A discrete molecular assembly in which metal–ligand connections surround a cavity. coordination number, preferred binding angles and ligand connectivity restrict possible cage stoichiometries.

A five-coordinate geometry with two axial and three equatorial positions. The ideal geometry has a threefold axis and an equatorial mirror plane.

The spatial arrangement of donor atoms around a central atom. coordination number counts neighbours but does not by itself distinguish geometries with the same number of donors.

Formation of a coordination complex through association of a central chemical atom or ion with donor groups. Different oxidation states can have different complex stabilities, coupling complexation to redox equilibrium.

A material carrying heat from a reactor core. heat capacity, transport properties, chemical compatibility, neutron interactions and stability must be considered together.

First author: Paolo Ferragina.

Author-hosted preprint: people.unipmn.it/manzini/papers/focs00draft.pdf

Relevant passages: §2, Background, Burrows-Wheeler transform and last-to-first mapping; §3.1, Figure 1, counting occurrences by backward search; §3.2, locating occurrences.

A color model describes colors using numerical components and rules for interpreting them. RGB uses red, green and blue components for additive representations; a subtractive printing model instead describes how colorants affect reflected light. A model alone does not fully define a reproducible color: a color space also specifies reference primaries, white point and transfer functions as needed. Consequently the same RGB triple can produce different colors on different uncalibrated devices. This distinction is essential when converting images between displays, files and physical prints.

A small longitudinal electric field drives conductor current in a lossy coaxial line. Its cross product with the azimuthal magnetic field sends energy radially into both conductors, where it becomes heat; forward power decreases with distance.

Immobilized metal affinity chromatography retains suitable ligands, including polyhistidine-tagged proteins, on a stationary phase bearing coordinated metal ions. Contaminants can also bind, so affinity recovery alone does not establish purity or identity.

Ion-exchange chromatography separates molecules by interactions with a charged stationary phase. Buffer pH controls charge state, and ionic strength can modulate retention and elution; the relevant charge depends on the whole molecular surface.

protein A affinity chromatography purifies suitable immunoglobulins through interaction with immobilized protein A. Binding and elution conditions, aggregation and process-related contaminants still require separate control.

Chiral chromatography separates enantiomers using a chiral environment, usually a chiral stationary phase. The two enantiomers form transient diastereomeric interactions with that environment and can therefore have different retention.

An ordinary achiral separation often cannot distinguish enantiomers because their bulk properties are identical in an achiral environment. A successful chiral chromatogram can measure an enantiomer ratio, provided the peaks are resolved and detector responses are interpreted correctly. Peak order alone does not establish absolute configuration without an external assignment.

Gas chromatography separates compounds carried by a gaseous mobile phase through a stationary phase. Components partition differently between the flowing gas and the stationary material, producing different retention times.

Analytes must enter the gas phase without unacceptable decomposition under the measurement conditions. For example, a volatile organic mixture can be separated before mass spectrometry identifies the eluting components. Retention depends on temperature and column chemistry, so boiling point alone does not uniquely determine the elution order.

A refractive index detector measures the difference in refractive index between a sample stream and a reference. In liquid chromatography, a solute passing through the detector can change that difference and produce a signal.

The signal depends on both solute concentration and the solute's refractive-index increment relative to the solvent. Temperature drift or changing mobile-phase composition can also shift the baseline, so a peak is not automatically a substance-specific identification.

Garner's algorithm solves a system $x\equiv a_i(\mathrm{mod}{m}_i)$ for pairwise coprime moduli by constructing a mixed-radix expansionAfter fixing earlier digits, let $P_i={\prod }_{j<i}{m}_j$ and $s_i={\sum }_{j<i}{c}_j{P}_j$. The next digit is $c_i\equiv (a_i-s_i)P_i^{-1}(\mathrm{mod}{m}_i)$. Coprimality ensures that the modular inverse exists.

For $x\equiv 2(\mathrm{mod}3)$, $x\equiv 3(\mathrm{mod}5)$, $c_0=2$ and $c_1\equiv (3-2)3^{-1}\equiv 2(\mathrm{mod}5)$, giving $x=8$ modulo fifteen. The mixed-radix form constructs the Chinese remainder theorem solution incrementally.

Publisher: doi.org/10.1038/353239a0

Authors' institutional record: researchportalplus.anu.edu.au/en/publications/direct-measurement-of-colloidal-forces-using-an-atomic-force-micr/

The gas-phase fundamental entries include C=O stretch $1746$, symmetric C–H stretch $2783$, antisymmetric C–H stretch $2843$, and wag $1167\mathrm{c}{\mathrm{m}}^{-1}$, with the $C_{2v}$ labels used in the exam. The listed fundamentals provide an independent assignment check, rather than a solution source.

Institutional experimental account: www.nist.gov/pml/photoionization-co2-arpes/photoionization-co2-experimental-procedure

Cited material: state-resolved measurements leaving the carbon-dioxide cation in its $X{}^2{\Pi }_g$ electronic ground state.