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NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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CRISPR/Cas9 Genome Editing01:28

CRISPR/Cas9 Genome Editing

The CRISPR-Cas system serves as a bacterial defense mechanism against invading genetic elements such as viruses and plasmids, forming the foundation for its adaptation as a powerful genome-editing tool. Originally discovered in prokaryotes, this system has been repurposed to revolutionize genetic engineering across a wide range of organisms, including plants, animals, and humans. The core component, Cas9, is an endonuclease derived from Streptococcus pyogenes, capable of introducing...
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Synthesis and Decomposition Reactions02:17

Synthesis and Decomposition Reactions

Synthesis and decomposition are two types of redox reactions. Synthesis means to make something, whereas decomposition means to break something. The reactions are accompanied by chemical and energy changes. 
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Measurement: Derived Units03:02

Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, time, temperature, electric current, amount of substance, and luminosity. These are called the SI base units.
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Curve Sketching and Derivatives01:22

Curve Sketching and Derivatives

Understanding the behavior of a function through its first and second derivatives is essential for analyzing its graph. Derivatives provide insight into where a function increases or decreases, where it attains local maxima or minima, and how its curvature behaves across different intervals.The first derivative of a function reveals the slope of the tangent line at any given point. Points where the derivative is zero or undefined are considered critical, as they often indicate potential extrema...
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Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
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