Regularity of non-stationary subdivision: a matrix approach
In this paper, we study scalar multivariate non-stationary subdivision
schemes with integer dilation matrix M and present a unifying, general approach
for checking their convergence and for determining their Hölder regularity (latter in
the case M = mI,m ≥ 2). The combination of the concepts of asymptotic similarity
and approximate sum rules allows us to link stationary and non-stationary settings
and to employ recent advances in methods for exact computation of the joint spectral
radius. As an application, we prove a recent conjecture by Dyn et al. on the Hölder regularity
of the generalized Daubechies wavelets. We illustrate our results with several
The current state of methods of the solution of boundary problems of mechanics of continuous environments is characterized. It is noted that packages of applied programs applied in engineering practice are based on the methods leading to solutions of boundary problems in the form of massifs of numbers. As a shortcoming the im-possibility of a reliable assessment of an error of such decisions for the majority of complex engineering chal-lenges is noted. As the alternative is stated an essence of a fictitious canonic regions method. It is shown that its application leads to solutions of boundary problems not in the form of massifs of numbers, but in the form of the functions which are identically satisfying with to the differential equations of boundary problems. The main ad-vantage of the fictitious canonic regions method - high precision of received results and possibility of a reliable assessment of their error. The review of stages of development of the fictitious canonic regions method is executed. The review of the works devoted to its application for the solution of scientific and engineering problems is executed.
The article describes the problem of convergence of technical and eco-nomic education through the use of marketing categories. The scheme of inter-action and interpenetration of scientific disciplines at the present stage of devel-opment of society is also presented in the article. The article examines the evolu-tionary forms of the fundamental categories of marketing – the rate of use-value, and the mechanism of convergence of technological and economic education in a bipolar economy.
Hankuk University of Foreign Studies held an international conference which introduced and discussed the case studies and programs of regional experts regarding analyzing regions and areas of development
This paper argues that modeling granularity and approximation (Krifka 2007; Lewis 1979) is crucial for capturing important aspects of the distribution and interpretation of adjectives and their modifiers, modulo certain differences between modified adjectives and numerals. In addition, the paper presents supporting experimental results with minimizers like slightly and maximizers like completely.
The paper deals with the radar target discrimination problem performed on complex radar images. The approach based on radial basis function (RBF) artificial neural network (ANN) is proposed for the identification of point scatterers placed within a radar image. The renewed concept of simple adaptive units as the foundation for network assembling allows one to design an ANN-based feature extraction scheme for the two-dimensional signal processing. It was shown that ANN implementing RBF neural processing units could be applied for the identification of radar targets described by the set of separated scatterers, even in cases where the relative distance between the scatterers is comparable to or less than the effective width of each scatterer. The obtained results indicate a high accuracy estimation of separate scatterer centers in the presence of noise which is not limited to the stationary case but supposed to be cyclostationary. It was also shown that the parameters describing the coordinates of scattering centers could be successfully extracted from the trained ANN after about one hundred epochs spent on ANN training process, which is carried out by means of modified gradient descent method. The main result is to demonstrate the possibility of using neural networks to automatically analyze radar images, which is an integral part of a set of tasks that form the target recognition problem. The proposed algorithm implements an approach of identification systems made using a neural network training procedures.
In this paper we study convergence among Russian regions. We find that while there was no convergence in 1990s, the situation changed dramatically in 2000s. While interregional GDP per capita gaps still persist, the differentials in incomes and wages decreased substantially. We show that fiscal redistribution did not play a major role in convergence. We therefore try to understand the phenomenon of recent convergence using panel data on the interregional reallocation of capital and labor. We find that capital market in Russian regions is integrated in a sense that local investment does not depend on local savings. We also show that economic growth and financial development has substantially decreased the barriers to labor mobility. We find that in 1990s many poor Russian regions were in a poverty trap: potential workers wanted to leave those regions but could not afford to finance the move. In 2000s (especially in late 2000s), these barriers were no longer binding. Overall economic development allowed even poorest Russian regions to grow out of the poverty traps. This resulted in convergence in Russian labor market; the interregional gaps in incomes, wages and unemployment rates are now below those in Europe. The results imply that economic growth and development of financial and real estate markets eventually result in interregional convergence.
The historical changes in Central and Eastern Europe demanded suitable paths for the transition from centrally planned to market based economies. The lack of relevant experience added to the challenge, giving rise to the incalculable risks of implementing untested policies. By focusing on monetary policy, trade, and convergence, this volume addresses some of the most urgent economic policy issues in the transition economies of Central and Eastern Europe and beyond.
The article reveals the problem of convergence of direct and inverse problems in Earth Sciences, describes the features and application of these problems, discloses analytical features of direct and inverse problems. The convergence criteria and conditions for convergence were presented. This work is supported by the Grant of the Government of the Russian Federation for support of scientific research, implemented under the supervision of leading scientists in Russian institutions of higher education in the field "Space Research and Technologies" in 2011–2013.
This thought-provoking monograph analyzes long- medium- and short-term global cycles of prosperity, recession, and depression, plotting them against centuries of important world events. Major research on economic and political cycles is integrated to clarify evolving relationships between the global center and its periphery as well as current worldwide economic upheavals and potential future developments. Central to this survey are successive waves of industrial and, later, technological and cybernetic progress, leading to the current era of globalization and the changes of the roles of both Western powers and former minors players, however that will lead to the formation of the world order without a hegemon. Additionally, the authors predict what they term the Great Convergence, the lessening of inequities between the global core and the rest of the world, including the wealth gap between First and Third World nations.
Among the topics in this ambitious volume:
· Why politics is often omitted from economic analysis.
· Why economic cycles are crucial to understanding the modern geopolitical landscape.
· How the aging of the developed world will affect world technological and economic future.<
· The evolving technological forecast for Global North and South.
· Where the U.S. is likely to stand on the future world stage.
Economic Cycles, Crises, and the Global Periphery will inspire discussion and debate among sociologists, global economists, demographers, global historians, and futurologists. This expert knowledge is necessary for further research, proactive response, and preparedness for a new age of sociopolitical change.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.