The Life and Work of R.A. Rankin (1915–2001)

Robert Alexander Rankin, an eminent Scottish number theorist and, for several decades, one of the world's foremost experts in modular forms, died on January 27, 2001 in Glasgow at the age of 85. He was one of the founding editors of The Ramanujan Journal. For this and the next two issues of the The Ramanujan Journal, many well-known mathematicians have prepared articles in Rankin's memory. In this opening paper, we provide a short biography of Rankin and discuss some of his major contributions to mathematics. At the conclusion of this article, we provide a complete list of Rankin's doctoral students and a complete bibliography of all of Rankin's writings divided into five categories: (1) Research and Expository Papers; (2) Books; (3) Books Edited; (4) Obituaries; (5) Other Writings.     

Uniqueness of Fourier–Jacobi models: The Archimedean case

We prove uniqueness of Fourier–Jacobi models for general linear groups, unitary groups, symplectic groups and metaplectic groups, over an Archimedean local field.     

The Moore–Penrose inverse of the incidence matrix of complete multipartite and bi-block graphs

A bi-block graph is a connected graph all of whose blocks are complete bipartite graphs. We give a combinatorial interpretation of the Moore–Penrose inverse of the incidence matrix of a complete multipartite graph and a bi-block graph.     

A historical teaching module on ‘the unreasonable effectiveness of mathematics’: Boolean algebra and Shannon circuits

This article describes the design and implementation of a historical teaching module, where Danish upper secondary students studied primary source material from the mathematicians R W Hamming, G Boole and C E Shannon. The module is an example of a so-called HAPh-module, which focuses on elements of the history, application and philosophy of mathematics. A previous version was presented at the History and Pedagogy of Mathematics (HPM) meeting in Deajeon, Korea in 2012.     

The Mathematics in Society Project: a new conception of mathematics(1) †

The Mathematics in Society Project (MISP) began in 1980 as an international association of mathematics educators in three continents. The main purpose of MISP is the writing of innovative secondary school mathematics courses based on a new conception of mathematics itself. The starting point for MISP was the fact that mathematics in school is found to be difficult and unpleasant by the great majority of pupils, but mathematics in society is widely diffused and used implicitly by most people. MISP therefore sees mathematics as a ‘living body’ representing all its uses (implicit and explicit) in society, in contrast to the ‘skeleton’ concept of mathematics which has led to such failure in schools. The gradual development of this new conception is informally analysed in the style of Kuhn and Lakatos.

     

The odd log-logistic Topp–Leone G family of distributions: heteroscedastic regression models and applications

We introduce a new class of distributions and provide a comprehensive treatment of its mathematical properties. The maximum likelihood method is discussed to estimate the parameters of the new model by means of Monte-Carlo simulation study. The heteroscedastic regression models with long-term survival are introduced to model data sets with the non homogeneity of the error variances in the presence of cured individuals. The potentiality of the proposed models is illustrated by means of four real data sets.     

Polylogarithms,functional equations and more: The elusive essays of William Spence (1777–1815)

The little-known Scottish mathematician William Spence was an able analyst, one of the first in Britain to be conversant with recent continental advances, and having original views. His major work on “logarithmic transcendents” gives the first detailed account of polylogarithms and related functions. A theory of algebraic equations was published just after his early death; and further essays, edited by John Herschel, were published posthumously. The most substantial of these concern an extension of his work on “logarithmic transcendents”, and the general solution of linear differential and difference equations. But awareness of Spence?s works was long delayed by their supposed unavailability. Spence?s life, the story of his “lost” publications, and a summary of all his essays are here described.     

Fuzzy (Θ, S)-continuity and fuzzy (Θ, S)-closed graphs

The concept of (,s)-continuity [6] is considered and studied in fuzzy setting. It is seen that althought it is independent with each of the concepts of fuzzy continuity [2], fuzzy -continuity [10], fuzzy almost continuity [1] and fuzzy semicontinuity [1]; it implies fuzzy weak continuity [1], but the converse may not be true. The image of a compact fts [2] under a fuzzy (,s)-continuous surjective function isS-closed [5]. Finally the concepts of fuzzy (,s)-closed graphs, fuzzy (,s)-T ₂ spaces and fuzzy Urysohn spaces are introduced and mainly their connections with fuzzy (,s)-continuity are studied.