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Radical Chain-Growth Polymerization: Chain Branching

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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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Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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Olefin Metathesis Polymerization: Ring-Opening Metathesis Polymerization (ROMP)01:16

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Ring-opening metathesis polymerization or ROMP involves strained cycloalkenes as starting materials. The mechanism of ROMP proceeds by reacting cycloalkene with Grubbs catalyst to give metallacyclobutane intermediate which undergoes a ring-opening reaction to form new carbene. The new carbene reacts with another molecule of cycloalkene. Repetition of these steps leads to the formation of an unsaturated open-chain polymer product. All these steps are reversible, however, relieving the ring...
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Recursive Prefix-Free Parsing for Building Big BWTs.

Marco Oliva, Travis Gagie, Christina Boucher

    Biorxiv : the Preprint Server for Biology
    |January 30, 2023
    PubMed
    Summary

    Recursive prefix-free parsing significantly reduces memory usage for building run-length encoded Burrows-Wheeler Transforms (BWT). This novel approach optimizes parse size for large, repetitive inputs, improving scalability.

    Area of Science:

    • Computer Science
    • Algorithms
    • Data Structures

    Background:

    • Prefix-free parsing is crucial for BWT construction, suffix arrays, and compressed suffix trees.
    • Existing methods face challenges with parse size scalability for large, repetitive datasets.

    Conclusions:

    • Recursive prefix-free parsing offers a scalable solution for BWT construction.
    • The implemented algorithm provides substantial memory efficiency for large datasets.
    • Open-source implementation facilitates further research and application.

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