The history and ideas of Marxism: the relevance for OR

Journal of the Operational Research Society - The paper examines the origins of Marxism in Europe in the second half of the 19th century in the context of the industrial and political revolutions...     

The ascending chain condition for real ideas

If A is a ring satisfying the ascending chain condition for real ideals, then this condition is also satisfied by the polynomial ring A[X]. However, an example is given to illustrate that the condition need not to hold in the power series ring A[[X]]. It is also shown that if every real prime ideal is the real ideal generated by finitely many elements, then the ring satisfies the ascending chain condition for real ideals. So, the analogues of Hilbert basis theorem and Cohen's theorem hold for real ideals.     

KRS and Powers of determinantal ideas

The goal of this paper is to determine Göbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and Cohen–Macaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted's Theorem on the Knuth–Robinson–Schensted correspondence.     

The origins and history of the fields medal

The Fields Medal is the most distinguished unternational award in mathematics. John Charles Fields felt strongly the lack of a Novel Prize in mathematics. He was also disturbed, as Chairman of the Committee of the 1924 International Mathematical Congress, by the scars left from the Versailles Treaty which marred the international character of the Congress. This paper traces the evolution of the award from incidents in Fields' background, through its formal inception at meetings of the University of Toronto Committee fir the 1924 Congress, to its eventual establishment and the first awards at the Oslo International Congress in 1936. Included are a list of all Fields Medal winners to date, the text of Fields' proposal for the establishment of the award, and relevant excerpts from minutes of the Toronto Committee, and a photograph of the medal.     

The history of mathematics education in Brazil

This paper describes the broad lines of the development of mathematics education in Brazil since 1500, emphasizing the development of secondary mathematics education. We divide this history into seven major periods, based on the political and cultural development of Brazilian society, and stress the characteristics of each period.     

The early history of convergence acceleration methods

The history of convergence acceleration methods in the 17th century is surveyed. Acceleration methods are classified into three categories.     

New ideas regarding the geometry of space-time and gravitation

In the present survey on the basis of an analysis of the problem of the energy-momentum of the gravitational field in the general theory of relativity it is shown that this theory is unsatisfactory as a concrete realization of Einstein's idea of the connection of the geometry of space-time with matter. A new theory of gravitation is proposed which alters established ideas of space-time, makes it possible to describe all present gravitational experiments, and predicts a number of fundamental consequences.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 21, pp. 3–215, 1982.     

The ideas of Krylov and Bogolyubov in the theory of differential equations and mathematical physics and their development

A brief survey is presented of some ideas and results of Krylov and Bogolyubov in the theory of differential equations and mathematical physics, and also of their further development and application.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 291–302, March, 1990.Communication presented to the First Meeting of the Kiev Mathematical Society, June 6, 1989.     

Mathematical optimization ideas for biodiversity conservation

Several major environmental issues like biodiversity loss and climate change currently concern the international community. These topics that are related to the development of human societies have become increasingly important since the United Nations Conference on Environment and Development (UNCED) or Earth Summit in Rio de Janeiro in 1992. In this article, we are interested in the first issue. We present here many examples of the help that using mathematical programming can provide to decision-makers in the protection of biodiversity. The examples we have chosen concern the selection of nature reserves, the control of adverse effects caused by landscape fragmentation, including the creation or restoration of biological corridors, the ecological exploitation of forests, the control of invasive species, and the maintenance of genetic diversity. Most of the presented models are – or can be approximated with – linear-, quadratic- or fractional-integer formulations and emphasize spatial aspects of conservation planning. Many of them represent decisions taken in a static context but temporal dimension is also considered. The problems presented are generally difficult combinatorial optimization problems, some are well solved and others less well. Research is still needed to progress in solving them in order to deal with real instances satisfactorily. Moreover, relations between researchers and practitioners have to be strengthened. Furthermore, many recent achievements in the field of robust optimization could probably be successfully used for biodiversity protection, a domain in which many data are uncertain.