Basic Sets

2021 ◽  
pp. 219-230
Author(s):  
Satya Sundar Sethy
Keyword(s):  
Basic Sets

PAL – Propositional Algorithmic Logic

1981 ◽  
Vol 4 (3) ◽  
pp. 675-760
Author(s):  
Grażyna Mirkowska
Keyword(s):  
Data Structures ◽  
Completeness Theorem ◽  
Natural Numbers ◽  
First Order ◽  
Algorithmic Logic ◽  
Axiomatic Systems ◽  
Nondeterministic Program ◽  
Basic Sets

The aim of propositional algorithmic logic is to investigate the properties of program connectives. Complete axiomatic systems for deterministic as well as for nondeterministic interpretations of program variables are presented. They constitute basic sets of tools useful in the practice of proving the properties of program schemes. Propositional theories of data structures, e.g. the arithmetic of natural numbers and stacks, are constructed. This shows that in many aspects PAL is close to first-order algorithmic logic. Tautologies of PAL become tautologies of algorithmic logic after replacing program variables by programs and propositional variables by formulas. Another corollary to the completeness theorem asserts that it is possible to eliminate nondeterministic program variables and replace them by schemes with deterministic atoms.

The Absorption Energy and Equilibrium Structure Analysis of CH4 on Coal Molecules

2013 ◽  
Vol 807-809 ◽  
pp. 2366-2370
Author(s):  
Hua Ping Yang ◽  
Ming Li ◽  
Zheng Xin Yan ◽  
Dong Zhi Yan
Keyword(s):  
Structure Analysis ◽  
Dft Method ◽  
Equilibrium Structure ◽  
Atomic Charges ◽  
Absorption Model ◽  
Absorption Energy ◽  
Molecule Model ◽  
Basic Sets

The coal molecule model and the absorption model of coal and methane were established according to Van der Walls force. The coal molecule model and the absorption model of coal and methane were optimized and obtained absorption energy and equilibrium structure with the DFT method with 6-311G++ basic sets. The effects of coal molecule on the absorption position, absorption energy and absorption distance of CH4 were presented by analyzing the Mulliken atomic charges of coal molecules.

Analysis of Adsorbed Methane Gas Structure and Mullikan Charges

2014 ◽  
Vol 962-965 ◽  
pp. 1118-1122
Author(s):  
Hua Ping Yang ◽  
Ming Li
Keyword(s):  
Adsorption Process ◽  
Adsorption Equilibrium ◽  
Dft Method ◽  
Model Structure ◽  
Dispersion Forces ◽  
Methane Gas ◽  
Adsorbed Methane ◽  
Molecule Model ◽  
Equilibrium Geometries ◽  
Basic Sets

The methane molecule model, the coal molecule model and the absorption model of coal and methane have been thoroughly investigated using the DFT method,Van der Walls force radius as boundary conditions as well. The investigations focuses on optimizing the three types of model structure. Meanwhile, adsorption equilibrium geometries with 6-311G++ basic sets have been established. Through the model analysis of the changes in the structure and Millikan charge from free state to the adsorption states, the results indicate that the adsorption process of methane gas on the coal in the Van der Walls force mainly dispersion forces and induction force, methane molecules are polarized in the adsorption process, the electric dipole moment.

scholarly journals On 2-Diffeomorphisms with One-Dimensional Basic Sets and a Finite Number of Moduli

2016 ◽  
Vol 16 (4) ◽  
pp. 727-749
Author(s):  
V. Z. Grines ◽  
Z. Grines ◽  
S. Van Strien
Keyword(s):  
Finite Number ◽  
One Dimensional ◽  
Basic Sets

scholarly journals Basic Sets of Special Monogenic Polynomials in Fréchet Modules

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Gamal Farghaly Hassan ◽  
Lassaad Aloui ◽  
Allal Bakali
Keyword(s):  
Functional Analysis ◽  
Clifford Analysis ◽  
General Type ◽  
Convergence Properties ◽  
Special Monogenic Polynomials ◽  
Basic Sets

This article is concerned with the study of the theory of basic sets in Fréchet modules in Clifford analysis. The main aim of this account, which is based on functional analysis consideration, is to formulate criteria of general type for the effectiveness (convergence properties) of basic sets either in the space itself or in a subspace of finer topology. By attributing particular forms for the Fréchet module of different classes of functions, conditions are derived from the general criteria for the convergence properties in open and closed balls. Our results improve and generalize some known results in complex and Clifford setting concerning the effectiveness of basic sets.

scholarly journals Smale spaces via inverse limits

2013 ◽  
Vol 34 (6) ◽  
pp. 2066-2092 ◽  
Author(s):  
SUSANA WIELER
Keyword(s):  
Dynamical System ◽  
Inverse Limits ◽  
Canonical Coordinates ◽  
Chaotic Dynamical System ◽  
Smale Space ◽  
Smale Spaces ◽  
Special Case ◽  
Basic Sets

AbstractA Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale’s Axiom $A$ systems are a key class of examples. We consider the special case of irreducible Smale spaces with zero-dimensional contracting directions, and characterize these as stationary inverse limits satisfying certain conditions.

Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets

2020 ◽  
Vol 84 (5) ◽  
pp. 862-909
Author(s):  
V. Z. Grines ◽  
E. D. Kurenkov
Keyword(s):  
One Dimensional ◽  
Basic Sets
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