The relationship among three types of rough approximation pairs

2014 ◽  
Vol 60 ◽  
pp. 28-34 ◽  
Author(s):  
Guilong Liu ◽  
Kai Zhu
Keyword(s):  
Rough Approximation ◽  
The Relationship

scholarly journals Rough Approximation Operators on a Complete Orthomodular Lattice

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 164
Author(s):  
Songsong Dai
Keyword(s):  
Boolean Algebra ◽  
Orthomodular Lattice ◽  
Orthomodular Lattices ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Distributive Law ◽  
Complete Orthomodular Lattice ◽  
The Relationship

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

Cation mobilities in liquid and supercritical C1–C4 hydrocarbons

1980 ◽  
Vol 58 (14) ◽  
pp. 1490-1494 ◽  
Author(s):  
Norman Gee ◽  
Gordon R. Freeman
Keyword(s):  
Free Path ◽  
Ion Mobility ◽  
Diffusion Coefficients ◽  
Critical Region ◽  
Mean Free Path ◽  
Liquid Viscosity ◽  
Boiling Points ◽  
Rough Approximation ◽  
The Relationship ◽  
Lower Liquid

The relationship between ion mobility and liquid viscosity is commonly expressed as μ [Formula: see text] η−m. In hydrocarbons the value of m tends to be near 1.0 at η > 5 mP, m > 1.0 at ~5 < η < 1 mP, and m < 1.0 at η < 0.5 mP. Thus there is a maximum in a plot of μη against η−1 and Walden's rule (m = 1.0) is only a rough approximation. The decrease of μη as the critical region is approached is accompanied by an increase in the ratio of diffusion coefficients Dmolec/Dion. Ion mobilities in the liquids well below their normal boiling points are chiefly controlled by the fluidity. At higher temperatures and concomitant lower liquid densities and viscosities μη first increases, due to an increasing ion mean free path, then decreases as the critical region is approached, due to the increasing liquid compressibility and consequent electrostriction about the ion.

Monadic NM-algebras

2019 ◽  
Vol 27 (6) ◽  
pp. 812-835
Author(s):  
Juntao Wang ◽  
Pengfei He ◽  
Yanhong She
Keyword(s):  
Representation Theorem ◽  
Predicate Logic ◽  
Algebraic Semantics ◽  
Subdirectly Irreducible ◽  
Approximation Spaces ◽  
Rough Approximation ◽  
Subdirect Representation ◽  
Algebraic Foundation ◽  
The Relationship ◽  
Monadic Filters

Abstract In this paper, we investigate universal and existential quantifiers on NM-algebras. The resulting class of algebras will be called monadic NM-algebras. First, we show that the variety of monadic NM-algebras is algebraic semantics of the monadic NM-predicate logic. Moreover, we discuss the relationship among monadic NM-algebras, modal NM-algebras and rough approximation spaces. Second, we introduce and investigate monadic filters in monadic NM-algebras. Using them, we prove the subdirect representation theorem of monadic NM-algebras, and characterize simple and subdirectly irreducible monadic NM-algebras. Finally, we present the monadic NM-logic and prove its (chain) completeness with respect to (strong) monadic NM-algebras. These results constitute a crucial first step for providing an algebraic foundation for the monadic NM-predicate logic.

scholarly journals Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 95
Author(s):  
Radwan Abu-Gdairi ◽  
Mostafa A. El-Gayar ◽  
Tareq M. Al-shami ◽  
Ashraf S. Nawar ◽  
Mostafa K. El-Bably
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Real Life ◽  
Life Problems ◽  
Rough Approximation ◽  
Affirmative Solution ◽  
The Relationship ◽  
Topological Models ◽  
Day By Day ◽  
Generalized Rough Sets

The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.

scholarly journals Empirical modeling of the relationship between decision sight distance and stopping sight distance based on AASHTO

2018 ◽  
Vol 4 (48) ◽  
pp. 7-25
Author(s):  
Shy BASSAN
Keyword(s):  
Friction Coefficient ◽  
Empirical Relationship ◽  
Design Guidelines ◽  
Empirical Modeling ◽  
Highway Design ◽  
Deceleration Rate ◽  
Sight Distance ◽  
Rough Approximation ◽  
Stopping Sight Distance ◽  
The Relationship

The paper introduces implementation of highways' stopping sight distance (SSD) and decision sight distance (DSD) based on AASHTO modeling assumptions. SSD characterizes the necessary distance for highway vehicles to stop safely in front from an obstacle. SSD is a function of vehicle speed, perception reaction time, deceleration rate, and grade based on AASHTO and most highway design international guidelines. The deceleration rate which is assumed constant (3.4 m/sec2) based on AASHTO 2011 is generally controlled by the friction coefficient depending on the road surface conditions. A driver's demanded deceleration rate may not exceed the range of friction coefficient according to various pavement conditions. Although SSD is generally sufficient to allow skilled and alert drivers to the stop their vehicles under regular situations, this distance is insufficient when information is difficult to comprehend. A DSD should be provided in highways geometric design when the driver is required to detect an unexpected or difficult to perceive information source. Interchanges (specifically exit ramps) and intersections, and required changing in driver direction of travel, changes in the basic cross section such as toll plaza, lane drop, are typical scenarios where driver needs DSD in the safety manner. The introduction of the two sight distance types (SSD and DSD) is a perquisite for empirical modeling of the relationship between DSD and SSD. The modeling refers to DSD for rural highways, suburban roads, and urban roads based on AASHTO models. Specifically the paper covers DSD three avoidance maneuver types of stopping (types A, A1, B) and three maneuver types of speed, path, and direction changing (types C,D, E) for the three roadway categories. The major parameters that control these avoidance types are pre-maneuver times, and pre-maneuver plus maneuver times. The empirical relationship proposed in this study simplifies the process of evaluating the decision sight distance based on stopping sight distance record, based on AASHTO models, without the need of strenuous estimation of the DSD model maneuver and deceleration parameters. Such a simplified correlation has not been found in the literature except a rough approximation documented in the British highway design guidelines.

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Choosing a Markov blanket

2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr
Keyword(s):  
Markov Blanket ◽  
Target Article ◽  
The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

Tinkering with cognitive gadgets: Cultural evolutionary psychology meets active inference

2019 ◽  
Vol 42 ◽  
Author(s):  
Paul Benjamin Badcock ◽  
Axel Constant ◽  
Maxwell James Désormeau Ramstead
Keyword(s):  
Evolutionary Psychology ◽  
Research Program ◽  
Active Inference ◽  
Innovative Research ◽  
Cognitive Faculties ◽  
Cultural Evolutionary ◽  
The Relationship

Abstract Cognitive Gadgets offers a new, convincing perspective on the origins of our distinctive cognitive faculties, coupled with a clear, innovative research program. Although we broadly endorse Heyes’ ideas, we raise some concerns about her characterisation of evolutionary psychology and the relationship between biology and culture, before discussing the potential fruits of examining cognitive gadgets through the lens of active inference.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

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