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Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
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Structural Organization of the Human Body: An Overview01:18

Structural Organization of the Human Body: An Overview

It is convenient to consider the body's structures in terms of fundamental levels of organization that increase in complexity: subatomic particles, atoms, molecules, organelles, cells, tissues, organs, organ systems, and organisms.
To study the chemical level of organization, scientists consider the simplest building blocks of matter: subatomic particles, atoms, and molecules. All matter in the universe is composed of one or more unique pure substances called elements, familiar examples of...
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Proteomics01:33

Proteomics

A proteome is the entire set of proteins that a cell type produces. We can study proteomes using the knowledge of genomes because genes code for mRNAs, and the mRNAs encode proteins. Although mRNA analysis is a step in the right direction, not all mRNAs are translated into proteins.
Proteomics is the study of proteomes' function. It involves the large-scale systematic study of the proteome to denote the protein complement expressed by a genome. Scientist Mark Wilkins coined the term...
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Space Trusses01:25

Space Trusses

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...
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State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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Space Trusses: Problem Solving01:29

Space Trusses: Problem Solving

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
Consider a tripod consisting of a tetrahedral space truss with a ball-and-socket joint at C. Suppose the height and lengths of the horizontal and vertical...
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