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Transformations of Functions I01:29

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A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
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Transformations of Functions II01:29

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Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c,...
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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
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Area of Science:

  • Biomedical Engineering
  • Materials Science
  • Oncology

Background:

  • Fluorescence and photoacoustic imaging offer distinct advantages in cancer diagnosis.
  • Combining these imaging modalities often involves trade-offs due to mechanism interference.

Purpose of the Study:

  • To develop a smart organic nanoparticle capable of switching between photoacoustic and fluorescence imaging pathways.
  • To investigate the potential of this nanoparticle for enhanced cancer diagnosis and surgical guidance.

Main Methods:

  • Rational molecular design of a dithienylethene (DTE) core with 2-(1-(4-(1,2,2-triphenylvinyl)phenyl)ethylidene)malononitrile (TPECM) units (DTE-TPECM).
  • Photo-switching the nanoparticle's energy deactivation pathway upon external light trigger.
  • Evaluation of nanoparticle performance in vitro and in vivo for photoacoustic and fluorescence imaging.

Main Results:

  • The DTE-TPECM nanoparticle demonstrated switchable photoacoustic and fluorescence imaging capabilities.
  • The molecule transitions between ring-closed (photoacoustic) and ring-opened (fluorescence/photodynamic) states.
  • In vivo studies showed improved outcomes in cancer surgery using the nanoparticle for preoperative imaging and intraoperative visualization/therapy.

Conclusions:

  • The developed smart nanoparticle overcomes the limitations of combined imaging modalities.
  • This agent facilitates precise tumor removal through multi-modal imaging and therapy.
  • The findings highlight the potential of rational molecular design for advanced cancer diagnostic and therapeutic tools.