A quark-line diagram can show how existing valence quarks are regrouped into outgoing hadrons while gluons exchange momentum and colour. Alternatively, a quark-antiquark pair can annihilate and create a different flavour pair with zero net flavour. Such drawings enforce global charge, baryon number and flavour constraints; they are not controlled perturbative calculations of an exclusive low-energy hadronic amplitude because binding is nonperturbative.

For a thin lens, relative arrival times follow the difference of $\frac{1}{2}|\theta -\beta {|}^2-\psi (\theta )$ between images, multiplied by $(1+z_l)D_l{D}_s/(c{D}_{ls})$. Both geometry and gravitational potential contribute; an additive delay common to all images is unobservable.

An anagram of a finite string is another string with exactly the same number of occurrences of each symbol. Thus $aab$ and $aba$ are anagrams; $abb$ is not. Equivalently, the second string is obtained by a permutation of the positions.

If a length-$n$ string has symbol multiplicities $m_1,\dots ,m_r$, its number of distinct anagrams is the multinomial coefficient $n!/(m_1!\cdots m_r!)$. Dividing by the factorials removes position permutations that only exchange equal symbols. The count depends on multiplicities, not the original ordering.

A palindrome is a finite string equal to its reversal. For example, the strings $010$ and $0110$ are palindromes.

An infinite binary word is Sturmian if it has exactly $n+1$ distinct contiguous subwords of length $n$ for every positive integer $n$.

A substring is a contiguous segment of a string. It differs from a subsequence, whose selected characters need not be adjacent.

String rewriting transforms a string by replacing an occurrence of the left side of a rule $\ell \to r$ with its right side, leaving the surrounding context unchanged. A system may offer several applicable rules or positions, so a reduction need not be deterministic.

For example, $ab\to ba$ changes $aab$ to $aba$ and then $baa$. A system is terminating if no infinite chain of rewrites exists; it is confluent if any two results reached from the same string can be rewritten to a common result. Together these properties give a unique irreducible normal form. This is useful for deciding equality in algebraic presentations and for implementing symbolic simplification.

A cyclic rotation of a string $xy$ is the string $yx$, where $x$ and $y$ are consecutive pieces. For example, rotating ABC left once gives BCA. A length-$n$ string has $n$ rotation positions, though repeated letters can make some resulting strings identical.

A string suffix consists of all characters from some position to the end of a string. For example, TAC has suffixes TAC, AC, C and the empty string. Sorting these in lexicographic order groups all suffixes beginning with a given query into one interval.

Persistence of a response state within an individual after the initial stimulus has ended, distinguished from inheritance through reproduction.

HSFA2 is a heat-shock transcriptional regulator involved in sustained stress responses in Arabidopsis thaliana. Its role in somatic stress memory can outlast its direct occupancy of target regions.

Experiments found transient association of HSFA2 with memory-related loci together with longer-lasting histone methylation and altered responses to a subsequent heat exposure. The distinction between the initial response and later memory is crucial: HSFA2 dependence of the latter does not imply dependence of every immediate heat response.^[ref]

The fractional change in the length of a material line in a specified direction. For infinitesimal deformation with unit direction $\mathbf{n}$, it is $\mathbf{n}\cdot \mathbf{\epsilon }\mathbf{n}$, where $\mathbf{\epsilon }$ is the small strain tensor.

A nonzero vector $d$ is a direction vector of a line if the line has a parametrization $r=p+td$, $t\in \mathbb{R}$, for some point $p$. Replacing $d$ by a nonzero scalar multiple describes the same line; dividing by its Euclidean norm gives a unit vector in one of the two orientations. A cross product of two nonparallel normal vectors supplies a direction vector for the intersection of their planes.

The viscous penetration depth is the distance over which a time-periodic shear velocity driven by an oscillating boundary decays by $1/e$ in a semi-infinite Newtonian fluid. The momentum diffusion equation gives $u=U_0{e}^{-z/\delta }\cos (\omega t-z/\delta )$. Both attenuation and phase lag are controlled by $z/\delta$. The corresponding fluid-displacement amplitude has the same spatial decay, because dividing each velocity amplitude by the common angular frequency does not change their ratio.

In random sequential adsorption, objects are proposed at random positions and accepted only if they do not overlap previously accepted objects. Accepted objects remain fixed; rejected proposals change nothing. In one dimension, sequentially placing fixed-length intervals on a line models irreversible parking. A jammed configuration admits no further allowed placement but need not cover the entire line: leftover gaps can be too small to fit another interval. The acceptance rule creates dependence between locations, so the final configuration is not a collection of independent random placements. This provides a simple model for irreversible surface deposition.

The unsigned Stirling number of the first kind $c(n,k)$ is the number of permutations on $n$ labels with $k$ disjoint permutation cycles. It satisfieswith impossible indices giving zero. Either label $n$ forms its own cycle, or it is inserted immediately after one of the $n-1$ old labels in an existing cycle; deleting $n$ reverses either construction. Thus $c(4,2)=c(3,1)+3c(3,2)=2+9=11$. The same recurrence relation gives the coefficient identity $x(x+1)\cdots (x+n-1)={\sum }_{k}c(n,k)x^k$.

Eliminating a common far-detuned intermediate state with single-photon couplings $\hslash {\Omega }_1/2$ and $\hslash {\Omega }_2/2$ gives effective Rabi angular frequency of magnitude $|{\Omega }_1{\Omega }_2|/(2|\Delta |)$. The complex laser phases set the coupling phase, and differential AC Stark shifts change the two-photon resonance.

The creation-operator matrix element $⟨n+1|a^{†}|n⟩=\sqrt{n+1}$ makes emission into a radiation mode proportional to $n+1$. The $n$ part is stimulated emission and the remaining part is spontaneous emission. Absorption has the corresponding occupation factor $n$.