Mathematical Problems in Engineering / 2015 / Article / Tab 2

Research Article

Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

Table 2

Comparison of ECT and FCT.

ECTFCT

Fundamental theories ① Implicit function theorem
② Morse lemma     
③ Thorn splitting lemma 
Research contentThe non-Morse critical point (or singular) of the potential function
Potential functionElementary function (polynomial functions) Functional
State variables
Non-Morse critical points
Control variables
Catastrophic conditions

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.