Preferential activation of one receptor-linked response relative to another, defined against a reference ligand and appropriate system controls. Different amplification or receptor reserve can mimic apparent bias.^[ref]

The capacity of a signalling system to produce a maximal response without occupancy or activation of all receptors. It makes observed maximal response an unreliable direct measure of intrinsic ligand efficacy.

A protein family involved in regulation and signalling of activated receptors; recruitment can alter receptor coupling and trafficking.

A Gα family member that activates phospholipase C signalling.

The resulting cleavage of a membrane phosphoinositide generates inositol trisphosphate and diacylglycerol. These products can engage calcium release and kinase regulation in different cellular locations, so one receptor can initiate several coordinated downstream effects. ^[ref]

A Gα family member that can stimulate adenylyl cyclase.

Receptor-promoted nucleotide exchange helps activate the switch, and GTP hydrolysis contributes to termination. Increased cyclic AMP then regulates effectors such as protein kinase A, turning a cell-surface recognition event into intracellular phosphorylation. ^[ref]

A Gα family member that can inhibit adenylyl cyclase.

The GDP/GTP cycle changes its interaction with receptors, beta-gamma subunits and effectors. Inhibition of adenylyl cyclase is a common family property, while the resulting cellular response also depends on other targets and local cyclic AMP breakdown. ^[ref]

The prime signature of $n={\prod }_{i=1}^r{p}_i^{a_i}$ is the multiset of positive prime exponents $a_i$, conventionally sorted. For example, $12=2^2\cdot 3$ and $45=3^2\cdot 5$ both have signature $(2,1)$. Quantities such as the divisor function and the number of ordered factorizations depend on this signature rather than the particular primes.

A real function on an interval is unimodal if there is a point $m$ such that it is nondecreasing to the left of $m$ and nonincreasing to the right. This convention describes a single peak and allows flat regions. Some optimization texts instead use the corresponding single-valley convention, so the direction must be specified.

For example, $f(x)=-(x-2{)}^2$ has its peak at $2$. A unimodal density can describe a distribution with one mode, while unimodality of an objective allows interval-elimination search methods. Concavity implies peak unimodality, but unimodality alone does not require the chord inequalities of concavity.

An integer-valued function is a function whose values all lie in $\mathbb{Z}$, even if its input domain is not discrete. For example, the floor function $x\mapsto \lfloor x\rfloor$ maps $\mathbb{R}$ to $\mathbb{Z}$, while the prime-counting function assigns an integer to every real bound.

A polynomial can be integer-valued on integers without having integer coefficients: $x(x-1)/2$ takes integer values for every $x\in \mathbb{Z}$. Its behavior is specified by both its formula and its input domain. On a connected topological SPACE, a continuous integer-valued function is constant, because distinct integer values are separated by open gaps.

For real atomic scattering factors, $F(-\mathbf{h})=F(\mathbf{h}{)}^{\ast }$ and $I(-\mathbf{h})=I(\mathbf{h})$.

Friedel-Crafts acylation attaches an acyl group to an aromatic carbon through electrophilic substitution. Lewis-acid activation of an acyl chloride is often represented by an acylium ion or strongly polarized contact pair.

electrophilic aromatic substitution that installs an alkyl group on an aromatic ring.

A lubricant is a substance introduced between contacting surfaces to reduce resistance to relative motion, wear or both. In fluid-film operation, the surfaces are separated by a layer whose viscous stress transmits the load and motion. A converging gap can generate lubrication pressure that supports a normal load while the solids remain apart.

When the film is too thin to prevent microscopic contact, surface interactions also matter; a low-viscosity fluid alone does not guarantee low friction. A simple comparison is to slide a loaded block over the same surface before and after applying a controlled film and measure the required tangential force. Changing load, speed and temperature can change the operating regime. The lubricant still dissipates mechanical energy through shearing and other losses, so reduced dry contact does not imply zero resistance.

The dimensionless ratio between an appropriate tangential friction force and normal load in a specified contact model. Static limiting and sliding coefficients differ, and nanoscale adhesion can invalidate a simple load-independent ratio.

A concentric diffractive focusing element with successive zone boundaries chosen to differ by half a wavelength of optical path to a focus. Alternating transmitting and absorbing zones suppress cancellation between neighboring half-period zones. For an incident plane wave, the paraxial boundaries satisfy $r_j^2=j\lambda f$. The outermost zone width controls the finest transverse scale, and the focal length varies with wavelength.

A scalar aperture approximation that sums the secondary waves reaching an observation point. For a point source with incident spherical amplitude $A{e}^{iks}/s$, one common forward-normal convention isHere $s$ and $r$ are source-to-aperture and aperture-to-observer distances and $K$ is an obliquity factor. The Fresnel diffraction approximation retains quadratic path phase; Fraunhofer diffraction additionally neglects the quadratic phase across the aperture. Kirchhoff boundary assumptions do not give an exact electromagnetic solution at a sharp edge.

For an opaque half-plane whose edge lies height $h$ above the direct source–receiver ray, the paraxial parameter is $v=h\sqrt{2(d_1+d_2)/(\lambda d_1{d}_2)}$. The unobstructed half-aperture supplies the Cornu spiral chord from $v$ to infinity. Division by the full-aperture chord gives the displayed intensity transmission. It is $1/4$ at grazing incidence, approaches one well into the illuminated region and tends to zero deep in shadow.^[ref]

For the classical monatomic caloric model, energy conservation in expansion from $V_i$ to $V_f$ gives $T_f-T_i=2aN(1/V_f-1/V_i)/(3k_B)$. Attractions make the gas cool. The formula assumes homogeneous equilibrium states, not a two-phase coexistence state.