scholarly journals A noncommutative version of Farber's topological complexity

2017 ◽  
Vol 49 (2) ◽  
pp. 1
Author(s):  
Vladimir Manuilov
Keyword(s):  
Topological Complexity ◽  
Noncommutative Version

Dehydration-driven evolution of topological complexity in ethylamonium uranyl selenates

2017 ◽  
Vol 247 ◽  
pp. 105-112 ◽  
Author(s):  
Vladislav V. Gurzhiy ◽  
Sergey V. Krivovichev ◽  
Ivan G. Tananaev
Keyword(s):  
Topological Complexity

scholarly journals Topological complexity of frictional interfaces: friction networks

2012 ◽  
Vol 19 (2) ◽  
pp. 215-225 ◽  
Author(s):  
H. O. Ghaffari ◽  
R. P. Young
Keyword(s):  
Topological Complexity ◽  
Type Ii ◽  
Stored Energy ◽  
Fracture Permeability ◽  
Radiated Energy ◽  
Universal Power Law ◽  
Shear Rupture ◽  
Crack Type ◽  
Network Properties ◽  
Highly Correlated

Abstract. Through research conducted in this study, a network approach to the correlation patterns of void spaces in rough fractures (crack type II) was developed. We characterized friction networks with several networks characteristics. The correlation among network properties with the fracture permeability is the result of friction networks. The revealed hubs in the complex aperture networks confirmed the importance of highly correlated groups to conduct the highlighted features of the dynamical aperture field. We found that there is a universal power law between the nodes' degree and motifs frequency (for triangles it reads T(k) ∝ kβ (β ≈ 2 ± 0.3)). The investigation of localization effects on eigenvectors shows a remarkable difference in parallel and perpendicular aperture patches. Furthermore, we estimate the rate of stored energy in asperities so that we found that the rate of radiated energy is higher in parallel friction networks than it is in transverse directions. The final part of our research highlights 4 point sub-graph distribution and its correlation with fluid flow. For shear rupture, we observed a similar trend in sub-graph distribution, resulting from parallel and transversal aperture profiles (a superfamily phenomenon).

scholarly journals A Representation Theorem for Archimedean Quadratic Modules on ∗-Rings

2009 ◽  
Vol 52 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Jakob Cimprič
Keyword(s):  
Algebraic Geometry ◽  
Representation Theory ◽  
Representation Theorem ◽  
Commutative Rings ◽  
Real Algebraic Geometry ◽  
New Approach ◽  
Noncommutative Version ◽  
Quadratic Modules ◽  
Rings With Involution ◽  
Associative Rings

AbstractWe present a new approach to noncommutative real algebraic geometry based on the representation theory of C*-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand–Naimark representation theorem for commutative C*-algebras. A noncommutative version of Gelfand–Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution.

scholarly journals Noncommutative Friedmann equations in effective LQC

2020 ◽  
Vol 29 (06) ◽  
pp. 2050039
Author(s):  
Luis Rey Díaz-Barrón ◽  
Abraham Espinoza-García ◽  
S. Pérez-Payán ◽  
J. Socorro
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Quantum Cosmology ◽  
Equations Of Motion ◽  
Loop Quantum Cosmology ◽  
Friedmann Equations ◽  
Noncommutative Version ◽  
Previous Proposal ◽  
Free Scalar ◽  
Raychaudhuri Equations

In this work, we construct a noncommutative version of the Friedmann equations in the framework of effective loop quantum cosmology, extending and applying the ideas presented in a previous proposal by some of the authors. The model under consideration is a flat FRW spacetime with a free scalar field. First, noncommutativity in the momentum sector is introduced. We establish the noncommutative equations of motion and obtain the corresponding exact solutions. Such solutions indicate that the bounce is preserved, in particular, the energy density is the same as in the standard LQC. We also construct an extension of the modified Friedmann equations arising in effective LQC which incorporates corrections due to noncommutativity, and argue that an effective potential is induced. This, in turn, leads us to investigate the possibility of an inflationary era. Finally, we obtain the Friedmann and the Raychaudhuri equations when implementing noncommutativity in the configuration sector. In this case, no effective potential is induced.

SUBSTRUCTURAL INQUISITIVE LOGICS

2019 ◽  
Vol 12 (2) ◽  
pp. 296-330 ◽  
Author(s):  
VÍT PUNČOCHÁŘ
Keyword(s):  
Fuzzy Logic ◽  
General Theory ◽  
Propositional Logic ◽  
Substructural Logics ◽  
Substructural Logic ◽  
Fuzzy Logics ◽  
Inquisitive Semantics ◽  
Semantic Framework ◽  
Noncommutative Version ◽  
Image Position

AbstractThis paper shows that any propositional logic that extends a basic substructural logic BSL (a weak, nondistributive, nonassociative, and noncommutative version of Full Lambek logic with a paraconsistent negation) can be enriched with questions in the style of inquisitive semantics and logic. We introduce a relational semantic framework for substructural logics that enables us to define the notion of an inquisitive extension of λ, denoted as ${\lambda ^?}$, for any logic λ that is at least as strong as BSL. A general theory of these “inquisitive extensions” is worked out. In particular, it is shown how to axiomatize ${\lambda ^?}$, given the axiomatization of λ. Furthermore, the general theory is applied to some prominent logical systems in the class: classical logic Cl, intuitionistic logic Int, and t-norm based fuzzy logics, including for example Łukasiewicz fuzzy logic Ł. For the inquisitive extensions of these logics, axiomatization is provided and a suitable semantics found.

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