Quasistochastic semigroup as a generalized group

Yudin, V. V.; Ershov, A. D.

doi:10.1007/bf00836689

Cited by 7 publications

(12 citation statements)

References 2 publications

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“…. }, which confirms the semigroup properties of P − -system (26). It is clear that the algebraic properties of the two components P + and P − are identical.…”

Section: The Penrose System As the Proper Fibonacci Subsemigroupsupporting

confidence: 80%

“…From what was said above, we conclude that in both cases of the collapsing Fibonacci and Penrose processes, we cannot introduce quasiprobability measures on matrix orbits and we therefore cannot construct an entropy functional. The Eddington time arrow can therefore be created only by the expanding Fibonacci-Penrose semigroup [25], [26].…”

Section: The Penrose System As the Proper Fibonacci Subsemigroupmentioning

confidence: 99%

“…In addition to the right semigroup, we also have the left semigroup obtained as a result of the group bundle of Penrose inverse semigroups (GBPIS) [23]- [26] analogous to GBFIS (19).…”

Section: The Penrose System As the Proper Fibonacci Subsemigroupmentioning

confidence: 99%

“…It is already useful on this level to introduce the notion of the group bundle of Fibonacci inverse semigroups (GBFIS) [23]- [26]:…”

Section: The Group Bundle Of Inverse Fibonacci Semigroupsmentioning

confidence: 99%

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The Fibonacci-Penrose semigroup formalism and morphogenetic synthesis of quasicrystal mosaics

Yudin¹,

Startzev²,

Permyakova³

2011

Theor Math Phys

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We construct the group bundle for the inverse Fibonacci semigroups in the axiomatic approach framework. The proper Fibonacci semigroup is the corresponding group bundle for the Penrose semigroups, which can be interpreted as the generating grammar of the morphogenetic synthesis of the pentasymmetric Penrose parquet in the numbers of tiling by golden rhombuses. This morphogenetic synthesis of the Penrose parquet satisfies the scaling principle. Parquet plates are not absolutely rigid, and the relations between their metric characteristics are governed by the golden section and other magic numbers. The characteristic form factors of three-level dual alphabets are the corresponding invariants. We realize the morphogenetic synthesis in the examples of square-octagonal and bihexagonal lattices. We consider cumulative properties of magic series and the evolutionary aspects of semigroup orbits in the entropy representation.

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“…. }, which confirms the semigroup properties of P − -system (26). It is clear that the algebraic properties of the two components P + and P − are identical.…”

Section: The Penrose System As the Proper Fibonacci Subsemigroupsupporting

confidence: 80%

Section: The Penrose System As the Proper Fibonacci Subsemigroupmentioning

confidence: 99%

“…In addition to the right semigroup, we also have the left semigroup obtained as a result of the group bundle of Penrose inverse semigroups (GBPIS) [23]- [26] analogous to GBFIS (19).…”

Section: The Penrose System As the Proper Fibonacci Subsemigroupmentioning

confidence: 99%

“…It is already useful on this level to introduce the notion of the group bundle of Fibonacci inverse semigroups (GBFIS) [23]- [26]:…”

Section: The Group Bundle Of Inverse Fibonacci Semigroupsmentioning

confidence: 99%

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The Fibonacci-Penrose semigroup formalism and morphogenetic synthesis of quasicrystal mosaics

Yudin¹,

Startzev²,

Permyakova³

2011

Theor Math Phys

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“…Here, α refers to the ME susceptibility which is inherent to Cr 2 O 3 and possesses interesting temperature dependence. 13 In the absence of the ME energy, Cr 3+ ions in a buckled layer take their equilibrium positions with nominal displacement. With the applied ME energy, the displacement between Cr 3+ ions with opposite spins within the buckled layer changes and the surface develops an uncompensated spin arrangement with all spins pointing up (e.g.…”

Section: Structural Features and Computational Methodsmentioning

confidence: 99%

Modeling temperature dependent exchange bias in systems with magnetoelectric chromia

Ahmed

Victora

2017

AIP Advances

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Exchange bias in a magnetoelectric Cr2O3/ferromagnet system at finite temperature, based on the formation of a domain wall in Cr2O3, has been investigated using Monte Carlo simulation. It has been shown that the calculation of the exchange bias based on domain wall formation yields a more realistic value than that calculated using interfacial exchange coupling between Cr2O3 and the adjacent ferromagnet. Possible shortcoming of the magnetoelectric effect in setting the switchable exchange bias in the low temperature regime has also been demonstrated based on an energy threshold requirement. Specifically, it has been found that the magnetoelectric effect becomes intrinsically less effective in switching the exchange bias at low temperature, thus making the applicability of the system limited to only a certain temperature range.

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The Fibonacci fractal is a new fractal type

Yudin¹,

Startzev

2012

Theor Math Phys

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Quasistochastic semigroup as a generalized group

Cited by 7 publications

References 2 publications

The Fibonacci-Penrose semigroup formalism and morphogenetic synthesis of quasicrystal mosaics

The Fibonacci-Penrose semigroup formalism and morphogenetic synthesis of quasicrystal mosaics

Modeling temperature dependent exchange bias in systems with magnetoelectric chromia

The Fibonacci fractal is a new fractal type

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