Stellar variability that contaminates a planetary radial-velocity or photometric signal. Rotating active regions, changes in convective line shifts, oscillations and granulation can produce apparent velocities. A common spectral shift, line-shape diagnostics, activity indicators and simultaneous photometry provide different tests; none is an automatic numerical probability.

Steel microstructure describes the spatial arrangement of phases, grains, defects, and precipitates in a steel. Ferrite, austenite, cementite-containing mixtures, and martensitic structures are important examples.

These features influence dislocation motion and fracture, connecting thermal processing with mechanical performance. Overall carbon percentage alone cannot specify a steel's microstructure or uniquely determine its properties.

A chromium-bearing steel whose protective surface film can confer corrosion resistance. Composition, microstructure and environment determine whether that protection persists.

A steel with an austenitic, face-centered cubic matrix in the specified condition. Alloying and temperature determine its stability.

Data centering subtracts the sample mean from every observation, separately for each coordinate of multivariate data. The resulting coordinate sample means are zero.

An isolated energy shell gives the microcanonical ensemble; a heat bath fixes $T$ for the canonical ensemble; a heat and particle reservoir fixes $T,\mu$ for the grand canonical ensemble. Constraints determine the allowed fluctuations and which thermodynamic potential is useful.

Crystal polymorphism is the existence of different crystal structures for the same chemical substance. Each crystal polymorph can have its own mass density, melting behavior and range of stability on a phase diagram. A different external shape of the same crystal structure alone does not establish a different crystal polymorph.^[ref]

At fixed temperature and pressure, compare the chemical potentials of the possible crystal polymorphs. The lower value determines the stable bulk thermodynamic phase; equality permits phase coexistence when neither form is beaten by another thermodynamic phase. A higher-chemical potential form can persist through metastability, so finding it in a sample does not by itself locate an equilibrium boundary.

For a nonnegative integer $n$, compute its integer square root $r=\lfloor \sqrt{n}\rfloor$ and accept exactly when $r^2=n$. An approximate square root must be corrected with exact integer comparisons before this equality is tested. This procedure distinguishes a squareness test from merely approximating a square root.

The square part of a positive integer $n={\prod }_p{p}^{e_p}$ is its largest square divisor, ${\prod }_p{p}^{2\lfloor e_p/2\rfloor }$. Dividing $n$ by its square part leaves the squarefree part.

For a nonnegative real number $x$, the squarefree counting function counts positive square-free integers:For example, $Q(10)=7$, counting $1,2,3,5,6,7,10$. The Möbius function gives the exact formulaTo see why, consider ${\sum }_{d^2\mid n}\mu (d)$. Only square-free integers $d$ contribute. Choosing their prime factors from the primes whose squares divide $n$ gives the product ${\prod }_{p^2\mid n}(1-1)$. This is one when there are no such prime factors and zero otherwise, so it is the indicator function of squarefreeness. Summing over the positive integers $n\le x$ and exchanging two finite sums leaves $\lfloor x/d^2\rfloor$ multiples of each $d^2$. The floor function makes the formula exact for nonintegral $x$ too.

The squarefree part of a positive integer $n$ is the unique squarefree integer $s$ such that $n=s{t}^2$ for a positive integer $t$. For example, the squarefree part of $72=2^3{3}^2$ is $2$. It retains precisely the primes with odd prime exponents; the radical of an integer instead retains every distinct prime factor.

A structure in which spores are produced. One unbranched bryophyte sporophyte bears a single sporangium; branching sporophytes can distribute several sporangia on one body.

The weak-gain state generated by an undepleted pump contains a vacuum term and a photon-pair amplitude. A continuum pair amplitude combines the pump spectrum with a phase-matching factor $L\mathrm{sinc}(\Delta kL/2)e^{i\Delta kL/2}$. Its joint spectrum determines spectral correlations and the purity attainable by heralding one partner.

Detection of one member of a pair conditions the other mode towards a one-photon state. Imperfect collection reduces heralding efficiency; unresolved spectral correlations can leave a mixed state, and multiple pairs can contaminate the heralded output. Filtering can improve purity while reducing brightness. Heralding is conditional preparation, not deterministic conversion of every pump pulse.

Place the reservoir chemical potential between the lower and higher Zeeman-split one-electron dot levels. The excited state can leave while the ground state remains trapped; a time-resolved charge sensor detects the temporary empty state. Thermal errors, missed fast tunnelling and relaxation before escape limit fidelity.

Suppression of charge transfer by spin symmetry and the Pauli exclusion principle. For a double quantum dot, a $(1,1)$ singlet state can enter the lowest $(0,2)$ singlet, whereas a $(1,1)$ triplet state is blocked if the required $(0,2)$ triplet lies above the accessible energy window. Spin mixing or relaxation can lift blockade.

Map states with unequal escape rates ${\Gamma }_f\gg {\Gamma }_s$ onto distinct charge outcomes after an interval between their characteristic escape times. Both removal energies can lie above the reservoir chemical potential, so their splitting need not be thermally resolved. A useful rate difference must have a physical origin: a demonstrated single-dot example uses a two-electron singlet state and triplet state with different occupied orbitals. A bare single-electron Zeeman pair in the same orbital does not automatically provide the required rate contrast.^[ref]

For $H=c(p_x{\sigma }_x+p_y{\sigma }_y)$ with $c>0$ and physical spin matrices, $⟨\mathbf{S}{⟩}_s=s(\hslash /2)\hat{\mathbf{p}}$. The positive-energy branch is parallel and the negative-energy branch antiparallel to momentum. Both are collinear; no preferred spin direction is defined at zero momentum.