Africa and Latin America: united again

Changes in the environment of the early Earth drove the evolution of organisms. As prokaryotic organisms in the oceans began to photosynthesize, they produced oxygen. Eventually, oxygen saturated the oceans and entered the air, resulting in an increase in atmospheric oxygen concentration, known as the oxygen revolution approximately 2.3 billion years ago. Therefore, organisms that could use oxygen for cellular respiration had an advantage. More than 1.5 years ago, eukaryotic cells and...

Another method of radical formation is the elimination process. It is the opposite of the addition route and is driven by the instability of the radical. For example, as depicted in Figure 1, dibenzoyl peroxide yields a pair of unstable radicals upon homolysis. Given its instability, this radical spontaneously undergoes elimination via a C–C bond cleavage to form a relatively more stable phenyl radical. The mechanism involves cleavage of the bond between the α and β positions with respect...

Radicals can be formed by adding a radical to a spin-paired molecule. This is typically observed with unsaturated species, where the addition of a radical across the π bond leads to the production of a new radical by dissolving the π bond. For example, the addition of a Br radical to an alkene yields a carbon-centered radical.
Similar to charge conservation in chemical reactions, spin conservation is implicit for radical reactions. Accordingly, the product formed must possess an...

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...

Latitudes and departures are essential concepts in surveying, providing a systematic way to analyze the projections of traverse lines. These projections allow surveyors to interpret a line's north-south and east-west components, which are crucial for precisely calculating areas, bearings, and lengths. Latitude is the north-south projection of a line, calculated as the product of the line's length and the cosine of its bearing. Departure, conversely, is the east-west projection obtained by...

A bond can be broken either by heterolytic bond cleavage to form ions or homolytic bond cleavage to yield radicals. A fishhook arrow is used to represent the motion of a single electron in homolytic bond cleavage. There are two main sources from which radicals can be formed:
Radicals from spin-paired molecules:
Radicals can be obtained from spin-paired molecules either by homolysis or electron transfer. While two radicals are formed in the former, an electron is added in the...