Patrick D. F. Ion

University of Michigan | U-M · Department of Mathematics

We recall some of the reasons why we want and do not yet have a Global Digital Mathematics Library (GDML), both before and after the setting up of a GDML WG at the Seoul 2014 ICM. The recent founding of an International Mathematical Knowledge Trust (IMKT) in Waterloo ON, Canada is an important move in the right direction. The IMKT’s form and initia...

A decade after a resolution in 2006 by the International Mathematical Union endorsing the notion of a global digital mathematics library, and following a thorough report on possibilities written under the auspices of the US National Research Council in 2012, an 8-person Working Group, set up in 2014, is still working toward implementations of some...

There are new roles for software in mathematical knowledge management (MKM). Three simple initial examples of MKM roles will be considered here. The first is software applied to the mathematical subject classification (MSC). The second example is MathML (mathematics markup language), a standard from the W3C, now in its third edition, and hoping to...

Mathematics is an ancient and honorable study. It has been called The Queen and The Language of Science. The World Wide Web is something brand-new that started only about a quarter of a century ago. But the World Wide Web is having a considerable effect on the practice of mathematics, is modifying its image and role in society, and can be said to h...

The Mathematics Subject Classification (MSC), maintained by the American Mathematical Society’s Mathematical Reviews (MR) and FIZ Karlsruhe’s Zentralblatt für Mathematik (Zbl), is a scheme for classifying publications in mathematics. While it is widely used, its traditional, idiosyncratic conceptualization and representation did not encourage wide...

The Mathematics Subject Classification (MSC) is a widely used scheme for classifying documents in mathematics by subject. Its traditional, idiosyncratic conceptualization and representation makes the scheme hard to maintain and requires custom implementations of search, query and annotation support. This limits uptake e.g. in semantic web technolog...

Collaboration is key to scientific research, and increasingly to mathematics. This paper contains a longitudinal investigation of mathematics collaboration and publishing using the proprietary database Mathematical Reviews, maintained by the American Mathematical Society. The database contains publications by several hundred thousand researchers ov...

The most comprehensive subject classification scheme in mathematics is the MSC (Mathematics Subject Classification), based originally on an AMS classification scheme, a standard more than 20 years ago. Zentralblatt MATH and Mathematical Reviews jointly developed the first MSC 1990. The current version is MSC 2010 following another 10-year update. W...

The number of publications in mathematics increases faster each year. Presently far more than 100,000 mathematically relevant journal articles and books are published annually. Efficient and high-quality content analysis of this material is important for mathematical bibliographic services such as ZBMath or MathSciNet. Content analysis has differen...

Knowledge management in mathematics has a long history. With the formation of “Jahrbuch über die Fortschritte der Mathematik” in 1868 a systematic analysis of content of a comprehensive set of mathematical publications, what would be termed today the core of mathematical knowledge, was started. The leading reviewing services in mathematics – former...

This specification defines the Mathematical Markup Language, or MathML. MathML is an XML ap- plication for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on the World Wide Web, just as HTML has enabled this functionality for text. This...

What is mathematical knowledge and how can it be managed? There are not only differing views around on the management aspect but there is no real clarity or consensus on what mathematical knowledge is; indeed there are questions as to what knowledge is and what mathematics is. For the sake of definiteness I will adopt a particular stance from which...

This specification defines the Mathematical Markup Language, or MathML. MathML is an XML application for describing mathematical notation and capturing both its structure and content. The goal of MathML is to enable mathematics to be served, received, and processed on the World Wide Web, just as HTML has enabled this functionality for text. This s...

Introduction The subject of math symbol fonts has been one of the major topics of interest at the 10th European T E X Conference (EuroT E X'98), which was held on March 29--31, 1998 at St. Malo, France as part of the 2nd Week on Electronic Publishing and Digital Typography (WEPT '98). During the conference a paper summarizing the activities of the...

ate was done by Ron Graham [3], but it does not aim to be complete. We should also point out that portions of our data can provide fairly large, interesting "real-life" graphs on which to test graph algorithms, in the spirit of [1]. Since the data change over time, both because of additional collaborations and because of corrections to inaccurate i...

Desktop publishing will become a significant business in the next few years. Already on the market are several systems that are easy to use and produce quite acceptable output; other systems available are much harder to use, but provide much greater flexibility and more sophisticated output. One such system is TeX (pronounced teck as in technology)...

In a previous paper [6] it was shown that a certain two-parameter dilation of a given strongly continuous self-adjoint contraction semigroup, called the time-orthogonal unitary dilation, gives rise to noncommutative Feynman-Kac formulae through the mechanism of Boson second quantisation in Fock space. This paper explores the modifications of this t...

An analysis of Feynman-Kac formulae reveals that, typically, the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group...

Da wir uns nur fr die Momente interessieren, werden die Rauschprozesse als lineare Funktionale auf Tensoralgebren dargestellt. Die zeitgeordneten Momente des weien Rauschens werden nach dem Stratonowitsch-Verfahren durch Approximation mit farbigem Rauschen berechnet. Um die zeitgeordneten Momente algebraisch als Funktional einer Algebra verstehen z...

A dilation of a self-adjoint contraction semigroup is constructed which consists of a unitary evolution in which the evolution operators for disjoint time intervals act in mutually orthogonal supplementary Hilbert spaces. On second quantizing, one obtains noncommutative Feynman-Kac formulae for perturbed semigroups which are related to the Boson no...

The equivalence of a Gibbsian equilibrium condition and the KMS condition is proven for one-dimensional quantum lattice systems with a finite range interaction at arbitrary temperature, and for quantum lattice systems of arbitrary dimension, with a finite body interaction, at high temperature.

As the Web gains in importance and as the needs of mathematical formalism on the Web are beginning to be met by MathML, it is an opportune time to reflect on the design decisions made by the W3C Math Working Group that resulted in the verbose markup language for transport of math on the Web that MathML turns out to be. The T E X community need not...