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Applications of non-Archimedean analysis in the block hierarchical rock mass mechanics
The article considers applicability of non-Archimedean analysis to multi-scale rock mass modeling based on the concept of dissipation function. In the capacity of coordinates, the author introduces non-Archimedean lines of infinite hierarchy. Basic definitions of univariate analysis are generalized for a two-dimensional case.
А. Ф. Ревуженко
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Lawrence Narici, Edward Beckenstein
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1997
The present chapter is purely mathematical. The reader, who is more interested in physics than mathematics can omit this chapter and go directly to Chapter 4, where the formalism of m-adic quantum mechanics (which describes a finite precision of measurements) will be presented.
A. Khrennikov
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The present chapter is purely mathematical. The reader, who is more interested in physics than mathematics can omit this chapter and go directly to Chapter 4, where the formalism of m-adic quantum mechanics (which describes a finite precision of measurements) will be presented.
A. Khrennikov
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Non-Archimedean analysis and a wave-type pseudodifferential equation on finite adèles
Journal of Pseudo-Differential Operators and Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victor A. Aguilar-Arteaga +2 more
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2011
Non-Archimedean analysis is an appropriate modeling tool for hierarchical multi-level systems.
O. Iordache
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Non-Archimedean analysis is an appropriate modeling tool for hierarchical multi-level systems.
O. Iordache
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Advances in Non-Archimedean Analysis
2011Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t.
Helge Glöckner +2 more
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Review of Non-Archimedean Analysis
1998In this section we will give a rapid presentation of those properties of non-Archimedean analysis necessary for later sections. For more we refer the reader to [BGR1], [Bru1], [Kob1], [R1,144–159], [L1], and the first two chapters of [DGS1].
D. Goss
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Rock mass deformation modeling using the non-Archimedean analysis
Journal of Mining Science, 2008The non-Archimedean space is a multi-scale one. The paper shows that this face is applicable to developing mathematical models of rocks exhibiting a hierarchy of structural levels. A closed model, considering anisotropy and weakening of a rock mass, is constructed.
S. V. Lavrikov +2 more
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Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models
1997I. Measurements and Numbers. II. Fundamentals. III. Non-Archimedean Analysis. IV. The Ultrametric Hilbert Space Description of Quantum Measurements with a Finite Exactness. V. Non-Kolmogorov Probability Theory. VI. Non-Kolmogorov Probability and Quantum Physics. VII. Position and Momentum Representations. VIII.
A. Khrennikov
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