Siljak’s Conjecture on the existence of a symmetric positive definite matrix V having a specified structure and satisfying Liapunov’s matrix equation A*V+VA= -W is shown to be true in cases when A is an orthogonal matrix; when A is a symmetric matrix; when A is a normal matrix or A is the...

Exogenous technical progress can have uneven impacts on productivity contingent on absorptive capacity, structural congruence and trade intensity. The paper illustrates the role of enabling behind-the-border factors for effective absorption and is pertinent for discussing issues like ‘Europe...

The formation of the European Union (EU) is the one of the biggest political – economic events of the last 50 years. The aim of this study is to develop EU economy functioning system dynamic model. Main research method is system dynamics. General scheme of EU economy system dynamic model is...

I argue that a form of consciousness may be found in American economic history, one which is both mathematically demonstrable and important. In this book I present a model of economic and political growth based upon systematic addition. We begin with a philosophic model of trade (pp. 34-46);...

In the first section we recall Bak Sneppen model and its evolutions. In this paper we wish to present some simplified cases in which explicit computations via Markov chains are possible, hence reaching a better understanding of some rather hidden phenomena of the general case: in particular...

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance Σ , we propose a test for Σ being banded with possible diverging bandwidth. The test is adaptive to the “large p , small n ” situations without assuming a specific parametric distribution for...

Thinking about the development of the unifying mathematical approach to solve the problem on the evaluation of market risk of the global equity index portfolio in the highly volatile global capital markets, the authors focus their attention to an increasing necessity of application of the...

The article represents a brief review and development of the plenary report in the Moscow Institute of Physics and Technology. Three existing tools of sub-interval analysis (sub-interval arithmetic, incomplete data analysis and images) are reviewed and elements of two new tools (sub-interval...

We introduce a new kind of representation of a not necessarily total preorder, called strong multi-utility representation, according to which not only the preorder itself but also its strict part is fully represented by a family of multi-objective functions. The representability by means of...

In Albers & Albers (Spring, 2013) we demonstrated that the historic development of U.S. real GNP, 1869-present, may be structured in recurring 14-year periods. A steady-state rate of growth of 3.4969% is thereby calculated, generating an increase in real GNP proportional to the famous “Golden...