Sentence examples for linear notation from inspiring English sources

In this entry we use a linear notation, eschewing superscripts and subscripts.

On this basis, and using an extremely compressed linear notation for proofs which is at the opposite extreme of Frege's space-occupying proofs, Łukasiewicz proves around 140 theorems in a mere 19 pages.

This is a linear notation developed by Daylight Information Systems that describes the connection table of a molecule and may optionally encode chirality.

The merge operation is also used for combining a sentence DRS with the DRS representing the preceding discourse, so the idea is that there is no principled distinction between (clausal) conjunction and sentence concatenation.[2] Officially, DRSs are set-theoretical objects, but in this article we use a linear notation.

In the beginning of a sketcher session, the main page of the sketcher is loaded by the client, where a session ID is transmitted to the server and either an empty structure object is created, a structure object is generated by decoding a linear notation string (e.g., a SMILES, SMARTS, or InChI), or a structure object is pulled directly from a PubChem database subsystem (e.g., by CID).

Since the second half of the 20th century, chemical structure linear notations have become well established as alternative to classical nomenclature.

The encoding examples illustrate the application of CurlySMILES formats and rules to derive linear notations for selected structures including stereoisomers, fragments, ring molecules with delocalized charge, coordination compounds, macromolecules, nanostructures as well as doped and surface-functionalized materials.

Linear algebra notation is sometimes useful for compactness.

By, we denote the range of a map, and for a closed linear operator, the notation represents the domain of endowed with the graph norm,,.

The basic linear mixed model notation was: y = X b + Z a + e where y = vector of phenotypes (TKC, EPG or weight traits), b = vector of fixed effects included in the model, as described previously, X = incidence matrix for fixed effects, a = vector of random animal effects, Z = incidence matrix of random animal effects and e = random residual effects.

The main line is the section between ports 1 and 2 and the coupled line is the section between ports 3 and 4. Since the directional coupler is a linear device, the notations on figure 1 are arbitrary.