We examine the asymptotic behaviour of the call price surface and the associated Black-Scholes implied volatility surface in the small time to expiry limit under the condition of no arbitrage. In the final section, we examine a related question of existence of a market model with non-convergent implied volatility. We show that there exist arbitrage free markets in which implied volatility may fail to converge to any value, finite or infinite.

Candida auris, first described from an ear infection in Japan, is the most talked about multidrug resistant emerging pathogenic fungal species. Its environmental niche remained a mystery until its first isolation from wetlands of the Andaman Islands, India in 2020. We screened a subset of the world's largest sequence repository, the Sequence Read Archive at NCBI using a DNA metabarcoding approach, based on either the ITS1 or ITS2 region of the official primary fungal DNA barcode, to identify potential environmental sources of C. auris. Our search identified 34 matches with partial C. auris ITS sequences from seven metabarcoding studies, providing wider evidence for the presence of C. auris outside human-maintained facilities.

An introductory, pedagogical review of the generalized Langevin equation (GLE) within the classical regime is presented. It is intended to be accessible to biophysicists with an interest in molecular dynamics (MD). Section 1 presents why the equation may be of interest within biophysical modeling. A detailed elementary first principles derivation of the (multidimensional) Kac–Zwanzig model is presented. The literature is reviewed with a focus on biophysical applications and representation by Markovian stochastic differential equations. The relationship with the Mori–Zwanzig formalism is discussed. The framework of model reduction and approximation is emphasized. Some open problems are identified.

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Ernest William Denham, who died on 27 August 2019 three weeks short of his 97 th birthday, spent all his archival career at the Public Record Office and is probably best known to archivists outside the PRO as their teacher of palaeography and diplomatic, as liaison officer with places of deposit for public records or as a member of the Council of the British Records Association. 1 Denny (as he preferred to be known) was born on 16 September 1922 and grew up in Dalston, east London, the son of William and Beatrice Denham. He attended Wilton Street Primary School, where he already showed his academic qualities, winning a scholarship to the City of London School for Boys. From there he won another scholarship to Merton College, Oxford, where he began to read classics. His time there was interrupted in 1942 by wartime service with naval intelligence in which, after a crash course in basic Japanese at Bletchley Park, he worked as a translator alongside the codebreakers at HMS Anderson in Colombo, Ceylon (now Sri Lanka). Needless to say, he kept his specific duties a close secret until the role of Bletchley Park and its codebreakers became public knowledge in the mid-1970s, and even then remained reluctant to discuss them. On returning to Merton after the war he switched to law and after graduation he worked briefly as assistant secretary with Plant Protection Ltd (a subsidiary of ICI) before entering the civil service examination, in which he was proud to have been placed immediately above Ian Bancroft, later Permanent Secretary in the Civil Service Department and Head of the Civil Service. At that time appointments to the Public Record Office were made on the basis of general civil service examinations not, as later, by specific recruitment, and in 1949 Denny was posted to the PRO as an assistant keeper. He was to spend the rest of his working life there. At that time most of the work of assistant keepers was focused on the medieval and early modern records, but Denny soon found himself on a different path when he was appointed secretary of the Master of the Rolls' Archives Committee, established to consider legislation necessary to deal with the bulk of more recent (especially wartime) records still held in government departments. The selection and transfer to the PRO of public records of enduring value and questions of public access to them were to be the area in which he would work for most of his career. In 1952 he became secretary of the Inspecting Officers Committee established by the Public Record Office Act 1877 to draw up schedules authorizing the disposal of public records considered to be of no further administrative value by transfer to the PRO or destruction. 1952 also saw the establishment of the Grigg Committee on Public Records and its report of 1954 was very critical of the cumbersome and legalistic Inspecting Officers Committee system, proposing new, less formal arrangements for dealing with the selection and safekeeping of public records which ought to be permanently