Limn Number 7

Infrastructure has always had a privileged relationship to both expertise and the public in modern government. But in the early 21st century, this relationship is inflected in novel ways. The purposes public infrastructure was meant to serve-welfare, quality of life, economic development, and so on-persist. But they are often conceptualized differently, promoted by different agencies, and articulated through novel technological and collective relations. This issue of Limn explores new formations of infrastructure, publicness, and expertise.The contributions examine how new forms of expertise conceive the public and make claims in its name, how publics are making novel claims on experts (and claims to expertise), and how earlier norms and techniques of infrastructure provisioning are being adapted in the process.

This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

Introduction to Mathematical Proofs helps students develop the necessary skills to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural num

In this paper, the neutrosophic norm has been defined on a soft linear space which is hereafter called neutrosophic soft normed linear space (NSNLS). Several characteristics of sequences defined in this space have been investigated here. Moreover, the notion of convexity and the metric in NSNLS have been introduced and some of their properties are established.

Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\psi$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$ to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarnik concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantine approximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarnik's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarnik's theorem opens up the Duffin-Schaeffer conjecture for Hausdorff measures.

This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians.The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions. Thus, for a perfect number n it holds σ(n) = 2n, where σ is the sum-of-divisors function, while for a pair of amicable numbers (n, m) it holds σ(n) = σ(m) = n + m. This is also an important part of the history of prime numbers, since the main formulas that generate perfect numbers and amicable pairs are dependent on the good choice of one or several primes of special form.Nowadays, the theory of perfect and amicable numbers contains many interesting mathematical facts and theorems, alongside many important computer algorithms needed for searching for new large elements of these two famous classes of special numbers.This book contains a list of open problems and numerous questions related to generalizations of the classical case, which provides a broad perspective on the theory of these two classes of special numbers. Perfect and Amicable Numbers can be useful and interesting to both professional and general audiences.

Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika

An investigation of the causes and consequences of the strange, ambivalent, and increasingly central role of infrastructure repair in modern life. Infrastructures--communication, food, transportation, energy, and information--are all around us, and their enduring function and influence depend on the constant work of repair. In this book, Christopher Henke and Benjamin Sims explore the causes and consequences of the strange, ambivalent, and increasingly central role of infrastructure repair in modern life. Henke and Sims offer examples, from local to global, to investigate not only the role of repair in maintaining infrastructures themselves but also the social and political orders that are created and sustained through them.