Raport de cercetare - Lorentz JÄNTSCHI

H(·,·) Σ(·) Σ(·) 2 ΣA(·) ΣA(·) 2 Σ(1/(·)) Σ(1/(·)) 2 ΣA(1/(·)) 2 ΣA(1/(·)) 2
H(D,CJD) 600 6954 60.5 242 7.971 1.315 3.308 0.783
H(D,CJΔ) 347 2491 27.5 63 19.834 10.582 9.493 7.652
H(D,CFD) 622 7616 60.5 242 7.717 1.278 3.308 0.783
H(D,CFΔ) 349 2571 27.5 63 19.813 10.580 9.493 7.652
H(D,SzD) 756 13048 60.5 242 7.389 1.250 3.308 0.783
H(D,SzΔ) 769 13500 60.5 242 7.333 1.238 3.308 0.783
H(Δ,CJD) 1292 32244 258.5 4718 3.574 0.255 0.896 0.075
H(Δ,CJΔ) 653 6885 104.5 702 7.676 1.243 2.252 0.412
H(Δ,CFD) 1338 35082 258.5 4718 3.437 0.244 0.896 0.075
H(Δ,CFΔ) 655 6965 104.5 702 7.655 1.241 2.252 0.412
H(Δ,SzD) 1564 51568 258.5 4718 3.189 0.224 0.896 0.075
H(Δ,SzΔ) 1592 53560 258.5 4718 3.166 0.222 0.896 0.075
÷ Produsul Schultz a două matrici S(·,A,·):
o Definiţie: S(X,A,Y)i,j=X(A+Y);
o Aplicaţii:
Schultz CJD CJΔ CFD CFΔ SzD SzΔ
A S(A,A,CJD) S(A,A,CJΔ) S(A,A,CFD) S(A,A,CFΔ) S(A,A,SzD) S(A,A,SzΔ)
D S(D,A,CJD) S(D,A,CJΔ) S(D,A,CFD) S(D,A,CFΔ) S(D,A,SzD) S(D,A,SzΔ)
Δ S(Δ,A,CJD) S(Δ,A,CJΔ) S(Δ,A,CFD) S(Δ,A,CFΔ) S(Δ,A,SzD) S(Δ,A,SzΔ)
o Indici pe matricile Schultz:
S(·,A,·) Σ(·) Σ(·) 2 ΣA(·) ΣA(·) 2 Σ(1/(·)) Σ(1/(·)) 2 ΣA(1/(·)) 2 ΣA(1/(·)) 2
S(A,A,CJD) 550.5 4833.5 61 248 8.76175 1.31487 3.47024 0.72197
S(A,A,CJΔ) 341.5 1987.5 35 59 16.89960 6.16609 8.11905 4.48810
S(A,A,CFD) 565.5 5205.5 64 292 8.46774 1.26196 3.41607 0.70670
S(A,A,CFΔ) 342.5 2003.5 35 59 16.81627 6.14526 8.11905 4.48810
S(A,A,SzD) 628.5 6339.5 61 248 7.90838 1.13978 3.47024 0.72197
S(A,A,SzΔ) 638.5 7171.5 63 342 7.49169 1.45677 3.43849 1.08596
S(D,A,CJD) 6358.5 728779 1215 137976 0.57811 0.00663 0.13649 0.00177
S(D,A,CJΔ) 3573.5 217760 712 45023 1.01352 0.01929 0.22652 0.00467
S(D,A,CFD) 6576 764461 1278.5 147548 0.55208 0.00590 0.12597 0.00145
S(D,A,CFΔ) 3591 219152 718.5 45529 1.00766 0.01898 0.22338 0.00450
S(D,A,SzD) 7440 1002756 1515.5 219149 0.49894 0.00496 0.11222 0.00123
S(D,A,SzΔ) 7786 1016184 1548.5 208403 0.47479 0.00423 0.10478 0.00102
S(Δ,A,CJD) 13560.5 3120452 2446 527736 0.27149 0.00139 0.06576 0.00039
S(Δ,A,CJΔ) 7227.5 887001 1330 150684 0.50828 0.00483 0.12147 0.00126
S(Δ,A,CFD) 14022 3290896 2598.5 573094 0.25910 0.00124 0.06093 0.00032
S(Δ,A,CFΔ) 7255 890817 1339.5 151878 0.50613 0.00476 0.12055 0.00123
S(Δ,A,SzD) 15724 4220049 2992.5 802176 0.23648 0.00106 0.05506 0.00028
S(Δ,A,SzΔ) 15684 4367127 2991.5 792573 0.23389 0.00108 0.05216 0.00025
Polinoame
Polinoamele au aplicaţii importante în topologia moleculară. Următoarele polinoame sunt definite:
÷ Polinomul caracteristic (ChP) asociat unui graf G [Bolboacă SD, Jäntschi L. 2007. How Good
the Characteristic Polynomial Can Be for Correlations? Int J Mol Sci 8(4):335-345] se obţine pe
baza matricii de adiacenţă A=A(G) astfel: ChP(G,X)=det[XI-A(G)]
÷ Polinoamele de numărare (CDi, CMx, CcM, CSz, CCf) se definesc astfel [Jäntschi L. 2007.
Characteristic and Counting Polynomials of Nonane Isomers. Cluj: AcademicDirect, p. 101]:
C(G,M,X) = Σk≥0|{Mi,j , |Mi,j| = k}|X k , unde M=D, Mx, cM, Sz, Cf.
În tabelul 10 este redată matricea caracteristică, iar în Tabelele 11-15 sunt redate matricile de
numărare CDi, CMx, CcM, CSz, CCf asociate grafului molecular din Tabelul 9.
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