A mechanism in which helping a persistent partner improves the actor’s later direct returns through that partner’s survival or productivity, without requiring an explicit repayment rule.

Information about an individual’s past behaviour that can alter its later interactions, including interactions with different partners. Reputation-based explanations require a mechanism for acquiring and using that information.

Discrimination among potential or previous partners. Repeat interactions support partner-specific responses only if the relevant information can be retained or reliably associated with a location.

A resource or service whose effects can benefit others as well as its producer. The spatial scale of benefits, production cost and competitive setting determine exploitation incentives.

The normal contact force is the component of a contact force perpendicular to the local contact surface. If $\mathbf{n}$ is the outward unit normal vector, a nonadhesive support exerts $N\mathbf{n}$ with $N\ge 0$; the remaining tangential component is associated with friction. Over an extended patch, the resultant follows by integrating the local contact pressure and allowing for changes in normal vector.

For a block at rest on a horizontal table with no other vertical loads, Newton's second law gives $N=mg$. On a stationary incline it gives $N=mg\cos \theta$, while in an accelerating lift $N$ changes with the lift's acceleration. Thus the normal contact force is a response required by the mechanical constraint, not an independently fixed multiple of mass. If maintaining contact would require a negative $N$ in a nonadhesive model, the bodies separate.

The tensile force magnitude needed to detach contacting surfaces during retraction. A force-probe measurement reads it from the force minimum relative to the noncontact baseline; roughness, capillary forces and contact geometry affect its interpretation.

Adhesion is attraction between different surfaces that can keep them attached after a compressive contact load is removed. It can arise from intermolecular forces or other interfacial interactions; a liquid bridge can also contribute a capillary force. The work needed to reversibly separate a unit area is an interfacial energy, whereas the measured pull-off force depends additionally on geometry and elastic deformation.

Pressing a spherical probe onto a specimen and then retracting it provides a direct test. Contact may persist while the apparatus reads a tensile force; detachment occurs only when that adhesive contact becomes unstable. Hertzian contact cannot describe this tensile branch because it neglects adhesion. Surface contamination, roughness and humidity can change a measurement even when the bulk Young's modulus stays fixed. This makes preparation of the interface as important as calibration of the force probe when comparing adhesive response.

An adhesive sphere-on-flat contact approximation combining Hertzian contact deformation with an attractive force outside the contact area. It is most appropriate for sufficiently stiff, small-radius contacts with a small Tabor parameter; a fitted reduced modulus is not automatically the sample Young's modulus.

A dimensionless measure comparing adhesive interaction range with elastic deformation in sphere contact. Small values favour the DMT contact approximation, while large values favour the JKR limit.

Hertzian contact is the small-contact solution for smooth bodies obeying linear elasticity, with friction and adhesion neglected. For a sphere of radius $R$ pressed into a flat surface by indentation $\delta$, the contact radius $a$ and compressive normal contact force $F$ satisfyThe reduced elastic modulus $E^{\ast }$ includes both bodies. The contact pressure is largest at the centre and falls to zero at the edge:These formulas describe an ideal contact patch, rather than a uniformly loaded disk.^[ref]

The increasing contact area explains the nonlinear load law even though the material itself obeys linear elasticity. In a probe experiment, $F^{2/3}$ should be proportional to $\delta$ in the Hertzian regime. Systematic departures can signal adhesion, plastic deformation, a thin specimen or a contact patch too large for the assumed local geometry.

The reduced elastic modulus combines the elastic compliance of two contacting isotropic bodies:Here $E_i$ is each body's Young's modulus and ${\nu }_i$ its Poisson's ratio. Both bodies deform under the same contact load, so their contributions to the indentation add. The factors involving Poisson's ratio account for the lateral constraint inherent in the local contact geometry.^[ref]

For identical materials, $E^{\ast }=E/[2(1-{\nu }^2)]$; against an effectively rigid probe, $E^{\ast }=E/(1-{\nu }^2)$ for the specimen. Thus even with a rigid probe, an indentation fit does not directly return Young's modulus. This matters when comparing Hertzian contact measurements with tensile testing, which imposes a different pattern of stress.

An antiperiplanar conformation places two specified bonds in approximately the same plane with a dihedral angle of $180^{\circ }$. The designation concerns those particular bonds, not the planarity of the entire molecule.

In many E2 elimination reactions, the carbon-hydrogen bond being broken and the carbon-leaving-group bond align antiperiplanar. This arrangement supports the orbital overlap required to form the new pi bond. In a cyclohexane chair, the condition often requires a trans-diaxial pair, linking conformational geometry directly to which elimination pathway is accessible.

The chair conformation is a low-energy nonplanar arrangement of the six-membered cyclohexane ring. Its carbon-carbon bonds are approximately staggered and its bond angles remain close to tetrahedral values, reducing torsional and angle strain.

Each ring carbon has one axial and one equatorial substituent position. A ring flip exchanges these positions while retaining whether each substituent points to the same or opposite side of the ring. Bulky substituents commonly prefer equatorial positions because this reduces unfavorable 1,3-diaxial interactions, making chair analysis useful for predicting conformational populations and reaction geometry.^[ref]

Ring inversion interconverts ring conformations while preserving covalent connectivity and configurational stereochemistry. In a cyclohexane chair flip, axial and equatorial labels exchange, while the up/down face of a given substituent is retained.

A gauche interaction concerns groups separated by an approximately $60^{\circ }$ torsion about a bond. Its energetic effect depends on the groups and electronic environment; not every gauche geometry is unfavorable.

Antiperiplanar geometry places two specified bonds at a torsion near $180^{\circ }$. It often enables favorable orbital alignment in E2 elimination and supports large vicinal proton couplings in an appropriate calibrated Karplus relation.

An electrical scanning-probe technique measuring resistance associated with current spreading from a small probe contact into a specimen. Inferring carrier concentration or conductivity requires appropriate contact conditions and calibration.

The kinetic energy selected in the hemispherical analysing field, distinguished from the kinetic energy before retarding entrance optics. At fixed geometry the absolute instrumental energy width is approximately proportional to pass energy.

The ratio of electron kinetic energy before retardation to hemispherical pass energy. This definition should be stated because a voltage-to-pass-energy ratio differs by one.

A cell comparing oxygen chemical potentials across an oxygen-ion-conducting electrolyte. With oxide-ion conduction and four electrons transferred per oxygen molecule, $E=RT\ln (p_2/p_1)/(4F)$ for consistently ordered terminals. Reference pressure, interface equilibrium and electronic leakage must be controlled.