Related Experiment Video
Updated: Jan 24, 2026

Live Cell Imaging during Mechanical Stretch
Published on: August 19, 2015
Stretches across for chaos
1Department of Applied Mathematics, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan.
Abstract:
In 2001, Kennedy et al. [Amer. Math. Mon. 108, 411-423 (2001) and Trans. Amer. Math. Soc. 353, 2513-2530 (2001)] showed a chaos lemma and stated the pseudoconjecture "stretches across implies existence of an invariant set." In this paper, we give a suitable definition of stretches across in topological sense so that the conjecture has an affirmative answer. More precisely, we show that there must be an orbit through a sequence of stretches across. In particular, a closed loop of stretches across implies existence of a periodic orbit. We also give the geometric meaning of stretches across and its relation with the global implicit function theorem.
Related Concept Videos
IR Frequency Region: X–H Stretching
IR Frequency Region: Alkyne and Nitrile Stretching
Comparing the stretching vibrational frequency of C≡C triple bonds with that of double and single bonds, it is evident that C≡C triple bonds exhibit a higher stretching frequency than C=C double and C–C single bonds. Similarly, the C≡N triple bond...
IR Frequency Region: Alkene and Carbonyl Stretching
Stretching frequencies are affected by several factors, such as resonance, inductive effects, ring strain, dipole moment, and hydrogen bonding. Consequently, the stretching frequency of the carbonyl double bond...
Homologous Recombination
Transcription
Transcription is the process of synthesizing RNA from a DNA sequence by RNA polymerase. It is the first step in producing a protein from a gene sequence. Additionally, many other proteins and regulatory sequences are involved in the proper synthesis of messenger RNA (mRNA). Regulation of transcription is responsible for the differentiation of all the different types of cells and often for the proper cellular response to environmental signals.
Transcription Can Produce Different Kinds...
In-vitro Mutagenesis

