States' rightsIn American political discourse, states' rights are political powers held for the state governments rather than the federal government according to the United States Constitution, reflecting especially the enumerated powers of Congress and the Tenth Amendment. The enumerated powers that are listed in the Constitution include exclusive federal powers, as well as concurrent powers that are shared with the states, and all of those powers are contrasted with the reserved powers—also called states' rights—that only the states possess.
Charge (physics)In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by the letter Q, and so the invariance of the charge corresponds to the vanishing commutator , where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues q of the generator Q.
Noetherian schemeIn algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets , noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus, a scheme is noetherian if and only if it is locally noetherian and quasi-compact. As with noetherian rings, the concept is named after Emmy Noether. It can be shown that, in a locally noetherian scheme, if is an open affine subset, then A is a noetherian ring.
Richardson extrapolationIn numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value . In essence, given the value of for several values of , we can estimate by extrapolating the estimates to . It is named after Lewis Fry Richardson, who introduced the technique in the early 20th century, though the idea was already known to Christiaan Huygens in his calculation of π. In the words of Birkhoff and Rota, "its usefulness for practical computations can hardly be overestimated.
AI alignmentIn the field of artificial intelligence (AI), AI alignment research aims to steer AI systems towards humans' intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues some objectives, but not the intended ones. It can be challenging for AI designers to align an AI system because it can be difficult for them to specify the full range of desired and undesired behaviors.
Mass–energy equivalenceIn physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicist Albert Einstein's formula: . In a reference frame where the system is moving, its relativistic energy and relativistic mass (instead of rest mass) obey the same formula. The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c2).
Complex planeIn mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
Charge conservationIn physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved. Charge conservation, considered as a physical conservation law, implies that the change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume.
Thermodynamic free energyIn thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system (the others being internal energy, enthalpy, entropy, etc.). The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point.
Zero-point energyZero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrational motion. Apart from atoms and molecules, the empty space of the vacuum also has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions (i.
Aitken's delta-squared processIn numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method, used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced this method in 1926. Its early form was known to Seki Kōwa (end of 17th century) and was found for rectification of the circle, i.e. the calculation of π. It is most useful for accelerating the convergence of a sequence that is converging linearly.
United States Bill of RightsThe United States Bill of Rights comprises the first ten amendments to the United States Constitution. Proposed following the often bitter 1787–88 debate over the ratification of the Constitution and written to address the objections raised by Anti-Federalists, the Bill of Rights amendments add to the Constitution specific guarantees of personal freedoms and rights, clear limitations on the government's power in judicial and other proceedings, and explicit declarations that all powers not specifically granted to the federal government by the Constitution are reserved to the states or the people.
