Visual sensitivity to ultraviolet wavelengths. Its relevance to a colour comparison depends on the receiver’s actual receptors and the illumination.

A signalling region that becomes positioned on the prospective anterior side of the mouse embryo and antagonizes posteriorizing signals, helping position the primitive streak.

virialization is relaxation toward a gravitationally supported bulk state satisfying an appropriate virial balance. For an isolated approximately stationary Newtonian system with negligible boundary terms, $2K+W\simeq 0$. It does not require every collisionless constituent to reach collisional thermal equilibrium, and ongoing infall, tides or pressure at a boundary modify the balance.

For a hydrostatic monatomic ideal gas with negligible external pressure, $2U+{\Omega }_f=0$, where gravitational potential energy is negative. The final total energy is therefore ${\Omega }_f/2$, giving the displayed radiated energy when no mass or other energy carrier escapes. The common $-{\Omega }_f/2$ result additionally takes the initial total energy to be negligible. Initial rest does not remove initial self-gravitational binding energy.

Expanding $p=n{k}_{B}T/(1-nb)-a{n}^2$ at $nb\ll 1$ gives the second virial coefficient $B_2=b-a/(k_{B}T)$ and the displayed higher density-series coefficients. These are the Van der Waals gas predictions, not exact coefficients for every fluid. The vanishing of $B_2$ at the Boyle temperature removes only the leading density correction.

vicinal coupling between protons on opposite sides of an alkene. In many ordinary terminal alkenes its magnitude exceeds the corresponding cis coupling.

vicinal coupling between protons on the same side of an alkene. A measured first-order splitting is an approximation if the spin system is appreciably strongly coupled.

The vinyl ether $\mathrm{C}{\mathrm{H}}_2=\mathrm{CH}-\mathrm{O}-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2\mathrm{Cl}$. Its terminal alkene hydrogens are diastereotopic.

An otherwise forbidden electronic transition gains intensity when accompanying molecular vibration supplies a symmetry factor that permits a nonzero electric dipole transition moment. A symmetry-allowed total vibronic state specifies a possible transition, while the coupling determines its actual strength.

The first-order dependence of a polyatomic rotational constant on vibrational occupations $v_i$, where $d_i$ is the degeneracy of normal mode $i$. The factor $d_i/2$ accounts for all of that mode's zero-point energy. A single band's change in rotational constant generally determines one ${\alpha }_i$, rather than every zero-point correction needed for $B_e$.

A hindlimb is the posterior paired limb of a tetrapod. Its segments and joints can be compared across walking, swimming, climbing and flying lineages. Similar topographic position does not require identical proportions or locomotor function.

If a trial quantum state is dominated by two energy eigenstates of distinct energies $E_a<E_b$, then its Rayleigh quotient is approximately their probability-weighted mean. Rearranging that mean gives the displayed relative admixture. Neglected states must make small contributions to the energy numerator as well as to wavefunction normalization; small probabilities alone need not suffice if their energies are large.

A product of two normalized $1s$ orbitals proportional to $e^{-\zeta r}$, combined with a singlet state, gives the fixed-nucleus helium atom trial energy $E(\zeta )={\zeta }^2-4\zeta +5\zeta /8$ in atomic units. Minimization gives $\zeta =27/16$ and $E=-729/256$ Hartree. Nuclear charge remains two in the Hamiltonian operator; varying $\zeta$ changes only the trial orbitals. The reduced orbital charge describes screening, while explicit dependence on electron separation can further lower the trial energy under the quantum variational principle.

An even one-dimensional confining potential preserves even and odd parity. Restricting a normalized trial state to the odd sector makes its Rayleigh quotient an upper bound on the lowest odd energy, which is the first excited energy for the usual nonsingular one-dimensional bound-state problem. This avoids contamination by the even ground state. For an adjustable-width odd Gaussian, optimize its own width rather than borrowing the ground-state optimum.

A historical isotope-enrichment technology using the different transport of isotopic gas molecules through a barrier. It was displaced commercially by much less electricity-intensive centrifuge technology. This is a historical principle, not a plant design or operating procedure.

A technology exploiting mass-dependent redistribution of gas under rotation. It became the dominant commercial uranium-enrichment technology with much lower electricity consumption than gaseous diffusion. No operating conditions or equipment specifications are supplied.

uranium with less uranium-235 than natural uranium. Addition to an immobilised plutonium inventory can dilute uranium-235 subsequently formed by plutonium-239 radioactive decay; chemical coexistence is not irreversible protection against deliberate separation.