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Fischer Projections02:18

Fischer Projections

Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

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 others.

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Related Experiment Video

Updated: Jun 12, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Three-dimensional optical Fredkin gate arrays applied to residue arithmetic.

M M Mirsalehi, J Shamir, H J Caulfield

    Applied Optics
    |June 18, 2010
    PubMed
    Summary

    A new 3-D architecture for optical networks enhances residue arithmetic operations. This 3-D model offers superior performance for processing large numbers compared to existing 2-D designs.

    Area of Science:

    • Computer Science
    • Optical Engineering
    • Arithmetic Circuits

    Background:

    • Traditional optical interconnection networks often utilize 2-D architectures.
    • Implementing complex arithmetic operations, especially with large numbers, presents computational challenges.
    • Residue arithmetic offers a method for simplifying large number computations.

    Purpose of the Study:

    • To analyze a recently proposed 3-D architecture for optical interconnection networks.
    • To apply this 3-D architecture to the implementation of residue arithmetic operations.
    • To evaluate the performance of the 3-D architecture against 2-D models for large number processing.

    Main Methods:

    • Theoretical analysis of a novel 3-D optical interconnection network architecture.

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    Last Updated: Jun 12, 2026

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
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  • Implementation of residue arithmetic operations utilizing the proposed 3-D architecture.
  • Comparative performance evaluation against established 2-D optical network models.
  • Main Results:

    • The 3-D architecture facilitates efficient residue arithmetic operations.
    • Demonstrated superiority of the 3-D architecture over 2-D models for handling large numbers.
    • The proposed architecture shows significant potential for high-performance computing.

    Conclusions:

    • The analyzed 3-D optical network architecture is effective for residue arithmetic.
    • This 3-D approach provides a significant advantage for large number processing in optical computing.
    • The findings suggest a new direction for designing advanced optical interconnection networks.