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The comparison theorem, which is an important theory of BSDE, was established by Peng [7] and then generalized by EL Karoui et al. [4].
Chen [2], Briand et al. [1] and Coquet et al. [3] worked on this subject and established some converse comparison theorems.
But unfortunately, when we apply BSDEs theory to option pricing (see El Karoui et al.[4]) or recursive utility (see Chen and Epstein[8]), we find that the generator g in these cases often does not satisfy .
(Comparison theorem EL Karoui [4])gy, .
EL Karoui, S.

Roth, W.H. et al[2] compared the one-dimensional spring model and the elastic-plastic soil model, and found the limitation of one-dimensional spring model.
Scott M. et al[3] put Loma Prieta earthquake waves and Northridge earthquake waves with different strengths on two typical high-pile wharfs and observed that the batter pile bears greater horizontal force than vertical pile, and the displacement of the wharf without batter piles increases 30%.
Compare to El-Centro and T2-II-1, the maximum displacement and accelerations along the model are the largest under T1-II-1 seismic wave.
And when the peak acceleration is 400Gal, the maximum displacement and acceleration of 7m wharf under T1-II-1 increase 38% and 27% compare to El-Centro wave.
Table 3 The maximum flexural moments of piles of 7m wharf [kN·m] Different pile 70Gal 400Gal El-Centro T1-II-1 T2-II-1 El-Centro T1-II-1 T2-II-1 Pile1 108.60 127.40 113.46 471.30 662.42 638.29 Pile2 169.40 219.02 204.35 800.40 1043.68 1032.00 Pile3 181.00 244.20 228.31 855.90 1060.36 1045.83 In Table 3, among the three seismic waves, the wharf suffers the largest flexural moments under far-fault seismic wave(T1-II-1), the structural flexural moments under T1-II-1are larger than that under El-Centro wave, and the increase rate could even reach 40%.

A second model was reported by various groups [7-9] that was based on the SSF expansion being driven by long-range stresses within the diode structure, however, the results of Ha et al. clearly disproved this notion [10].
In their rebuttal of this second driving force model, Ha et al. [10] went on stating that the driving force could be dependent upon a presumed thermodynamic favorability of the 3C-SiC polytype of the SSFs in comparison to the native 4H-SiC lattice, thereby favoring SSF formation.
However, recently, Caldwell et al. [11-13] and Miyanagi et al. [14] demonstrated that SSFs contract when the affected diodes or epilayers are annealed at relatively low temperatures (400-700 0C), this clearly illustrating that the 3C-SiC SSFs are not thermodynamically favorable.
This was verified by subsequent IV measurements, as well as by comparing EL images collected before and after the various IV traces.
EL images of D30R collected following saturation of the fV drift at 300C and 2470C are presented in c) and d), respectively.

We inputting Gaussian white noise measured vibration period, dynamic response with EL and Taft wave show the shock absorption effect of the soil.
We input the Gaussian white noise which measured vibration period of steel framework and input the Taft and EL waves which measured the dynamic response of steel frames.
We collected Gaussian white noise signal and used DASP software to do frequency analysis, and we collected EL and Taft waves signal do time-domain analysis.
The model structural stiffness threshold was value 2.558 × 103kN/m as the relative stiffness of the foundation soil, according to the test the structure get the additional period is ΔT and the upper structure stiffness K relationship is: ΔT = 0.019K +0.112 (2) The relationship of peak acceleration reduction and model superstructure stiffness K is: γ= - 0.028K2 +0.142 K +0.637 (3) Table 4 Peak acceleration of the top storey Condition number the top storey acceleration [m/s2] Acceleration reduction EL wave Taft wave In soil a0 On rigid foundationa In soil a0 On rigid foundation a EL wave a0/a Taft wave a0/a Mean value γ 1 2.091 3.036 1.389 1.604 0.689 0.866 0.778 2 0.819 1.143 1.482 1.965 0.717 0.754 0.736 3 1.321 1.830 1.749 1.578 0.721 1.108 0.915 4 3.545 5.916 2.824
[7] Shang Shouping, He Zhiwen,et al.

El-Adly et al. (2012) studied the use of jojoba and sulphurized jojoba as base stocks for lithium greases.
Activated carbon was prepared based on the method described by Gohoho et al. (2021) [13].
Syahir et al., “A review on bio-based lubricants and their applications,” J.
El-Adly, A.
El-Shazly, “Waste to Product: Feasibility of Egyptian Peanut Shell Transformation into a Useful Product,” Key Eng.

The density of EL at 25oC is 1.008 g/cm3.
Cloud point of EL is -5oC and flow point is -13oC [16].
Song et al. [26] used mesoporous carbon spheres containing arylsulphonic groups as esterification catalysts, reaching EL yield close to 100% (m/m).
Quantitative analysis of EL by gas chromatography showed that the purity of EL separated using simple distillation is 96.87%.
For 90 minutes the obtained EL yield was 67% (m/m).

Optimization Strategy for Molecular Dynamics Simulations of Nanometric Cutting of Aluminium Alloy using Molecular Modelling Victor Emeka Ejiofora and Khaled Abou-El-Hosseinb Ultra-High Precision Manufacturing Laboratory, Department of Mechatronics Engineering, Nelson Mandela University, Port Elizabeth, South Africa as217010350@mandela.ac.za, bKhaled.Abou-El-Hossein@mandela.ac.za Keywords: Molecular Modelling, Molecular Dynamics Simulations, Optimization Strategy, Rapidly Solidified Aluminium (RSA 431) Alloy, Nanometric Cutting.
The ratio between mass density and atomic mass of Al and the Al-alloying elements (R) accounts for the atomic concentration.
Table 3 presents computed Ratios (R) between mass density and atomic mass of Al and the Al-alloying elements of the RSA 431.
Abou-El-Hossein, "Aspects of ultra-high-precision diamond machining of RSA 443 optical aluminium," in Optical Manufacturing and Testing XI, 2015, pp. 44-49
Greer, "Size effects in Al nanopillars: Single crystalline vs. bicrystalline," Acta Materialia, vol. 59, pp. 4416-4424, 2011

El-Hofy1,a and A.
W. et al., Science, 291 (2001), 1947 [2] Wang, Z.
et al., Adv.
El-Hofy and A.
El-Hofy and A.

Park, et al.
Yu, et al.
Forrest, et al.
Yu, et al.
Shi, et al.

For the EL technique, either a patterned aluminum (Al) film or a processed diode was employed [6].
The glide of the Si-core PDs are shown in Figs. 1b, c and d after 1, 2 and 10 minutes of biasing, respectively, at 10 A/cm2 (the dark grid lines correspond to the patterned thin Al film for electrical contact to the epitaxial layer).
One can see in Fig. 3 that both the EL and the PL technique gave similar spectral responses.
offcut EL a) b) c) d) e) 100µµµµm C-core 50µµµµm Si-core C-core 0 min 1 min 2 min 10 min 950±12.5nm half- loops Fig. 1 a) EL image of an array of half-loop defects about 15 µm below the surface obtained at 10 A/cm 2 and with a longpass filter at 590 nm.
The EL spectra are the same over the current range from 0.1 - 10 A/cm-2 and also agree with the PL spectra.