A covalent inhibitor developed against KRAS G12C protein, also called sotorasib. Its state-dependent binding illustrates targeting a mutant small GTPase outside the nucleotide site.^[ref]

For the sign convention $u_t-6u{u}_x+u_{xxx}=0$ and any $\kappa >0$, the displayed negative solitary wave travels at speed $4{\kappa }^2$. To verify it, put $\xi =x-ct$ and write $u=U(\xi )$. The equation becomes $(-cU-3U^2+U^{\prime \prime }{)}^{\prime }=0$. A decaying profile has zero integration constant, so $U^{\prime \prime }=cU+3U^2$. Direct differentiation of the displayed profile gives $U^{\prime \prime }=4{\kappa }^{2}U+3U^2$, proving the result. Its depth is $2{\kappa }^2$, so narrower and deeper pulses travel faster. Changing the sign of the nonlinear term reverses the amplitude sign. This wave belongs to the soliton family of the Korteweg-De Vries equation.

Summing the Kohn-Sham equations over occupied normalized orbitals yields ${\sum }_i{f}_i{ϵ}_i=T_s+\int nv+2E_H+\int n{v}_{\mathrm{xc}}$. The exact ground-state energy functional is $T_s+\int nv+E_H+E_{\mathrm{xc}}$, so subtraction proves the correction in the title. Nuclear or lattice source self-energies must be added consistently. This accounting does not turn all auxiliary orbital eigenvalues into physical excitation energies.

A Knuth-Morris-Pratt automaton records how much of a fixed pattern matches the suffix of the text seen so far. State $j$ means the longest such prefix has length $j$; reading a symbol moves to the longest compatible prefix state. Reaching state $m$ reports a full length-$m$ match. For pattern aba, state two records suffix ab; reading a completes the match, while reading b falls back to state zero. A dense table for an alphabet of size $R$ uses $O(mR)$ preprocessing and storage, then constant work per text symbol.^[ref]

The number of gas molecules striking unit surface area per unit time. For an ideal gas in thermal equilibrium, $J=P/\sqrt{2\pi m{k}_{B}T}$. A deposited monolayer additionally depends on site density, sticking coefficient and desorption.

For isotropic velocity directions and normalized speed density $f(v)$, the number arriving at a plane per unit area and time is $d\Gamma =\frac{1}{2}nf(v)v\cos \theta \sin \theta d\theta dv$, over the incoming hemisphere. The cosine weights the normal speed, and the sine comes from solid angle.

For a slowly advancing piston in an isotropic gas, multiplying the stationary molecular arrival flux by the first-order energy gain $2mu{v}_x$ gives $dU/dt=pSu=-pdV/dt$. This is the microscopic form of adiabatic compression work. Higher-order terms matter for fast piston motion.

An isotope effect from a retained labeled bond at the reaction centre, often reflecting changes in hybridization and bending vibrations.

An isotope effect from a retained labeled bond adjacent to the reaction centre, often influenced by hyperconjugation and its geometry.

A keratinocyte in the basement-membrane-associated compartment of a stratified epithelium. Basal position does not establish that every such cell is actively dividing.

A Kaprekar constant is a nonzero fixed point of a specified Kaprekar routine, with the base and digit width held fixed. In base ten with four digits, $6174$ is one because $7641-1467=6174$; with three digits, $495$ is one because $954-459=495$.

Leading zeros must be retained during iteration. The familiar four-digit attraction result applies to inputs with at least two distinct digits; strings such as $7777$ go to zero. Other widths or bases can have different fixed points and cycles, so the phrase does not identify a base-independent numerical constant.