Capacity to generate several specified differentiated cell types. It does not imply ability to generate every cell type or a whole organism.

The local cellular and extracellular environment regulating stem-cell persistence, renewal and cell differentiation. In culture, supplied matrix and growth factors may substitute for components normally provided by neighbouring cells.

A self-renewing cell that supplies descendants to the germline. Division orientation relative to a stem-cell niche can help give daughters different developmental outcomes.

Experimental removal of a biological population defined by location or marker. The result depends on efficiency, duration, surviving cells, niche injury and the ability of other cells to replace the targeted state.

Maintenance of a renewing biological population through balanced outcomes across cells, without requiring every division to produce exactly one renewing daughter.

Capacity to generate the principal embryonic cell lineages under suitable conditions. Expression of one stem-cell marker alone does not establish this capacity.

An equilibrium statistical ensemble with fixed particle number, pressure and temperature, allowing volume and energy to fluctuate. With a temperature-independent volume measure, its joint weight is proportional to $e^{-\beta (E+PV)}$. Its normalization and any temperature-dependent prefactor must be specified when taking thermodynamic derivatives.

An electric-field shift or splitting of molecular rotational levels. The observed line shift is the difference of upper- and lower-level shifts, subject to polarization-dependent selection rules; shifting only one endpoint gives an incorrect spectral splitting.

The energy shift produced by an oscillating electric field, often called a light shift. For a far-detuned two-level drive with coupling $\hslash \Omega /2$ and $\Delta ={\omega }_L-{\omega }_{eg}$, the ground-state shift is approximately $\hslash |\Omega {|}^2/(4\Delta )$. Multilevel atoms can have polarization-dependent differential shifts.

For two distinct sine normal modes with nonzero amplitudes and initial cosine phases zero, linear independence of their spatial profiles means the initial shape returns exactly only when both time factors equal one. A rational frequency ratio ${\omega }_2/{\omega }_1=p/q$ in lowest terms gives first positive recurrence $2\pi q/{\omega }_1$. An irrational ratio gives no exact positive recurrence, although arbitrarily close two-mode returns exist. These statements refer to the complete spatial profile, not a displacement at one observation point.

A surface displacement constrained to vanish on all four sides of an ideal square has sine factors $\sin (n\pi x/L)\sin (m\pi y/L)$, with $n,m\ge 1$. The fundamental therefore has wavenumber $\sqrt{2}\pi /L$. This differs from the impermeable-wall condition in a closed tank, which permits cosine modes with a zero index. For an elastic plate a simply supported edge also supplies its bending boundary condition; clamping imposes a different problem.

For real negative displacement reflection amplitude $r=-a$, with $0<a<1$, useThis separates a travelling field and a standing field algebraically. Their individual powers cannot be treated as independent incident-power fractions because the two fields interfere. Reflected and transmitted power should instead be calculated from travelling-wave amplitudes with the appropriate characteristic impedance factors.

Removal of material by bombardment with energetic ions. Directional sputtering can transfer a mask pattern with less undercut than an isotropic wet etch; mask erosion, redeposition and surface damage remain possible.

A sputter-deposition method using a magnetic field near a target to confine electrons and sustain ionization efficiently. Multiple targets permit co-deposition. A local flux proportional to target power is a useful calibration model over a restricted range, rather than a universal linear law for composition or thickness.

For a specified electric-dipole transition, summing free radiation modes gives $A_{21}={\omega }_{21}^3|{\mathbf{d}}_{12}{|}^2/(3\pi {ϵ}_0\hslash c^3)$. Unresolved degenerate levels require sums over final substates and appropriate initial-state averages. Modified radiation environments alter the available modes.

Wide perfectly conducting plates with $d\ll c/{\omega }_0$ admit only a normal-electric-field transverse electromagnetic mode at the transition frequency. The electric-dipole interaction therefore couples to the normal component of the atomic transition dipole. A normal dipole has enhanced available mode density; an in-plane dipole has no allowed electric-dipole radiation channel below the higher-mode cutoffs. The conclusion assumes negligible changes to the atom and negligible absorption, leakage and symmetry-breaking mixing.

For constant mass density $\rho$ on $a<r<b$, the shell theorem gives zero gravitational field for $r\le a$, inward magnitude $4\pi G\rho (r^3-a^3)/(3r^2)$ for $a<r<b$, and $4\pi G\rho (b^3-a^3)/(3r^2)$ outside. These formulas agree continuously at both boundaries. The empty cavity has zero gravitational field but generally nonzero constant gravitational potential.

Evolution of reproductive isolation as a consequence of divergent ecological natural selection. Ecological differences or distinct reaction norms alone are insufficient unless they reduce gene flow.