Related papers: Rejoinder

CONTEXT: Data accessors allow one to read and write components of a data structure, such as the fields of a record, the variants of a union, or the elements of a container. These data accessors are collectively known as optics; they are…

This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published in the London Mathematics Society Lecture Notes Series. It gives a…

In this article, we will discover some new generalized identity regarding continued fractions. We will connect the results to Fibonacci numbers and Lucas numbers. For all the proof, we will use induction.

The content of this preprint together with additional material appears now in 0706.2154.

There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to…

This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the…

Revisions: reference added to: G. Gilbert, {\sl Nucl.Phys.} {\bf B328}, 159 (1989)

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized…

In this appendix we provide additional supplementary material to "A Collective, Probabilistic Approach to Schema Mapping." We include an additional extended example, supplementary experiment details, and proof for the complexity result…

A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.

We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions

We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals.

In this paper, we give two proofs of the wellfoundedness of recursive notation systems for $\Pi_N$-reflecting ordinals. One is based on $\Pi_{N-1}^0$-inductive definitions, and the other is based on distinguished classes.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

Comment on ``Gibbs Sampling, Exponential Families, and Orthogonal Polynomials'' [arXiv:0808.3852]

These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.

M\"obius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying…

Comment on paper by Blanchette and Zhang, Phys. Rev. Lett. 102, 144501 (2009).

This note is an (exact) copy of the report of Jaak Peetre, "Generalizing Ovchinnikov's Theorem". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…

We give a concise introduction to the theory of continuants and show how Perron used them in his proof of Tietze theorem on the convergence of infinite semi-regular continued fractions, as well as for the study of the convergence of purely…