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相关概念视频

Radical Chain-Growth Polymerization: Chain Branching01:17

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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Radical Chain-Growth Polymerization: Mechanism01:09

Radical Chain-Growth Polymerization: Mechanism

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The radical chain-growth polymerization mechanism consists of three steps: initiation, propagation, and termination of polymerization. The polymerization initiates when a free radical generated from the radical initiator adds to the unsaturated bond in the monomer. The unpaired electron of the free radical and one π electron in the unsaturated bond creates a σ bond between the free radical and the monomer. As a result, the other π electron in the unsaturated bond converts this...
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Radical Chain-Growth Polymerization: Overview01:10

Radical Chain-Growth Polymerization: Overview

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Chain-growth or addition polymerization is successive addition reactions of monomers with a polymer chain. In radical chain-growth polymerization, the reaction proceeds via a free-radical intermediate. The free radical is formed from radical initiators, which spontaneously generate free radicals by homolytic fission. Organic peroxides (such as dibenzoyl peroxide, as shown in Figure 1) or azo compounds are popular radical initiators. A low concentration ratio of radical initiator to monomer is...
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Hybridization of Atomic Orbitals II03:35

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sp3d and sp3d 2 Hybridization
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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Ziegler–Natta Chain-Growth Polymerization: Overview01:17

Ziegler–Natta Chain-Growth Polymerization: Overview

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Ziegler–Natta polymerization is another form of addition or chain‐growth polymerization used for synthesizing linear polymers over branched polymers. The catalyst used for polymerization is the Ziegler–Natta catalyst, named after Karl Ziegler and Giulio Natta, who developed it in 1953. This catalyst is an organometallic complex of titanium tetrachloride and triethyl aluminum, with the active form of the catalyst being an alkyl titanium compound. Using the Ziegler–Natta...
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相关实验视频

Updated: May 11, 2025

Author Spotlight: An Optimized Automated Method for Investigating Retinoic Acid Receptors in Neuronal Mitochondria
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使用斯特拉森算法的矩阵链乘法混合优化技术.

Srinivasarao Thota1, Thulasi Bikku2, Rakshitha T3

  • 1Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, 522503, India.

F1000Research
|April 17, 2025
PubMed
概括
此摘要是机器生成的。

本研究介绍了一种混合矩阵链乘法 (MCM) 方法,将动态编程与斯特拉森算法相结合. 优化的MCM显著加快了大型矩阵计算的速度,减少了执行时间和内存使用量.

关键词:
计算的复杂性.动态编程 动态编程混合优化 混合优化矩阵链乘法 矩阵链乘法斯特拉森的算法

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科学领域:

  • 计算数学 计算数学 计算数学
  • 计算机科学 计算机科学
  • 科学计算科学计算

背景情况:

  • 矩阵链乘法 (MCM) 在科学计算,图形和机器学习中至关重要.
  • 传统的MCM使用了带有Memoization的动态编程 (DP),但对于大矩阵而言,它存在O(n^3) 复杂性.
  • 对于大规模的计算,标准矩阵乘法是低效的.

研究的目的:

  • 为矩阵链乘法开发一种混合优化技术.
  • 通过将Strassen的算法集成到MCM中来加速矩阵乘法.
  • 为了减少计算复杂性,并提高大矩阵的效率.

主要方法:

  • 一种两阶段的方法: (i) 优化矩阵链顺序,使用上下DP和记忆,以及 (ii) 混合乘法策略.
  • 斯特拉森算法的选择性应用 (O(n^2.81)) 对n ≥128.8的矩阵.
  • 通过计算实验与传统的MCM和独立的Strassen算法进行比较.

主要成果:

  • 与传统方法相比,混合MCM方法实现了显著的加快速度 (4x-8x).
  • 对于大规模应用程序来说,已证明减少了内存消耗.
  • 保持了数值准确性,同时提高了性能.

结论:

  • 拟议的混合MCM方法有效地减少了执行时间和内存使用量.
  • 斯特拉森算法的选择性集成提高了大型矩阵的MCM效率.
  • 在矩阵运算中为并行计算和GPU加速开辟了道路.