Uniqueness property for quasiharmonic functions

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions

Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

Metric Density and Quasimobius Mappings

We study the notion of μ-density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between μ-density and homogeneous density is established. We also characterize μ-dense spaces as “arcwise” connected metric spaces in which “arcs” are the quasimobius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of n in terms of μ-density.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41618/1/11202_2004_Article_454811.pd

The formation and stages of development of interstate activities of the Heydar Aliyev Foundation

Since the founding of the Heydar Aliyev Foundation in 2004, this institution has been actively involved in large-scale international cultural relations. The purpose of creating this fund was to preserve and popularize the legacy of the national leader of the Azerbaijani people, Heydar Aliyev, to convey the truth about Azerbaijan to the world community, and to familiarize with its history, culture, and spiritual values. The purpose of this article is to determine the stages of formation and development of the Heydar Aliyev Foundation, to analyze the directions of its multi-vector activity and to justify the role of the Foundation in forming a positive image of independent Azerbaijan. Along with general logical methods, the methods of political monitoring, content analysis, historical and comparative analysis are used, which make it possible to highlight the complex of activities carried out by the Fund and to forecast the trends of its further activity. Since the foundation of the Foundation, important projects have been developed and successfully implemented to protect the welfare of the Azerbaijani people, protect their national heritage and moral values. The Heydar Aliyev Foundation, paying special attention to the expansion of cooperation with Islamic countries in the field of science and culture, ensured the achievement of the highest level of development of relations between Azerbaijan and the Islamic Organization for Education, Science and Culture. The Heydar Aliyev Foundation paid serious attention to the expansion of cooperation within the framework of the UN, which resulted in the adoption of the Program on creating conditions for the use of information and communication technologies by people with visual impairments. According to the results of the research, it was established that the Heydar Aliyev Foundation, in cooperation with the government, parliament and the Ministry of Foreign Affairs, plays the role of one of the effective means of implementing the foreign policy, social, humanitarian, political, economic and cultural strategy of Azerbaijan. The Foundation was able to form a positive image of Azerbaijan on an international scale, establishing constructive cooperation in all spheres, both with individual states and with influential international and regional organizations

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

One country, two systems? The heavy-tailedness of Chinese A- and H- share markets

Chinese A- and H– share markets operate in different institutional environments (emerging/developing v.s. developed) and thus may have different tail risk properties. This paper focuses on the analysis of heavy-tailedness properties of these two markets using recently developed robust inference methods. The equality of tail indices of returns for A and H dual-listed companies cannot be rejected, and some A- and H– share returns may have infinite second moments. Their heavy-tailedness properties did not change significantly with respect to the 2008 financial crisis and the date when the corresponding company starts to be dual-listed

Equity returns and sentiment

This paper analyzes approximately 100 Gigabytes of raw text data from Twitter with keywords “AAPL,” “S&P 500,” “FTSE100” and “NASDAQ” to explore the relationship between sentiment and the returns and prices on the Apple stock and the S&P 500, FTSE 100 and NASDAQ indices. The findings point to significant relationship and dependence between sentiment measures and the S&P 500 and FTSE 100 indices’ returns and prices. The econometric analysis of dependence between the aforementioned variables in the paper is presented in some detail for illustration of the methodology employed

Integrability of Lie systems through Riccati equations

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.Comment: Corrected typo

On the notion of conditional symmetry of differential equations

Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true'' and ``weak'' conditional symmetry. Their relationship with exact and partial symmetries is also discussed. An extensive use of ``symmetry-adapted'' variables is made; several clarifying examples, including the case of Boussinesq equation, are also provided.Comment: 18 page