On the intrinsic definition of local observables

1995 ◽  
Vol 35 (3) ◽  
pp. 237-250 ◽  
Author(s):  
Roberto Conti
Keyword(s):  
Local Observables ◽  
Definition Of ◽  
Intrinsic Definition

REVISITING Xor-IMPLICATIONS: CLASSES OF FUZZY (CO)IMPLICATIONS BASED ON f-Xor (f-XNor) CONNECTIVES

2013 ◽  
Vol 21 (06) ◽  
pp. 899-925 ◽  
Author(s):  
BENJAMÍN BEDREGAL ◽  
RENATA HAX SANDER REISER ◽  
GRAÇALIZ PEREIRA DIMURO
Keyword(s):  
Boundary Conditions ◽  
Unit Interval ◽  
End Points ◽  
Triangular Norms ◽  
Fuzzy Implications ◽  
Classical Definition ◽  
Definition Of ◽  
Exclusive Or ◽  
Intrinsic Definition ◽  
Fuzzy Connectives

The main contribution of this paper is the introduction of an intrinsic definition of the connective “fuzzy exclusive or” E (f-Xor E), based only on the properties of boundary conditions, commutativity and partial isotonicity-antitonicity on the the end-points of the unit interval U = [0,1], in a way that the classical definition of the boolean Xor is preserved. We show three classes of the f-Xor E that can be also obtained from the composition of fuzzy connectives, namely, triangular norms, triangular conorms and fuzzy negations. A discussion about extra properties satisfied by the f-Xor E is presented. Additionally, the paper introduces a class of fuzzy equivalences that generalizes the Fodor and Roubens's fuzzy equivalence, and four classes of fuzzy implications induced by the f-Xor E, discussing their main properties. The relationships between those classes of fuzzy implications and automorphisms are explored. The action of automorphisms on f-Xor E is analyzed.

scholarly journals Amplituhedron-like geometries

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gabriele Dian ◽  
Paul Heslop
Keyword(s):  
Canonical Form ◽  
Star Product ◽  
Natural Extension ◽  
Tree Level ◽  
Winding Number ◽  
Alternative Definition ◽  
Standard Definition ◽  
Definition Of ◽  
Intrinsic Definition ◽  
Simple Definition

Abstract We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

scholarly journals Active faults sources for the Pátzcuaro–Acambay fault system (Mexico): fractal analysis of slip rates and magnitudes <i>M</i><sub>w</sub> estimated from fault length

2018 ◽  
Vol 18 (11) ◽  
pp. 3121-3135
Author(s):  
Avith Mendoza-Ponce ◽  
Angel Figueroa-Soto ◽  
Diana Soria-Caballero ◽  
Víctor Hugo Garduño-Monroy
Keyword(s):  
Time Domain ◽  
Fractal Analysis ◽  
Active Faults ◽  
Slip Rate ◽  
Spatial Domain ◽  
Fault System ◽  
Slip Rates ◽  
Oblique Convergence ◽  
Definition Of ◽  
Intrinsic Definition

Abstract. The Pátzcuaro–Acambay fault system (PAFS), located in the central part of the Trans-Mexican Volcanic Belt (TMVB), is delimited by an active transtensive deformation area associated with the oblique subduction zone between the Cocos and North American plates, with a convergence speed of 55 mm yr−1 at the latitude of the state of Michoacán, Mexico. Part of the oblique convergence is transferred to this fault system, where the slip rates range from 0.009 to 2.78 mm yr−1. This has caused historic earthquakes in Central Mexico, such as the Acambay quake (Ms=6.9) on 19 November 1912 with surface rupture, and another in Maravatío in 1979 with Ms=5.6. Also, paleoseismic analyses are showing Quaternary movements in some faults, with moderate to large magnitudes. Notably, this zone is seismically active, but lacks a dense local seismic network, and more importantly, its neotectonic movements have received very little attention. The present research encompasses three investigations carried out in the PAFS. First, the estimation of the maximum possible earthquake magnitudes, based on 316 fault lengths mapped on a 15 m digital elevation model, by means of three empirical relationships. In addition, the Hurst exponent Hw and its persistence, estimated for magnitudes Mw (spatial domain) and for 32 slip-rate data (time domain) by the wavelet variance analysis. Finally, the validity of the intrinsic definition of active fault proposed here. The average results for the estimation of the maximum and minimum magnitudes expected for this fault population are 5.5≤Mw≤7. Also, supported by the results of H at the spatial domain, this paper strongly suggests that the PAFS is classified in three different zones (western PAFS, central PAFS, and eastern PAFS) in terms of their roughness (Hw=0.7,Hw=0.5,Hw=0.8 respectively), showing different dynamics in seismotectonic activity and; the time domain, with a strong persistence Hw=0.949, suggests that the periodicities of slip rates are close in time (process with memory). The fractal capacity dimension (Db) is also estimated for the slip-rate series using the box-counting method. Inverse correlation between Db and low slip-rate concentration was observed. The resulting Db=1.86 is related to a lesser concentration of low slip-rates in the PAFS, suggesting that larger faults accommodate the strain more efficiently (length ≥3 km). Thus, in terms of fractal analysis, we can conclude that these 316 faults are seismically active, because they fulfill the intrinsic definition of active faults for the PAFS.

Characterizations of p-Spaces

1971 ◽  
Vol 14 (3) ◽  
pp. 459-460 ◽  
Author(s):  
C. M. Pareek
Keyword(s):  
Definition Of ◽  
Intrinsic Definition

The concept of p-space is quite recent. It was introduced by Arhangel'skii [2]. The definition of p-space given in [2] involves compactification of the space. In view of the interesting properties of p-spaces obtained in [2], Alexadroff [1] suggested a problem of finding a direct intrinsic definition (without appeal to compactification). The main aim of this note is to answer the above problem.I am grateful to Dr. S. K. Kaul for his comments.

Small-world graphs: characterization and alternative constructions

2008 ◽  
Vol 40 (04) ◽  
pp. 939-965 ◽  
Author(s):  
Rama Cont ◽  
Emily Tanimura
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Small World ◽  
Random Perturbations ◽  
Regular Lattice ◽  
Scaling Properties ◽  
Probabilistic Formulation ◽  
Small World Graphs ◽  
Definition Of ◽  
Intrinsic Definition

Small-world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small-world graphs, based on a probabilistic formulation of scaling properties of the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), which are based on random perturbations of a regular lattice. We also propose alternative constructions of small-world graphs which are not based on lattices and study their scaling properties.

scholarly journals Small-world graphs: characterization and alternative constructions

2008 ◽  
Vol 40 (4) ◽  
pp. 939-965 ◽  
Author(s):  
Rama Cont ◽  
Emily Tanimura
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Small World ◽  
Random Perturbations ◽  
Regular Lattice ◽  
Scaling Properties ◽  
Probabilistic Formulation ◽  
Small World Graphs ◽  
Definition Of ◽  
Intrinsic Definition

Small-world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small-world graphs, based on a probabilistic formulation of scaling properties of the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), which are based on random perturbations of a regular lattice. We also propose alternative constructions of small-world graphs which are not based on lattices and study their scaling properties.

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