The phrase "and generalized by" is correct and usable in written English.
It can be used when discussing concepts, theories, or findings that have been broadened or applied to a wider context or group.
Example: "The results of the study were specific to a small population but were later generalized by researchers to apply to a larger demographic."
Alternatives: "and applied broadly" or "and extended to".
Quaternions were introduced by Hamilton [1] in 1843 and generalized by Clifford [2] in 1873.
The Dempster-Shafer (D-S) theory was developed by Arthur P. Dempster [27] and generalized by Glenn Shafer [28].
The so-called "replicator dynamics" were named by Taylor and Jonker (1978) and generalized by Schuster and Sigmund (1983) and Hofbauer and Sigmund (1988).
This relationship was first explored by Daudet [22] for the sine window case and generalized by Zhang [25] to other window cases.
This method is based on Simon's technique of harmonic approximation ([30]) and generalized by Duzaar and Grotowski in [31] in order to deal with partial regularity for nonlinear elliptic systems.
The vertical distribution of the particle mass in the column is parameterized according to Suzuki (1983), assuming a shape coefficient of 4. This parameterization was subsequently adopted, among others, by Armienti et al. (1988); Macedonio et al. (2005) and generalized by Pfeiffer et al. (2005).
A fan-in value, which is the number of unique callers of each method/function, was first introduced by Marin and others [7] and further generalized by Zhang and others [29] to propose clustering-based fan-in analysis (CBFA).
Then, we have chosen the urokinase structure (1SQO protein from the PDB [ 66]) for subsequent calculations: docking by the SOL program, postprocessing by the DISCORE program, quantum chemistry calculations by the MOPAC package, and generalized docking by the FLM program.
The aim of the present paper is to establish the stability problem of homomorphisms and generalized -derivations by using the fixed point method (see [7, 33 35]).
From then on, investigations have been carried out to obtain better and generalized versions by weakening contraction condition and analyzing connectivity of a graph (see [9 11]).
The solution is a combination of the eigenvectors and generalized eigenvectors multiplied by functions of the out-of-plane coordinate z.
