Tropical support sets in analysis of weak links and complementarity
Properties of increasing positively homogeneous functions are studied; in particular, their representations by use of tropical inner products with coefficients chosen from tropical support sets are described. An application to a model of economic complementarityand weak links is developed. It is shown that weak links do not necessary bound total factor productivity from below but in some cases constraint it from above.
This paper reports a Foresight exercise, which was carried out to develop a research strategy and a business model for the science park of Ankara University (AU). Science parks have been crucial elements of innovation systems both in developed and developing countries due to their role in bridging the gap between academia and business through knowledge spill-overs and spin-offs. Although there is a widespread consensus about the usefulness of the science park concept, the actual performance of science parks and how well they meet expectations have been controversial. This paper discusses the success factors for science parks. A three dimensional policy framework, which includes ‘complementarity’, ‘networking’ and ‘strategic scalar positioning’ is suggested to be taken into account during the design and operation of science parks. The paper describes the Foresight process and the policies and strategies developed by using the three dimensional policy framework proposed for the newly established science park at Ankara University.
This volume contains the proceedings of the International Workshop on Tropical and Idempotent Mathematics, held at the Independent University of Moscow, Russia, from August 26-31, 2012. The main purpose of the conference was to bring together and unite researchers and specialists in various areas of tropical and idempotent mathematics and applications. This volume contains articles on algebraic foundations of tropical mathematics as well as articles on applications of tropical mathematics in various fields as diverse as economics, electroenergetic networks, chemical reactions, representation theory, and foundations of classical thermodynamics. This volume is intended for graduate students and researchers interested in tropical and idempotent mathematics or in their applications in other areas of mathematics and in technical sciences
We introduce the notion of the tropical matrix pattern, which provides a powerful tool to investigate tropical matrices. The above approach is then illustrated by the application to the study of the properties of the Gondran–Minoux rank function. Our main result states that up to a multiplication of matrix rows by non-zero constants the Gondran–Minoux independence of the matrix rows and that of the rows of its tropical pattern are equivalent.
We also present anumber of applications of our main result. In particular, we showthat the problem of checking whether the Gondran–Minoux rank of a matrix is less than a given positive integer can be solved in a polynomial time in the size of the matrix. Another consequence of our main result states that the tropical rank, trop(A), and the determinantal rank, d(A), of tropical matrices satisfy the following inequalities: trop(A) ≥ √GMr(A), d(A) ≥ √GMr(A), trop(A) ≥ (d(A)+2)/3. As an important corollary of this result we obtain that if one of these functions is bounded then the other two are also bounded unlike the situation with the factor and Kapranov ranks.
The new economic-mathematical model based on complex variables theory and the new approach to complex variables usage in economics are suggested in the article. The comparison of modeling results of actual production processes using Cobb-Douglass production function and complex variables production function is conducted. It is shown that the instrumental base of economicmathematical methods can be widen with usage of complex variables theory.
In the present paper the game theory is applied to an important open question in economics: providing microfoundations for often-used types of production function. Simple differential games of bargaining are proposed to model a behavior of workers and capital-owners in processes of formation of a set of admissible factor prices or participants’ weights (moral-ethical assessments). These games result, correspondingly, in a factor price curve and a weight curve – structures dual to production function. Ultimately, under constant bargaining powers of the participants, the Cobb-Douglas production function is received.
Selected works of George Kleiner on economics and mathematics in occasion of his 70th birthday.
Into the Red explores the emergence of a credit card market in post-Soviet Russia during the formative period from 1988 to 2007. In her analysis, Alya Guseva locates the dynamics of market building in the social structure, specifically the creative use of social networks. Until now, network scholars have overlooked the role that networks play in facilitating exchange in mass markets because they have exclusively focused on firm-to-firm or person-to-person ties. Into the Reddemonstrates how networks that combine individuals and organizations help to build markets for mass consumption. The book is situated on the cutting edge of emerging interdisciplinary research, linking multiple layers of analysis with institutional evolution. Using an intricate framework, Guseva chronicles both the creation of a credit card market and the making of a mass consumer. These processes are placed in the context of the ongoing restructuring in postcommunist Russia and the expansion of Western markets and ideologies through the rest of the world.