On The Generalization of Fuzzy Rough Approximation Based on Asymmetric Relation

2005 ◽  
pp. 73-88
Author(s):  
Rolly Intan ◽  
Masao Mukaidono
Keyword(s):  
Rough Approximation ◽  
Asymmetric Relation

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

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.

scholarly journals A Molecular Theory of Filler Reinforcement Based upon the Conception of Internal Deformation (A Rough Approximation of the Internal Deformation)

1963 ◽  
Vol 36 (4) ◽  
pp. 1081-1106 ◽  
Author(s):  
Yoshiyasu Sato ◽  
Junji Furukawa
Keyword(s):  
Mechanical Properties ◽  
Surface Effect ◽  
Molecular Theory ◽  
Theoretical Treatment ◽  
Suitable Model ◽  
Cavitation Effect ◽  
Rough Approximation ◽  
Internal Mechanism ◽  
Internal Deformation ◽  
Filler Reinforcement

Abstract A molecular theory is presented in this paper which gives a method of analysis for the mechanical properties of filler-reinforced elastomers, based upon the concept of the internal deformation and the statistical theory of rubberlike elasticity. By using a suitable model and a few new concepts a proper analysis for such a heterogeneous system is obtained. From the theory the internal mechanism of filler reinforcement is understood. It is made clear that reinforcement consists of three effects: the volume effect, the surface effect, and the cavitation effect. From the theory, formulae for the tension, swelling tension, Young's moduli, local stress distribution, strain birefreingence, condition for swelling equilibrium, and so on are derived. It has long been recognized that rubbery substances and plastic materials are reinforced by incorporation of suitable powdery substances (reinforcing fillers) which improve their mechanical properties such as elastic modulus, hardness, stiffness, resilience, solvent resistance, plastic viscosity, tensile strength, tear resistance, etc. Although numerous attempts have been made to clarify and systematize the internal mechanism of filler reinforcement, there is at present no distinct picture of the mechanism, much less a satisfactory theoretical treatment of the phenomena.

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.

The electronic spectra of mixed crystals

1963 ◽  
Vol 271 (1345) ◽  
pp. 207-217 ◽  
Keyword(s):  
Intermolecular Interactions ◽  
Electronic Spectra ◽  
Mixed Crystal ◽  
Electronic States ◽  
Dipole Approximation ◽  
Mixed Crystals ◽  
Excited Electronic States ◽  
Guest Molecules ◽  
Rough Approximation ◽  
Crystal Properties

The excited electronic states of dilute mixed crystals are discussed in terms of the theory of intermolecular interactions in dipole-dipole approximation. Resonance interactions of the Davydov type, which are of the first importance in pure crystals, are absent. However, interactions between host and guest molecules are generally of com parable importance to second-order interactions in pure crystals, and lead to similar changes in absolute absorption intensities and polarization ratios. There is a substantial departure from oriented-gas behaviour, which can be regarded as only a rough approximation to mixed crystal properties.

Sign in / Sign up

Export Citation Format

Share Document