Lebesgue measureIn measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space. For n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called n-dimensional volume, n''-volume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration.
Weak hyperchargeIn the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted and corresponds to the gauge symmetry U(1). It is conserved (only terms that are overall weak-hypercharge neutral are allowed in the Lagrangian). However, one of the interactions is with the Higgs field. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum.
Measure (mathematics)In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge.
D mesonThe D mesons are the lightest particle containing charm quarks. They are often studied to gain knowledge on the weak interaction. The strange D mesons (Ds) were called "F mesons" prior to 1986. The D mesons were discovered in 1976 by the Mark I detector at the Stanford Linear Accelerator Center. Since the D mesons are the lightest mesons containing a single charm quark (or antiquark), they must change the charm (anti)quark into an (anti)quark of another type to decay.
LightLight or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). In physics, the term "light" may refer more broadly to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, microwaves and radio waves are also light.
Cross section (physics)In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns.
Measure spaceA measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the σ-algebra) and the method that is used for measuring (the measure). One important example of a measure space is a probability space. A measurable space consists of the first two components without a specific measure.
Parity (physics)In physics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection): It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity.
Rayleigh scatteringRayleigh scattering (ˈreɪli ), named after the 19th-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering particle (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength. Rayleigh scattering results from the electric polarizability of the particles.
NP-completenessIn computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.
Weak chargeIn nuclear physics and atomic physics, weak charge refers to the Standard Model weak interaction coupling of a particle to the Z boson. For example, for any given nuclear isotope, the total weak charge is approximately −0.99 per neutron, and +0.07 per proton. It also shows an effect of parity violation during electron scattering. This same term is sometimes also used to refer to other, distinct quantities, such as weak isospin, weak hypercharge, or the vector coupling of a fermion to the Z boson (i.e.
NP-hardnessIn computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H; that is, assuming a solution for H takes 1 unit time, Hs solution can be used to solve L in polynomial time.
