A band of diffraction contrast where local bending brings a crystal structure into a particular Bragg diffraction condition. Its position changes with specimen tilt.

An oscillation of transmitted or diffracted intensity with crystal thickness caused by coupled-wave electron diffraction. A uniform chemical composition can still show thickness fringes.

In an alternating-mass chain with nearest-neighbour spacing $a$ and cell length $2a$, the inter-sublattice Bloch coupling is proportional to $\cos qa$. At the first-zone edge $q=\pi /(2a)$ it vanishes. For $M>m$, the acoustic edge mode moves only the heavy sublattice and the optical edge mode only the light one. Their frequency difference is $\sqrt{2\alpha /m}-\sqrt{2\alpha /M}$. At long wavelength the acoustic displacements are in phase, whereas the optical mode has zero centre-of-mass displacement.

A member of the lineage containing the tuatara and squamates such as lizards and snakes.

The clade comprising the most recent common ancestor of living crocodilians and birds and all its descendants, including extinct dinosaurs. Being sister to this clade does not make turtles archosaurs.

A member of the turtle lineage, whose shell and skull underwent substantial modification. Molecular and fossil evidence support a diapsid origin, with living turtles commonly recovered as sister to archosaurs.

A lizard is a member of the reptile radiation that also contains snakes. The familiar four-legged form is not universal: some lineages have reduced limbs. Evolutionary relationships therefore cannot be inferred from limb presence alone.

The ratio of the heat flux needed to reach departure from nucleate boiling to the actual local heat flux. Greater values indicate more margin under the model and correlation used.^[ref]

An eta-quotient is a finite product of integer powers of Dedekind eta functions at rescaled arguments:Negative exponents place factors in the denominator; its formal modular weight is $\frac{1}{2}{\sum }_{\delta }{r}_{\delta }$. A product of this form is not automatically a holomorphic modular form: its transformation law and behavior at cusps require additional conditions.

In string and conformal field theory calculations, inverse eta powers package oscillator-state counting. For example, $\eta (\tau {)}^{-24}=q^{-1}{\prod }_{n\ge 1}(1-q^n{)}^{-24}$ displays the vacuum offset and the degeneracies of 24 independent chiral bosonic oscillators. Checking its leading power and modular weight provides a useful consistency check before combining it with zero-mode or ghost contributions.

In a spatially flat universe dominated by a positive constant energy density $ϵ$, the Friedmann equations give $H^2=8\pi Gϵ/(3c^2)$. On the expanding branch $a(t)=a_i{e}^{H(t-t_i)}$, so the scale factor doubles after $(\log 2)/H$. This concerns a linear length scale; the enclosed physical volume grows by a factor of eight over the same interval.

The ratio $M=\sigma /{\tau }_c$ connecting a macroscopic tensile flow stress to a reference critical resolved shear stress in a specified polycrystal model. Texture, slip families and compatibility assumptions matter. An order-three factor is a conventional estimate for randomly oriented cubic grains, distinct from the factor two for a perfectly oriented single slip system.

The regulated bare coupling $g_0$ is matched to the physical two-body scattering length. In the uniform one-loop grand potential this matching supplies the subtraction that makes $\frac{1}{2}\int d^{3}k/(2\pi {)}^3[E_k-{\epsilon }_k-\mu +{\mu }^2/(2{\epsilon }_k)]$ ultraviolet finite. Merely using the physical coupling in an unregulated zero-point integral would retain a divergent answer. The contact description and its cutoff cannot be extended to arbitrary momenta independently of that matching.

Compressed sparse row format stores a sparse $m\times n$ matrix using arrays of nonzero values, their column indices, and an array of $m+1$ row offsets. For zero-based row $i$, its entries occupy positions from $\mathrm{rowptr}[i]$ through $\mathrm{rowptr}[i+1]-1$.

For $A=\left(\begin{array}{ccc}0& 5& 0\\ 2& 0& 7\end{array}\right)$, one representation is $\mathrm{values}=(5,2,7)$, $\mathrm{col}=(1,0,2)$, $\mathrm{rowptr}=(0,1,3)$. Equal adjacent offsets encode an empty row. This permits matrix-vector product in $O(m+\mathrm{nnz})$ time without storing zeros. Whether columns are sorted or duplicates are permitted is an implementation convention.

When the mass is constant $V_{+}>0$ above the wall and $V_{-}<0$ below it, amplitude decay lengths are ${\xi }_{+}=\hslash c/V_{+}$ and ${\xi }_{-}=\hslash c/|V_{-}|$. A scalar transverse envelope multiplying a unit spinor has normalization $\sqrt{2/({\xi }_{+}+{\xi }_{-})}$. Density decays twice as fast as amplitude.

A branch $E=-\hslash c{k}_x$ gives a packet $f(y)ug(x+ct)$: it translates rigidly in the negative longitudinal direction while remaining transversely localized. Curvature of a more complete physical dispersion can restore packet spreading; the rigid result belongs to the exactly linear model.

Let a Hermitian matrix have distinct real eigenvalues with multiplicities $n_1,\dots ,n_k$. A unitary matrix commuting with it must preserve each eigenspace: if $Av=\lambda v$, then $A(Uv)=UAv=\lambda Uv$. Conversely, any unitary transformation acting independently on these mutually orthogonal eigenspaces commutes with $A$. The centralizer in $U(n)$ is therefore ${\prod }_{j}U(n_j)$. Imposing total determinant one gives the displayed subgroup inside the special unitary group $SU(n)$.

For multiplicities $(2,1)$ in SU(3), it is $S(U(2)\times U(1))\cong U(2)$, embedded by $U\mapsto \mathrm{diag}(U,(\det U{)}^{-1})$. Three distinct eigenvalues leave the diagonal maximal torus $U(1{)}^2$. This determines the unbroken group for a diagonal adjoint scalar field vacuum, including its global determinant constraint.

The Palaeogene is the geological period from 66.00 to 23.04 million years ago in the consulted chart. It contains the Paleocene, Eocene and Oligocene, preceding the Neogene within the Cenozoic.^[ref]

The Neogene is the geological period from 23.04 to 2.58 million years ago in the consulted chart. It contains the Miocene and Pliocene, between the Palaeogene and Quaternary.^[ref]

The Quaternary is the current geological period, beginning 2.58 million years ago. It contains the Pleistocene and Holocene epochs. Repeated major glacial cycles make its marine and continental records important for studying climate variability.^[ref]

A vacuum ray incident normally on a dielectric moving parallel to its surface becomes oblique in the material rest frame, with $\sin i=|\beta |$. For a transparent nonmagnetic dielectric, the rest-frame Brewster angle satisfies $\tan i_B=n$, giving $|{\beta }_B|=n/\sqrt{1+n^2}$. The reflected electric field is perpendicular to the plane containing the ray and the velocity. A real refractive index $n\ne 1$ is assumed; dispersion makes the condition implicit through the rest-frame frequency, and absorption generally removes exact extinction.