A spatial charge density describing the electric charge inside an atomic nucleus. In a static description centered on the nucleus, normalize it bywhere $Z$ is the atomic number and $e>0$ the elementary charge. A nuclear charge distribution is an average over a nuclear quantum state, rather than a photograph of immobile protons. Even when the average has spherical symmetry, individual nucleons need not sit on spherical shells. The proton charge radius and the internal charge density of the neutron also contribute: a distribution of pointlike proton centers is an approximation to a nuclear charge distribution, not its definition.

The experimental attraction is that an electron probes electric charge through the electromagnetic interaction, without itself feeling the nuclear force. Varying its momentum transfer changes the spatial scale tested. Long wavelengths mainly constrain a nuclear charge radius; shorter wavelengths can distinguish a diffuse edge from a sharper one through diffraction. Recovering the entire nuclear charge distribution from a finite range of noisy scattering data remains an inverse problem.

Movement of an atomic nucleus after it receives momentum, for example in a collision. A finite nuclear mass requires sharing kinetic energy as well as momentum; the fixed-target approximation neglects this motion.

Nuclear structure concerns the states and internal organization of an atomic nucleus, including nuclear energy levels, nuclear spin, spatial distributions and the interactions among nucleons. It connects the nucleus's constituents to observable excitation and decay patterns.

A nuclear level scheme organizes measured transition energies and assignments. Gamma decay constrains differences between levels, while reaction and scattering measurements provide complementary information about allowed transitions and spatial distributions. Several models can describe different aspects of the same nucleus; matching one transition energy alone does not establish a unique microscopic arrangement.

The total angular momentum of an atomic nucleus, including the orbital and intrinsic spin contributions of its constituent nucleons.

Nuclear isobars are different nuclides with the same mass number $A$ and different atomic numbers $Z$. They differ from isotopes, which have fixed $Z$. Beta decay connects neighboring nuclear isobars.

Evaporative cooling of atoms lowers the mean motional energy of a trapped gas by preferentially removing its more energetic atoms. Subsequent elastic collisions redistribute the remaining energy, producing a cooler approximately thermal sample.

In forced evaporative cooling, a decreasing trap-depth threshold or a radiofrequency evaporation knife continuously removes the high-energy tail. Losing atoms alone is insufficient: losses that sample all energies equally do not provide the same cooling mechanism. Useful evaporation increases phase-space density of an atomic gas while retaining enough collisions for rethermalization. An expansion measurement before and after evaporation tests the velocity distribution as well as the retained atom number.

Laser spectroscopy uses a tunable laser to interrogate energy levels through photon absorption, stimulated emission or fluorescence. A narrow optical source is useful only if the sample and readout preserve the information: Doppler broadening can hide closely spaced spectral lines even when the source itself is narrow.

An ion trap confines an ion using electromagnetic fields, allowing repeated interrogation of the same particle. The name also covers related traps for an electron. A Paul trap uses an oscillating electric quadrupole field; a Penning trap combines a static electric quadrupole field with a static magnetic field. Confinement creates time to measure an energy level, frequency or magnetic dipole moment; it does not itself cool the particle or identify its internal quantum state.

The obstacle is Earnshaw's theorem. In a charge-free neighbourhood the static electric potential $\Phi$ obeys Laplace's equation, ${\nabla }^2\Phi =0$. For a particle of fixed nonzero electric charge $Q$, the potential energy $Q\Phi$ is also a harmonic function. The maximum principle for harmonic functions excludes a strict interior minimum. For a quadratic example, the Hessian matrix has zero trace; it cannot have three positive eigenvalues. A static purely electric field therefore cannot supply three-dimensional stable confinement of a free point electric charge. Time variation in a Paul trap, and the velocity-dependent Lorentz force in a Penning trap, change the assumptions of this argument.

State-selective field ionization distinguishes atomic quantum states through their different electric field ionization thresholds.

A dynamic array is an array whose backing storage can grow as entries are appended. Dynamic array doubling is one growth policy with a deterministic amortized analysis.

An integer identifying a position in an array. With zero-based indexing and capacity $m$, valid array indices are $0,\dots ,m-1$. An array index identifies the slot rather than its stored value.

Unsigned lecture notes dated 23 April 1996, hosted by the University of California, Berkeley. Neither personal nor institutional authorship is established.

Lecture notes: people.eecs.berkeley.edu/~demmel/cs267/lectureSparseLU/lectureSparseLU1.html

Cited passages: Cholesky versus LU Decomposition, four phases; Left looking versus Right looking Cholesky; The Elimination Tree and Sources of Parallelism. Several later sections are marked under construction.

The Fc fragment comprises paired immunoglobulin heavy chain $C_{H2},C_{H3}$ portions, interacts with immune partners and lacks paratopes. Its name records historical crystallization.^[ref]

For example, Fc fragments can bind components of the complement system, illustrating a function distinct from epitope recognition.^[ref]

An isolated Fc fragment therefore separates one set of protein interactions from target recognition. In the connectivity example under Papain digestion of IgG, the Fc fragment contributes one connected product but zero antibody binding sites. Retaining it preserves different interaction surfaces; it does not restore either severed arm. Conversely, the two Fab fragments preserve the stipulated epitope-recognition sites while losing their connection to this common stem.

The antenna effective area converts incident energy flux into available received power for a specified direction and matched polarization of an electromagnetic wave. In a lossless free-space link, a transmitter of antenna gain $G$ at range $r$ and a receiver of effective area $A_{\mathrm{eff}}$ have $P_r/P_t=G{A}_{\mathrm{eff}}/(4\pi r^2)$. Impedance or polarization mismatch reduces the delivered power.