scholarly journals THE ZIEGLER SPECTRUM OF THE RING OF ENTIRE COMPLEX VALUED FUNCTIONS

2019 ◽  
Vol 84 (1) ◽  
pp. 160-177 ◽  
Author(s):  
SONIA L’INNOCENTE ◽  
FRANÇOISE POINT ◽  
GENA PUNINSKI ◽  
CARLO TOFFALORI
Keyword(s):  
Entire Complex ◽  
Ziegler Spectrum ◽  
Complex Valued

AbstractWe will describe the Ziegler spectrum over the ring of entire complex valued functions.

scholarly journals Algebras of symmetric analytic functions on Cartesian powers of Lebesgue integrable in a power $p\in [1,+\infty)$ functions

2021 ◽  
Vol 13 (2) ◽  
pp. 340-351
Author(s):  
T.V. Vasylyshyn
Keyword(s):  
Banach Space ◽  
Analytic Functions ◽  
Entire Functions ◽  
Complex Banach Space ◽  
Cartesian Power ◽  
Entire Complex ◽  
Continuous Complex ◽  
Fréchet Algebra ◽  
Algebraic Basis ◽  
Complex Valued

The work is devoted to the study of Fréchet algebras of symmetric (invariant under the composition of every of components of its argument with any measure preserving bijection of the domain of components of the argument) analytic functions on Cartesian powers of complex Banach spaces of Lebesgue integrable in a power $p\in [1,+\infty)$ complex-valued functions on the segment $[0,1]$ and on the semi-axis. We show that the Fréchet algebra of all symmetric analytic entire complex-valued functions of bounded type on the $n$th Cartesian power of the complex Banach space $L_p[0,1]$ of all Lebesgue integrable in a power $p\in [1,+\infty)$ complex-valued functions on the segment $[0,1]$ is isomorphic to the Fréchet algebra of all analytic entire functions on $\mathbb C^m,$ where $m$ is the cardinality of the algebraic basis of the algebra of all symmetric continuous complex-valued polynomials on this Cartesian power. The analogical result for the Fréchet algebra of all symmetric analytic entire complex-valued functions of bounded type on the $n$th Cartesian power of the complex Banach space $L_p[0,+\infty)$ of all Lebesgue integrable in a power $p\in [1,+\infty)$ complex-valued functions on the semi-axis $[0,+\infty)$ is proved.

What's the Message of Architecture?

2014 ◽  
pp. 126-136
Author(s):  
Аndrey G. Velikanov
Keyword(s):  
Separate Entity ◽  
Aesthetic Value ◽  
Current State ◽  
Entire Complex ◽  
History Of ◽  
The Aesthetic

Considers the aspects of architecture as a language able to express the current state and to prophetically indicate the upcoming changes. The aesthetic value of a construction cannot be perceived just as a separate entity, but it can be cognized in the context and not only a visual one, in space. It is necessary to see the entire complex of the accompanying phenomena, all the flow of the unfolding metaphors and values. In the model in view the figure of the author-creator must be reconsidered as no longer conforming to today's reality. The development of the Stalinist Empire style, as well as its transformations, is considered as one of the specific phenomena in the history of well-known constructions

DRAINAGE BASIN AS A COMPLEX SOCIO-NATURAL HIERARCHICAL SYSTEM

2020 ◽  
Vol 42 (3) ◽  
pp. 293-303
Author(s):  
VALERIY BONDAREV
Keyword(s):  
Drainage Basin ◽  
Temporal Analysis ◽  
Large River ◽  
Hierarchical Level ◽  
Effective Management ◽  
Drainage Basins ◽  
Time Intervals ◽  
Natural Systems ◽  
Spatial And Temporal Analysis ◽  
Entire Complex

The theoretical and methodological basis of the systems hierarchical spatial and temporal analysis of a drainage basin, which addresses the problems of effective management in socio-natural systems of different ranks, is considered. It is proposed to distinguish 9 orders of forms that are relevant to the analysis of drainage basins, where the first level is represented by individual aggregates and particles, and the last - by basins of large and the largest rivers. As part of the allocation of geological, historical and modern time intervals, the specificity of the implementation of processes in basins of different scales from changing states, through functioning to evolution is demonstrated. The interrelation of conditions and factors that determine the processes occurring within the drainage basins is revealed. It is shown that a specific combination of conditions and factors that determine processes in the drainage basin is associated with the hierarchy of the objects under consideration, i.e. the choice of a spatial-temporal hierarchical level is crucial for the organization of study within drainage basins. At one hierarchical level, some phenomenon can be considered as a factor, and at another - as a condition. For example, tectonic processes can be considered as an active factor in the evolution of large river basins in the geological perspective, but for small drainage basin, this is already a conservative background condition. It is shown that at the historical time the anthropogenic factor often comes to the fore, with the appearance of which in the functioning of the drainage basin, there is a need to take into account the entire complex of socio-environmental problems that can affect the sustainable state of various territories, especially in the field of water and land use. Hierarchical levels of managing subjects are identified, which are primarily responsible for effective management at the appropriate hierarchical level of the organization of the socio-natural system within the catchment area, starting from an individual to humankind as a whole.

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