The light-quark $sss$ member of the spin-three-halves baryon decuplet has strangeness $S=-3$, baryon number $B=1$, flavor hypercharge $Y=-2$, and isospin zero. The Gell-Mann--Nishijima formula gives electric charge minus one. Its position at the bottom of the decuplet's triangular weight diagram follows by replacing all three up or down quarks with strange quarks.

A baryon containing a charm quark. For one charm and two up/down quarks in the spatial ground state, light-diquark spin-isospin correlation gives the isosinglet Lambda c baryon and the isotriplet Sigma c baryon families.

An antibaryon is the antiparticle of a baryon. In the valence quark model it consists of three antiquarks in a colour singlet. Charge conjugation reverses its additive charges and third component of isospin, preserving total isospin and spin.

The baryon asymmetry is an excess of baryons over antibaryons. Here $n_B-n_{\bar{B}}$ counts net baryon number per unit volume, including the baryons bound in atomic nuclei. It is dynamically generated by baryogenesis. Once the antibaryon abundance is negligible, its photon-normalized value agrees with the usual baryon-to-photon ratio.

Consider equal initial abundances of a heavy boson $X$ and its antiparticle. Two decay channels with different baryon numbers, for example $X\to uu$ and $X\to \bar{d}{e}^{+}$, have branching fractions $r$ and $1-r$. The conjugate channels have branching fractions $\bar{r}$ and $1-\bar{r}$. Their mean baryon numbers are $r-1/3$ and $-\bar{r}+1/3$, so each particle-antiparticle pair produces $r-\bar{r}$, or $ϵ$ per decaying particle. Unequal branching fractions require CP violation; equal total decay widths are consistent with CPT symmetry. Baryon number cannot be assigned so that both channels conserve it. An initial abundance decaying outside thermal equilibrium, after inverse production becomes ineffective, can therefore generate a nonzero baryon asymmetry. At the microscopic level a decay-rate difference caused by CP violation requires interference of decay amplitudes with both a relative weak phase and an absorptive phase; complex couplings alone do not guarantee it. Subsequent baryon-number washout must be ineffective for the produced asymmetry to survive.

Baryon-number washout is erasure of a baryon asymmetry by reactions that violate baryon number. Inverse decays and scattering can drive the plasma toward its zero-asymmetry thermal equilibrium. The relevant comparison is their rate against the Hubble parameter, not just the decay width that initially produced the asymmetry.

In a steady axisymmetric barotropic fluid with purely azimuthal velocity $r\Omega {\mathbf{e}}_{\varphi }$ and a conservative body force, the barotropic enthalpy function obeys $\nabla (w+\Phi )=r{\Omega }^2{\mathbf{e}}_r$. Taking its curl yields the displayed cylindrical rotation law. The first integral is $w+\Phi -\int r{\Omega }^{2}dr=C$ in a connected fluid region. Baroclinic pressure and density need not satisfy this conclusion.

Bacillus megaterium is the historical species name used for strain KM in the lysozyme wall-removal experiment.

Typical Gram-negative bacteria have a relatively thin peptidoglycan layer between the cell membrane and a bacterial outer membrane.

Typical Gram-positive bacteria have a relatively thick peptidoglycan layer outside the cell membrane, without the bacterial outer membrane of typical Gram-negative bacteria. This is a representative cell envelope pattern, not a complete description of every member of bacteria.

Cyanobacteria are bacteria that perform oxygenic photosynthesis: light-dependent reactions release oxygen from water. Their photosynthetic machinery operates on thylakoid membranes without a chloroplast or a cell nucleus. This is a particularly useful counterexample to equating photosynthesis with being a plant. Chloroplasts descend from an ancestral cyanobacterial partner through endosymbiosis; present-day cyanobacteria are independent descendants, rather than chloroplasts waiting to become plants. See Alberts et al., Molecular Biology of the Cell: chloroplasts and cyanobacteria.

Escherichia coli, often abbreviated E. coli, is a bacterial species widely used to study DNA replication and gene expression. Its chromosome is in a nucleoid, and its ribosomes work in the cytoplasm, outside any cell nucleus. A result from one laboratory strain should not automatically be generalized to every member of the species.

The original 1997 report by Blattner and colleagues presented the K-12 MG1655 genome sequence as a circular chromosome of $4,639,221$ base pairs. See Blattner laboratory: original K-12 sequence and 1997 paper. As a bookkeeping example, one complete round of DNA replication from one such chromosome produces two daughter sequence copies totaling $2\times 4,639,221=9,278,442$ base pairs. This is twice the copied material, not twice the length of the reference genome; it does not specify the instantaneous DNA content of a rapidly growing E. coli cell.

Alphaproteobacteria are a bacterial group implicated in the ancestry of mitochondria. This relationship concerns common descent, not descent from a named modern member of Alphaproteobacteria.

An axon terminal is an output specialization at the end of an axon branch. At a typical chemical synapse, an arriving action potential opens voltage-gated calcium channels; calcium entry promotes exocytosis of synaptic vesicles, releasing neurotransmitter onto the target biological cell.^[ref]

One axon can branch into many axon terminals, so a single neuron can influence several targets. The terminal is the site of local chemical release, rather than a store of complete electrical impulses delivered unchanged across the synaptic cleft.

The axon initial segment is the specialized proximal region of an axon near the soma. In many neurons, its voltage-gated ion channels make it the site where an action potential begins. ^[ref]

In trans-autophosphorylation, one protein kinase chain phosphorylates another partner chain. “Auto” therefore does not require the modified site and catalytic active site to be on the same chain. The insulin receptor provides an activation-loop example; EGFR shows why autophosphorylation and catalytic activation need not be the same event.

The phase line of a scalar autonomous differential equation $\dot{x}=f(x)$ records its equilibrium points and the direction of motion between them. Zeros of $f$ mark equilibria; $f>0$ gives rightward arrows and $f<0$ gives leftward arrows. Local uniqueness prevents a nonconstant solution from crossing an equilibrium.

For example, $\dot{x}=x(1-x)$ has equilibria zero and one. Arrows point left for $x<0$, right for $0<x<1$ and left for $x>1$. Thus zero repels nearby states and one attracts them. Every solution starting in $(0,1)$ stays there and increases toward one: its limit cannot be an interior point where $f$ is positive.

This argument gives qualitative dynamics without solving the equation. Inward arrows on both sides indicate attraction, outward arrows indicate repulsion, and arrows in the same direction describe one-sided stability. The latter occurs at zero for $\dot{x}=x^2$: negative initial states approach it, while positive initial states move away.

Asymptotic simplicity requires a suitable smooth conformal completion with $\tilde{g}={\Omega }^{2}g$, $\Omega >0$ in the physical spacetime, and $\Omega =0$, $d\Omega \ne 0$ on null infinity, such that every inextendible null geodesic has both past and future endpoints there. It is stronger than merely possessing an asymptotically flat exterior. Null geodesics ending on singularities or on omitted finite-affine-distance horizons prevent this global condition.

A regular perturbation admits an asymptotic expansion about the limiting problem without changing its relevant scale or losing solutions or conditions. A regular perturbation of a simple algebraic root follows from the implicit function theorem. A full problem can still be a singular perturbation even when some individual solution branches are regular.

Rescale variables so that the terms responsible for the leading behaviour have comparable size. The resulting distinguished limit exposes a governing equation that may differ from the naive zero-parameter equation. Examples are dominant balance for algebraic roots and the derivative balance in a square-root boundary layer at a vanishing drift.