A Machine Proof System of Point Geometry Based on Coq

Lei, Siran; Guan, Hao; Jiang, Jianguo; Zeng, Yu; Rao, Yongsheng

doi:10.3390/math11122757

Cited by 7 publications

(3 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different multi-criteria decision making techniques are used by researchers to rank chemical structures. For more details see [22][23][24][25][26][27].…”

Section: Multi-criteria Decision Makingmentioning

confidence: 99%

Investigating hexagonal closed packed crystal lattice through QSPR modeling via linear regression analysis and Topsis

Aslam,

Saeed,

Kanwal

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

This research work covers three highly dominating reverse degree-based topological descriptors evaluated for the three-dimensional hexagonal close-packed (HCP) crystal structure lattice. HCP crystal lattice has a highly symmetrical and elegant crystal structure, and we have observed that results obtained from symmetrical structures draw symmetry in the numerical formulation obtained from topological descriptors. For this purpose, we will investigate whether the HCP lattice formed by an odd pair of unit cells is the best or an even pair of unit cells forming the lattice and how they behave in a dominating sense when investigated through the conclusions obtained from QSPR modeling. The QSPR model has been proposed to check the efficiency of each specified topological descriptor for five highly commendable physio-chemical properties: melting or boiling point, density, molar heat capacity, and enthalpy. Further, we have discovered the ideology to obtain the best possible structure when investigated and established on a statistically and mathematically strong proving and to what extent we can extract from QSPR to implement MCDM techniques, here considering TOPSIS that provide the best HCP structure lattice rankings. The obtained results may be helpful for researchers to better understand the structure and studying different physical/chemical properties of HCP crystal lattice

show abstract

“…Different multi-criteria decision making techniques are used by researchers to rank chemical structures. For more details see [22][23][24][25][26][27].…”

Section: Multi-criteria Decision Makingmentioning

confidence: 99%

Investigating hexagonal closed packed crystal lattice through QSPR modeling via linear regression analysis and Topsis

Aslam,

Saeed,

Kanwal

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…In this section, we will recall some definitions and notations from graph theory. For terminology and definitions from graph theory, we refer the reader to [11][12][13][14]. Some known results related to depth and Stanley depth are also given in this section.…”

Section: Preliminariesmentioning

confidence: 99%

Depth and Stanley Depth of the Edge Ideals of r-Fold Bristled Graphs of Some Graphs

Wang,

Sharif,

Ishaq

et al. 2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…For results related to neighborhood sum-degree-based indices, refer to [17,[20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Expected values of sum-based topological indices of random cyclodecane chains

Tang,

Yousaf,

Javaid Ashraf

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

Cyclodecanes, belonging to the class of aliphatic cycloalkanes, comprise non-aromatic carbon-atom rings. Within the 10-membered ring, cyclodecanes exhibit various isomers, characterized by different spatial arrangements of carbon atoms. Serving as model compounds in organic studies, cyclodecanes offer insights into the properties and reactivity of cyclic hydrocarbons. The chemistry of cyclodecane serves as a valuable foundation for understanding the behavior of more complex hydrocarbons. In this paper, we explore the potential probabilities of random cyclodecane chains $\mathbb{D}_t^{\rho}$ of length $t\geq3$. We derive exact expressions for the expected values of the modified second Zagreb index, inverse index, and second NDe index. A theoretical comparative analysis of these descriptors is provided, accompanied by graphical and numerical representations of the obtained results.

show abstract

A Machine Proof System of Point Geometry Based on Coq

Cited by 7 publications

References 33 publications

Investigating hexagonal closed packed crystal lattice through QSPR modeling via linear regression analysis and Topsis

Investigating hexagonal closed packed crystal lattice through QSPR modeling via linear regression analysis and Topsis

Depth and Stanley Depth of the Edge Ideals of r-Fold Bristled Graphs of Some Graphs

Expected values of sum-based topological indices of random cyclodecane chains

Contact Info

Product

Resources

About