On the asymptotic behavior of the average geodesic distance L and the compactness CB of simple connected undirected graphs whose order approaches infinity

The average geodesic distance L Newman (2003) and the compactness CB Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple connected undirected graphs G of order n, we study the behavior of L(G) and CB(G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and CB(G) lies within the interval [0;1/3] and [2/3;1], respectively. Moreover, for any not necessarily rational number β ∈ [0;1/3] (α ∈ [2/3;1]) we show how to construct the sequence of graphs {G}, |V(G)| = n → ∞, for which the limit of L(G)/n (CB(G)) is exactly β (α) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.

THE NARRATOR IN DORIS LESSING’S THE FIFTH CHILD

This paper reviewed the theoretic classification on narrator of fictions. The narrator of THE FIFTH CHILD was described according to voice and point of view. The conclusion is the narrator in the famous fiction of Doris Lessing’s was omniscient, heterodiegetic/non-character, overt and reliable in its voice. While the fiction was narrated with the shift of multifocalizers in the point of view both from a character, Harriet, who witnessed the events, and from a heterodiegetic narrator, who made comments and questions to focus the readers’ attention on what he narrates.

The classification of certain ASH C*-algebras of real rank zero

In this paper, using ordered total K-theory, we give a K-theoretic classification for the real rank zero inductive limits of direct sums of generalized dimension drop interval algebras.

Dealing with jokes in the ESL class: a pedagogical proposal centred on comprehension

This paper makes a pedagogical proposal to delve into jokes in the ESL classroom and sensitise learners to their complexity. It consists of five instructional phases and is based, on the one hand, on another proposal to teach the pragmatics of speech acts in an L2. On the other hand, this proposal relies on a relevance-theoretic classification of jokes made on the basis of the various linguistic, cultural and cognitive factors that humorists exploit in their production. Since it only centres on how different types of jokes can be distinguished and what their correct comprehension involves, it has a cognitive orientation and does not address issues connected with joke production. The proposal is devised for ESL students with an advanced level of English and ultimately seeks to develop their metalinguistic, meta-cultural and metacognitive abilities as a way of enabling them to grasp the humorousness of funny texts, appraise them and react to them in an appropriate way.***Lidando com piadas na aula de ESL: uma proposta pedagógica centrada na compreensão***Este artigo traz uma proposta pedagógica para aprofundar as piadas na sala de aula de ESL (Inglês como língua estrangeira, na tradução para a língua portuguesa) e sensibilizar os alunos a respeito de sua complexidade. Ela consiste em cinco fases instrucionais que, por um lado, baseia-se em outra proposta de ensino da pragmática dos atos de fala em uma L2 e, por outro lado, baseia-se em uma classificação teórica da relevância das piadas feitas com base nos vários fatores linguísticos, culturais e cognitivos que os humoristas exploram em sua produção. Como a proposta se concentra apenas em como os diferentes tipos de piadas podem ser distinguidos e em qual a correta compreensão envolvida, ela tem uma orientação cognitiva e não aborda questões relacionadas à produção da piada. A proposta é elaborada para estudantes de ESL com um nível avançado de inglês e, por conseguinte, busca desenvolver suas habilidades metalinguísticas, meta-culturais e metacognitivas como uma maneira de permitir-lhes compreender o humor de textos engraçados, avaliá-los e reagir a eles apropriadamente.

THE UNITAL EXT-GROUPS AND CLASSIFICATION OF C*-ALGEBRAS

The semigroups of unital extensions of separable C*-algebras come in two flavours: a strong and a weak version. By the unital Ext-groups, we mean the groups of invertible elements in these semigroups. We use the unital Ext-groups to obtain K-theoretic classification of both unital and non-unital extensions of C*-algebras, and in particular we obtain a complete K-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

On the K-theoretic classification of dynamically stable systems

This paper deals with the construction of a suitable topological [Formula: see text]-theory capable of classifying topological phases of dynamically stable systems described by gapped [Formula: see text]-self-adjoint operators on a Krein space with indefinite metric [Formula: see text].