric spaces is presented. We extract the information function of an ergodic dynamical system (X,T) from the relative information of T from the view point of observer χX, where X denotes the base space of the system. We also generalize the invariance of the information function of a dynamical system , under topological isomorphism, to the relative information functional.