Decision on Function of One Simple Separable Relation for the Minimal Covering of P*K

2014 ◽  
Vol 496-500 ◽  
pp. 2303-2305
Author(s):  
Yu Zhen Liu ◽  
Xing Bao Liu ◽  
Xin Fen Zhang
Keyword(s):  
Structure Theory ◽  
Function Structure ◽  
Minimal Covering ◽  
Partial Logic ◽  
Sheffer Function

In the function structure theory of multi-logic, decision on Sheffer function is an important role. It contains structure and decision of full multi-logic and partial multi-logic. Its decision is closely related to decision of completeness of function which can be done by deciding the minimal covering of full multi-logic and partial-logic. By theory of completeness of partial multi-logic, we prove that function of one simple separable ralation is not minimal covering of P*K under the condition of m=2, σ=e .

The Determination on Minimal Covering of Regular Separable Function Sets in Partial Four-Valued Logic

2010 ◽  
Vol 143-144 ◽  
pp. 1285-1289
Author(s):  
Xiao Qiang Zhou
Keyword(s):  
Structure Theory ◽  
Similar Relationship ◽  
Logic Function ◽  
Minimal Covering ◽  
Methods Of Determination ◽  
Separable Function ◽  
The Many ◽  
Sheffer Function

In the structure theory of many-valued logic function, the decision and constitution of the Sheffer function is a very important problem, which is reduced to the decision of the minimal covering of precomplete sets in the many-valued logic function sets. According to the completeness theory in partial k-valued logic and the similar relationship theory among precomplete sets, in this paper, the methods of determination on the minimal covering of regular separable function sets are found out, and the minimal covering of regular separable function sets in partial four-valued logic are decided.

Combining First-Principles and Data Modeling for the Accurate Prediction of the Refractive Index of Organic Polymers

2017 ◽  
Author(s):  
Mohammad Atif Faiz Afzal ◽  
Chong Cheng ◽  
Johannes Hachmann
Keyword(s):  
First Principles ◽  
Data Modeling ◽  
Accurate Prediction ◽  
Index Of Refraction ◽  
Structure Theory ◽  
Organic Polymers ◽  
Number Density ◽  
Lorenz Equation ◽  
In Silico Studies ◽  
Wide Range

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3–1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that an guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and highly economical path to determining the RI values for a wide range of organic polymers.

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