Limit relations between qq-Krall type orthogonal polynomials

In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification of a $q$-classical linear functional via the addition of one or two mass points. The limit relations between the $q$-Krall type modification of big $q$-Jacobi, little $q$-Jacobi, big $q$-Laguerre, and other families of the $q$-Hahn tableau are established.Comment: 19 Pages, 3 tables, 1 figur

The q-Racah-Krall-type polynomials

In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the \textit{standard} $q$-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained and some of their limit cases are discussed

On the limit of non-standard q-Racah polynomials

The aim of this article is to study the limit transitions from non-standard q-Racah polynomials to big q-Jacobi, dual q-Hahn, and q-Hahn polynomials such that the orthogonality properties and the three-term recurrence relations remain valid

A Comment on the Holographic Renormalization Group and the Soft Dilaton Theorem

The equivalence between the holographic renormalization group and the soft dilaton theorem is shown for a class of wrapped metrics solutions of the string beta function equations for the bosonic string.Comment: LaTeX,7 pages. Typos corrected. Minor change

On the Krall-type Askey-Wilson Polynomials

In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points $\pm1$. Several properties of such new family are considered, in particular the three-term recurrence relation and the representation as basic hypergeometric series

On ZZt × ZZ2 2-cocyclic Hadamard matrices

A characterization of ZZt × ZZ22 -cocyclic Hadamard matrices is described, de- pending on the notions of distributions, ingredients and recipes. In particular, these notions lead to the establishment of some bounds on the number and distribution of 2-coboundaries over ZZt × ZZ22 to use and the way in which they have to be combined in order to obtain a ZZt × ZZ22 -cocyclic Hadamard matrix. Exhaustive searches have been performed, so that the table in p. 132 in [4] is corrected and completed. Furthermore, we identify four different operations on the set of coboundaries defining ZZt × ZZ22 -cocyclic matrices, which preserve orthogonality. We split the set of Hadamard matrices into disjoint orbits, de- fine representatives for them and take advantage of this fact to compute them in an easier way than the usual purely exhaustive way, in terms of diagrams. Let H be the set of cocyclic Hadamard matrices over ZZt × ZZ22 having a sym- metric diagram. We also prove that the set of Williamson type matrices is a subset of H of size |H| t .Junta de Andalucía FQM-01

On the Properties of Special Functions on the linear-type lattices

We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference-recurrence relations for such functions. Finally, applications to $q$-classical polynomials are given

Cryptanalyzing a discrete-time chaos synchronization secure communication system

This paper describes the security weakness of a recently proposed secure communication method based on discrete-time chaos synchronization. We show that the security is compromised even without precise knowledge of the chaotic system used. We also make many suggestions to improve its security in future versions.Comment: 11 pages, 3 figures, latex forma

A learning-centred blended model for professional doctorates

A solid pedagogy can ensure the achievement of the learning outcomes set for any university qualification, whether at undergraduate or postgraduate level. Currently there is an urgent need for a wider consideration of appropriate pedagogies for doctoral programmes. This paper looks in particular at the characteristics of professional doctorates, which are typically studied part-time and focus on researching a professional setting. Based on the needs of these programmes, it proposes a learning-centred blended mode of delivery that fosters students’ engagement with activities anchored in the set learning outcomes. The range of activities aims at facilitating the multiple interactions necessary for competent researchers by making use of the resources, tools and spaces within two main learning environments: the virtual and the physical. This model prompts universities to consider appropriate pedagogies for the delivery of professional doctorates and suggests the need to ensure the alignment of their approaches with available technologies, educational policies, and practices of teaching and learning in their institutions. In order to ensure a successful implementation, such a consideration must also include effective action for the development of the relevant academic staff

Learning about Chinese-speaking cultures at a distance

This chapter focuses on the challenges posed by curriculum choices and pedagogical frameworks to the study of Languages of the Wider World in the UK. These languages reflect complex linguistic and cultural realities that do not fit into the traditional constraints of language education, which raises questions about the extent to which we can address the global and local dimensions of the target languages and cultures. I examine in particular the case of Chinese – a language family with multiple varieties and spoken by many communities in Asia and other parts of the globe – in the context of distance education. Issues surrounding language learning at a distance are discussed, as well as the role that teachers and technology play in supporting the development of language learners’ cultural awareness. While teachers can, in a face-to-face situation, exploit, expand and discuss cultural information, this possibility is very limited in distance learning. We will see how, at present, technology has taken on a major role in both formal and informal education, facilitating contact between learners and between learners and teachers (however distant they might be). For example, the Open University’s beginners’ Chinese course discussed here makes use of online forums to enable cultural interaction; initial examinations of these forums reveal the students to be diverse and mobile, and they also give us a sense of their cultural stances, and of the shapes of the beliefs, values and attitudes supported by their individual cultural backgrounds