Throughout its ~4.5 billion year history, the Earth has experienced periods of warming and cooling. However, the current drastic increase in global temperatures is well outside of the Earth’s cyclic norms, and evidence for human-caused global climate change is compelling. Paleoclimatology, the study of ancient climate conditions, provides ample evidence for human-caused global climate change by comparing recent conditions with those in the past.

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...

The position of the absorption signal of a sample is reported relative to the position of the signal of tetramethylsilane (TMS), which is added as an internal reference while recording spectra. The difference between the absorption frequencies of the sample and TMS (in Hz) is divided by the spectrometer operating frequency (in MHz) to obtain a dimensionless quantity called the chemical shift. It is reported on the δ (delta) scale and expressed in parts per million.
For instance, the proton...

The origin of Earth's ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be the beginning of the proper understanding of the phenomenon. Ocean tides are the result of gravitational tidal forces. These same tidal forces are present in any astronomical body; they are responsible for the internal heat that creates the volcanic activity on Io, one of Jupiter's moons, and the breakup of stars that get too close to...

Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred...

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...