Translation is the process of synthesizing proteins from the genetic information carried by messenger RNA (mRNA). Following transcription, it constitutes the final step in the expression of genes. This process is carried out by ribosomes, complexes of protein and specialized RNA molecules. Ribosomes, transfer RNA (tRNA), and other proteins produce a chain of amino acids—the polypeptide—as the end product of translation.
Translation Produces the Building Blocks of Life
Proteins are...

Lesson: Translation
Translation is the process of synthesizing proteins from the genetic information carried by messenger RNA (mRNA). Following transcription, it constitutes the final step in the expression of genes. This process is carried out by ribosomes, complexes of protein and specialized RNA molecules. Ribosomes, transfer RNA (tRNA), and other proteins produce a chain of amino acids—the polypeptide—as the end product of translation.
Translation Produces the Building Blocks of...

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.

Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...