# KKM Theory and Applications in Nonlinear Analysis by George Xian-Zhi Yuan

By George Xian-Zhi Yuan

This reference offers a lucid advent to the foundations and purposes of Knaster-Kuratowski-Mazurkiewicz (KKM) concept and explores comparable themes in nonlinear set-valued research.

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**Example text**

10) H = Ho - “Hu3(2n3,2). 1 1) 4 = 40 - A denotes the spin-orbit interaction constant, A, is its rotational dependence, B, D, Hare the usual rotational and centrifugal distortion constants, p and q are the A doubling constants, y is the spin-rotation interaction constant, and the z’s represent the changes in the related constants from their ground state values. The quantum number K is the absolute value of the sum of A and I denoting, respectively, the orbital and the vibrational angular momenta along the molecular axis.

10) where r12 and r23 are instantaneous values of the bond lengths NN and NO and ∆α is the instantaneous value of the bond angle (NN, NO). rNN and rNO are equilibrium lengths of the NN and NO bonds. Line mixing. This subject has been considered extensively in previous pages between XLIX and LIV. 2 on page LIV, a brief mention has been made about a simple model in the case of isolated Q branch profiles for Strong-Collision-type Modelling (SCM) of line coupling coefficients [95Har]. It gave satisfactory results for N2O.

Dυ1 , υ2 , l 2 , υ3 , J | Ᏼ eff | υ1 – 1, υ2 – 2, l 2 ± 2, υ3 + 1, J F = 3 40000 0 FL(14) kυ0000 1 (υ2 ϯ l 2) (υ2 ϯ l 2 – 2) (υ3 + 1) [ J (J + 1) – l 2 (l 2 ± 1)] · [ J (J + 1) – (l 2 ± 1) (l 2 ± 2)]. 5) Introduction LVII Third-order anharmonic interaction matrix element. Dυ1 , υ2 , l 2 , υ3 , J | Ᏼ eff | υ1 , υ2 – 4, l 2 , υ3 + 1, J F = 4 υ2 – l 2) (υ2 00 + l 2 ) (υ2 –3 l 200 – 2) (υ2 + 0 l2 – 0 2) (20 υ3 + 1) . 6) Fourth-order anharmonic interaction matrix elements. 8) Dυ1 , υ2 , l 2 , υ3 , J | Ᏼ eff | υ1 – 3, υ2 + 2, l 2 , υ3 + 1, J F = 4l520 0 00 7 υ1 – 2) (υ1 00 – 1) υ1 (υ2 –3 Fe(13) k(00 2 + 2) (υ2 + l 2 + 2) (υ3 + 1).