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Chain Reactions01:29

Chain Reactions

Chain reactions involve highly reactive transient species, such as atoms or free radicals, as intermediates. These intermediates facilitate rapid reactions over an extended period. The process includes a series of steps: a reactive intermediate is consumed, reactants are converted to products, and the intermediate is regenerated. This cycle enables continuous repetition, amplifying the production of products with a small amount of intermediate. Chain reactions often utilize free radicals as...
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Radical Chain-Growth Polymerization: Chain Branching

The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...
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Anionic Chain-Growth Polymerization: Mechanism

The mechanism for anionic chain-growth polymerization involves initiation, propagation, and termination steps. In the initiation step, a nucleophilic anion, such as butyl lithium, initiates the polymerization process by attacking the π bond of the vinylic monomer. As a result, a carbanion, stabilized by the electron‐withdrawing group, is generated. The resulting carbanion acts as a Michael donor in the propagation step and attacks the second vinylic monomer, which acts as a Michael acceptor.
Line Loss01:10

Line Loss

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Related Experiment Video

Updated: May 29, 2026

Ubiquitin Chain Analysis by Parallel Reaction Monitoring
08:33

Ubiquitin Chain Analysis by Parallel Reaction Monitoring

Published on: June 17, 2020

On the chain code of a line.

L D Wu1

  • 1Division of Applied Mathematics, Brown University, Providence, RI 02912; Department of Computer Science, Fudan University, Shanghai, China.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study presents an algorithm to verify Freeman

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Area of Science:

  • Computer Vision
  • Image Analysis
  • Digital Geometry

Background:

  • Chain codes are used to represent digital lines.
  • Freeman's 1970 criteria define properties of line chain codes.
  • Rosenfeld's chord property offers an alternative line characterization.

Purpose of the Study:

  • To present an algorithmic interpretation of Freeman's line chain code criteria.
  • To prove this algorithm's efficacy in identifying line chain codes.
  • To demonstrate the equivalence between this algorithm and Rosenfeld's chord property.

Main Methods:

  • Algorithm development based on Freeman's criteria.
  • Formal proof of algorithm correctness for line recognition.
  • Mathematical proof establishing equivalence with Rosenfeld's chord property.

Main Results:

  • An algorithm is presented that precisely identifies chain codes representing lines.
  • The algorithm is proven to be a valid line recognition method.
  • Equivalence is demonstrated between the proposed algorithm and the chord property.

Conclusions:

  • The presented algorithm effectively characterizes digital lines using chain codes.
  • This work bridges Freeman's criteria and Rosenfeld's property through algorithmic proof.
  • Provides a robust method for line detection in digital images.