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Related Concept Videos

Asymptotes in Rational Functions01:30

Asymptotes in Rational Functions

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A rational function is defined as the quotient of two polynomials:  where Q(x)≠0, These functions often exhibit asymptotes, which are the lines that the graph approaches but never touches. These asymptotes are classified based on how the function behaves near specific values of the input.Vertical asymptotes occur where the denominator is zero, and the numerator is not, causing the function to be undefined. These are found by solving Q(x)=0. For example:  has a vertical...
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Integration of Rational Functions Using Partial Fractions01:29

Integration of Rational Functions Using Partial Fractions

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Rational functions are expressions written as the ratio of two polynomials, and their integrals are evaluated by simplifying the integrand into manageable parts. These functions are classified as proper or improper based on the degrees of the numerator and denominator.A rational function is proper when the degree of the numerator is less than the degree of the denominator. In this case, partial fraction decomposition is used to rewrite the function as a sum of simpler rational terms. The...
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There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
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Many proteins form complexes to carry out their functions, making protein-protein interactions (PPIs) essential for an organism's survival. Most PPIs are stabilized by numerous weak noncovalent chemical forces. The physical shape of the interfaces determines the way two proteins interact. Many globular proteins have closely-matching shapes on their surfaces, which form a large number of weak bonds. Additionally, many PPIs occur between two helices or between a surface cleft and a...
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Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...
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Rational Expressions01:28

Rational Expressions

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Rational expressions are algebraic fractions in which both the numerator and the denominator are polynomials. These expressions follow the arithmetic rules of numerical fractions but require extra care due to the presence of variables. A fundamental part of working with rational expressions is identifying values that make the expression undefined, typically those that result in division by zero or undefined radicals.Determining the DomainThe domain of a rational expression includes all real...
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Rational Design of Semiconductor Nanostructures for Functional Subcellular Interfaces.

Ramya Parameswaran1,2, Bozhi Tian3,4,5

  • 1The Graduate Program in Biophysical Sciences , The University of Chicago , Chicago , Illinois 60637 , United States.

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|April 19, 2018
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Semiconducting nanostructures offer novel ways to interface with cells, enabling sensing and modulation of biological behaviors. This research explores their design for biointerfaces, intracellular sensing, and controlling cellular functions for biomedical applications.

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Area of Science:

  • Biophysics
  • Materials Science
  • Cell Biology

Background:

  • Cells process physical and environmental cues, responding to biochemical, mechanical, and electrical signals.
  • Aberrant cellular signal processing is linked to various diseases.
  • New materials are needed to sense and modulate these cellular pathways.

Purpose of the Study:

  • To review rational design approaches for semiconducting nanowires as biointerfaces.
  • To highlight discoveries in subcellular biointerfaces using these materials.
  • To discuss intracellular sensing and modulation of cellular behaviors.

Main Methods:

  • Rational design of semiconducting nanostructures (nanowires) with controlled micro- and nanoscale features.
  • Utilizing nanocasting and mesoscale chemical lithography for material synthesis.
  • Investigating material-cell interactions at both intra- and extracellular levels.

Main Results:

  • Semiconducting nanostructures provide tunable electrical, optical, and mechanical properties for biointerfacing.
  • Achieved robust biointerfaces at the subcellular level.
  • Demonstrated intracellular electrical and mechanical sensing capabilities.
  • Showcased modulation of cellular behaviors via material topography and physical stimuli.

Conclusions:

  • Semiconducting nanostructures are promising for fundamental biophysical research and clinical applications.
  • Future work will focus on designing specific cell-interacting materials and understanding cellular communication.
  • Potential applications include neurological disease treatments and hybrid information processing systems.