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Keywords: agent-based simulation model, spread of the dengue fever, swarm platform. AbstractThe dengue fever is today the most spread arbovirosis in Brazil. Transmitted only by the female Aedes aegypti mosquito, it reaches its peek during the hot and humid Brazilian summer season. While there are many approaches to analyze the spread of the dengue fever, most of them focus on developing a mathematical model to represent that process. One disadvantage of such approach is to neglect the importance of micro-level behavior, focusing instead on the macro-level aspects of the system. This work proposes an agent-based model of the spread of the dengue fever arbovirosis, where agents interact between themselves and the environment representing the process of dissemination of the disease. This model will be implemented and simulated through the Swarm platform and the simulation results will then be analyzed.

In this paper, we apply the concepts of fuzzy sets to Lie algebras in order to introduce and to study the notions of solvable and nilpotent fuzzy radicals. We present conditions to prove the existence and uniqueness of such radicals.MSC 2010: 17B99, 08A72 IntroductionLie algebras were discovered by Sophus Lie [4]. There are many applications of Lie algebras in several branches of physics. The notion of fuzzy sets was introduced by Zadeh [8]. Fuzzy set theory has been developed in many directions by many scholars and has evoked a great interest among mathematicians working in different fields of mathematics. Many mathematicians have been involved in extending the concepts and results of abstract algebra. The notions of fuzzy ideals and fuzzy subalgebras of Lie algebras over a field were first introduced by Yehia in [7]. In this paper, we introduce the notion of solvable and nilpotent fuzzy radical of a fuzzy algebra of Lie algebras and investigate some of their properties. The results presented in this paper are strongly connected with the results proved in [1,2,3]. Fuzzy setsIn this section, we present the basic concepts on fuzzy sets which will be used throughout this paper. A new notion is introduced and results are proved for guiding the construction of the main theorems of this work. Definition 1. A mapping of a non-empty set X into the closed unit interval [0, 1] is called a fuzzy set of X. Let μ be any fuzzy set of X, then the set {μ(x) | x ∈ X} is called the image of μ and is denoted by μ(X). The set {x | x ∈ X, μ(x) > 0} is called the support of μ and is denoted by μ * . In particular, μ is called a finite fuzzy set if μ * is a finite set, and an infinite fuzzy set otherwise. For all real t ∈ [0, 1] the subsetDefinition 2. Let X be a non-empty set and {ν i } i∈I an arbitrary family of fuzzy sets of X. One defines the fuzzy set of X i∈I ν i , called union, asRemark 3. Let us note that if {ν i } i∈I is a family of fuzzy sets of X, then i∈I [ν i ] t ⊆ i∈I ν i t , for all t ∈]0, 1]. Definition 4. Let X be a non-empty set. One says that a family of fuzzy sets of X {ν i } i∈I satisfies the second sup property if for all x ∈ X there is an index iThus, a family of fuzzy sets of X {ν i } i∈I satisfies the second sup property if, and only if, i∈I ν i (x) ∈ {ν i (x) | i ∈ I}, for all x ∈ X. Proposition 5. Let X be a non-empty set and {ν i } i∈I an arbitrary family of fuzzy sets of X. Then i∈I ν i t = i∈I [ν i ] t for all t ∈]0, 1] if, and only if, the family {ν i } i∈I satisfies the second sup property.

This paper proposes a dialogue based interface for virtual environments of learning with a Multiagent approach. Here, it's shown both aspects involved with the motivation and conception of this interface project, the conceptual and the technological aspect. In the conceptual aspect, the concepts related to distance learning and learning process are presented in the context of interfaces for virtual environment for education. In the technological aspect, it's presented the multi-agent based systems, chatterbots systems and the AIML language applied in the context of the conceptual needs. Finally, based on these concepts and technologies, the paper's contribution is a project for a virtual environment of learning, a middleware architecture based on a multi-agent approach.

Let A and B be two factor von Neumann algebras. In this paper, we proved that a bijective mapping Φ:A→B satisfies Φ(a∘b+ba∗)=Φ(a)∘Φ(b)+Φ(b)Φ(a)∗ (where ∘ is the special Jordan product on A and B, respectively), for all elements a,b∈A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then Φ is a unitary isomorphism or a conjugate unitary isomorphism.