scholarly journals Dynamical multifractal zeta-functions and fine multifractal spectra of graph-directed self-conformal constructions

2015 ◽  
Vol 36 (6) ◽  
pp. 1922-1971 ◽  
Author(s):  
V. MIJOVIĆ ◽  
L. OLSEN
Keyword(s):  
General Class ◽  
Zeta Functions ◽  
Continuous Functions ◽  
Precise Information ◽  
Multifractal Spectra ◽  
Conformal Measures

We introduce multifractal pressure and dynamical multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the fine multifractal spectra of graph-directed self-conformal measures and the fine multifractal spectra of ergodic Birkhoff averages of continuous functions on graph-directed self-conformal sets.

A Generalization of Epstein Zeta Functions

1949 ◽  
Vol 1 (4) ◽  
pp. 320-327 ◽  
Author(s):  
S. Minakshisundaram
Keyword(s):  
Zeta Function ◽  
Analytic Continuation ◽  
General Class ◽  
Zeta Functions ◽  
Epstein Zeta Function ◽  
Image Position

§ 1. An Epstein zeta function (in its simplest form) is a function represented by the Dirichlet's series where a1… ak are real and n1, n2, … nk run through integral values. The properties of this function are well known and the simplest of them were proved by Epstein [2, 3]. The aim of this note is to define a general class of Dirichlet's series, of which the above can be viewed as an instance, and to discuss the problem of analytic continuation of such series.

scholarly journals Multifractal spectra and multifractal zeta-functions

2016 ◽  
Vol 91 (1) ◽  
pp. 21-82 ◽  
Author(s):  
V. Mijović ◽  
L. Olsen
Keyword(s):  
Zeta Functions ◽  
Multifractal Spectra

Musical Anhedonia

2020 ◽  
Vol 31 (2) ◽  
pp. 62-68
Author(s):  
Sara E. Holm ◽  
Alexander Schmidt ◽  
Christoph J. Ploner
Keyword(s):  
Quality Of Life ◽  
Nucleus Accumbens ◽  
Brain Damage ◽  
Parietal Cortex ◽  
Neurological Disorders ◽  
Brain Regions ◽  
Precise Information ◽  
Exact Localization ◽  
High Prevalence

Abstract. Some people, although they are perfectly healthy and happy, cannot enjoy music. These individuals have musical anhedonia, a condition which can be congenital or may occur after focal brain damage. To date, only a few cases of acquired musical anhedonia have been reported in the literature with lesions of the temporo-parietal cortex being particularly important. Even less literature exists on congenital musical anhedonia, in which impaired connectivity of temporal brain regions with the Nucleus accumbens is implicated. Nonetheless, there is no precise information on the prevalence, causes or exact localization of both congenital and acquired musical anhedonia. However, the frequent involvement of temporo-parietal brain regions in neurological disorders such as stroke suggest the possibility of a high prevalence of this disorder, which leads to a considerable reduction in the quality of life.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

Study of the structural degradation of steel 15Kh5M upon continuous duty

2020 ◽  
Vol 86 (1) ◽  
pp. 38-43
Author(s):  
Vladimir A. Kim ◽  
Valeriya V. Lysenko ◽  
Anna A. Afanaseva ◽  
Khasan I. Turkmenov
Keyword(s):  
Grain Boundaries ◽  
Structural Changes ◽  
Structural Transformations ◽  
Structural Degradation ◽  
Structural Arrangement ◽  
Dispersed Particles ◽  
Complex Process ◽  
Multifractal Spectra ◽  
Steel 15Kh5m ◽  
Complex Indicators

Structural degradation of the material upon long-term thermal and force impacts is a complex process which includes migration of the grain boundaries, diffusion of the active elements of the external and technological environment, hydrogen embrittlement, aging, grain boundary corrosion and other mechanisms. Application of the fractal and multifractal formalism to the description of microstructures opens up wide opportunities for quantitative assessment of the structural arrangement of the material, clarifies and reveals new aspects of the known mechanisms of structural transformations. Multifractal parameterization allows us to study the processes of structural degradation from the images of microstructures and identify structural changes that are hardly distinguishable visually. Any quantitative structural indicator can be used to calculate the multifractal spectra of the microstructure, but the most preferable is that provides the maximum range of variation in the numerical values of the multifractal components. The results of studying structural degradation of steel 15Kh5M upon continuous duty are presented. It is shown that structural degradation of steel during operation under high temperatures and stresses is accompanied by enlargement of the microstructural objects, broadening of the grain boundaries and allocation of the dispersed particles which are represented as point objects in the images. The processes of structural degradation lead to an increase in the range of changes in the components of the multifractal spectra. High values of complex indicators of structural arrangement indicate to an increase in heterogeneity and randomness at the micro-scale level, but at the same time, to manifestation of the ordered combinations of individual submicrostructures. Those structural transformations adapt the material to external impacts and provide the highest reliability and fracture resistance of the material.

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