Traveling waves for the cubic Szego equation on the real line

We consider the cubic Szego equation i u_t=Pi(|u|^2u) on the real line, with solutions in the Hardy space on the upper half-plane, where Pi is the Szego projector onto the non-negative frequencies. This equation was recently introduced by P. Gerard and S. Grellier as a toy model for totally non-dispersive evolution equations. We show that the only traveling waves are rational functions with one simple pole. Moreover, they are shown to be orbitally stable, in contrast to the situation of the circle S^1 studied by the above authors, where some traveling waves were shown to be unstable.Comment: 24 pages, added references, small revision of the second part of the proof of Theorem 2.1 (p.8-9

Explicit formula for the solution of the Szeg\"o equation on the real line and applications

We consider the cubic Szeg\"o equation i u_t=Pi(|u|^2u) in the Hardy space on the upper half-plane, where Pi is the Szeg\"o projector on positive frequencies. It is a model for totally non-dispersive evolution equations and is completely integrable in the sense that it admits a Lax pair. We find an explicit formula for solutions of the Szeg\"o equation. As an application, we prove soliton resolution in H^s for all s>0, for generic data. As for non-generic data, we construct an example for which soliton resolution holds only in H^s, 0<s<1/2, while the high Sobolev norms grow to infinity over time, i.e. \lim_{t\to\pm\infty}|u(t)|_{H^s}=\infty if s>1/2. As a second application, we construct explicit generalized action-angle coordinates by solving the inverse problem for the Hankel operator H_u appearing in the Lax pair. In particular, we show that the trajectories of the Szeg\"o equation with generic data are spirals around Lagrangian toroidal cylinders T^N \times R^N.Comment: Small modifications in the proof of Proposition 1.3, changed the order in the proof of Theorem 1.9, replaced the proof of \chi proper mapping in Theorem 1.

BARRIERS IN THE MATHEMATICAL MODELLING OF DECISION-MAKING

Decision-making is becoming increasingly complex as the number of stakeholders rises,the number of decision-makers rises as well, the implications to consider are various and far-reaching,risks and uncertainties abound and the regulatory framework is growing increasingly complex.Decision-making is caught between the need to thoroughly document and substantiate a choice in frontof oneself and others, on one hand, and the potential traps that increase in number and impact as thecomplexity of the decision-making process increases, on the other hand. The present paper sought topresent critically the main types of downfalls that a decision-making model may face at the level of anindividual decision-maker. Our approach was to put into relation some of the most notablecontributions from various perspectives in order to obtain an integrated overview of the challengesfaced by decision sciences in formulating a both thorough and life-like decision-making model. Weidentified with this occasion three main potential weaknesses in formal decision modeling:unquantifiable factors, such as feelings or morals, excessive formalism and simplification of modelsthat make them vulnerable to paradoxes, and finally cognitive biases that deviate models from anobjective path. Though scientific literature on each of these topics abounds, it is time to integrate it andset the basis for comprehensive and multi-perspective modeling of decisions.decision, decision-making, decision theory, game theory, economic modeling

THE FUTURE OF THE JAPANESE MARKETING

It should not be surprising that Japanese marketing practices vary from traditional Western marketing practices, because marketing is the process of satisfying wants and needs and these desires vary tremendously among cultures. In fact, it would have been surprising if differences were not seen because, in many aspects, the American culture and the Japanese culture are practically diametrical opposites. Of all the business disciplines, marketing is by far the most culturally sensitive. The critical questions most Japanese ask are not "Am I making any money?" or, "How much money am I making?" but rather, "Am I a leader in my business?" "How do I compare with my competitors?" "What must I do to survive in the 21st century?" Technological self-sufficiency, market share, and industrial rank (status) are the key phrases in Japanese business practices. The Japanese system of decision-making imposes a predisposition to enter new technologies to keep up or gain an advantage on competitors. The Japanese undertake a research project not because it will solve a particular problem, but because it may contribute to solving a number of seemingly unrelated problems. Americans, in contrast, are more narrowly focused.japanese marketing, japanese culture, american culture, decisionmaking

Application of the funding GAP method in the process of financing regional development in Romania

The present paper aims at analyzing the framework and the methodology for applying the funding gap method in order to determine the level of structural funds co-financing in the process of financing regional development in Romania, through the Regional Operational Programme (ROP) co-financed from the European Fund for Regional Development (ERDF).structural funds, GAP method, regional development