The phrase "achieved by a number of" is correct and usable in written English.
It can be used when discussing the methods or processes through which a particular result or outcome has been obtained, often in a formal or academic context.
Example: "The improvements in efficiency were achieved by a number of innovative strategies implemented over the past year."
Alternatives: "accomplished through several" or "realized by various".
Neovascularization in situ can be achieved by a number of methods.
Not a single low-income country met the target, which was achieved by a number of high-income countries before the MDGs were introduced.
This can be achieved by a number of mechanisms: stem cell asymmetric division maintains stem cell numbers; stem cell symmetric division increases them; maintenance of a stem cell niche maintains the conditions for commitment to the stem cell fate for some types of stem cell; stem cells may arise de novo from other cell types.
That the show doesn't play out like an overheated comic book is partly due to the talent of its creator and writer, Neil Cross, for hard-boiled dialogue and creepy, clever scenes of psychotic mayhem, and partly to the artful depiction of a harsh, dystopian modern London achieved by a number of directors and cinematographers under the production design of Paul Cross.
The best individual is eventually achieved by a number of evolution steps (generations).
This process includes overcoming the resistance of the receiving culture or theory, which may be achieved by a number of strategies of "normalization" that Goffman, for instance, deftly demonstrates in his development of the concept of "face-work".
Furthermore a simple scale-up can be achieved by a numbering-up of droplets.
Validation of the derived analytic results and the proposed numerical procedure is achieved by studying a number of theoretical examples.
Validation of the derived simple solution set and the proposed procedure to generate further sets is achieved by studying a number of theoretical examples.
The optimisation of the structural modes of the panel is then achieved by placing a number of constraint masses and stiffeners of optimum size and weight at optimum locations on the plate.
These different results are achieved by changing a number of parameters in the dielectrophoresis process and the SWNT samples.
