The phrase "a basis is given" is correct and usable in written English.
It can be used in contexts where you are indicating that a foundation or starting point has been established for a discussion, argument, or analysis.
Example: "In this research paper, a basis is given for understanding the impact of climate change on biodiversity."
Alternatives: "a foundation is provided" or "a premise is established."
The dimension of the polynomial ring F[x] introduced above is countably infinite, a basis is given by,,, A fortiori, the dimension of more general function spaces, such as the space of functions on some (bounded or unbounded) interval, is infinite.
> -wrap-foot> A detailed summary of site-based and overall analysis on a lesion basis is given in Table 2. Of all 593 detected lesions, PET identified 381 (64%) true-positive lesions, CT 482 (81%), PET/CT 545 (92%) and wbMRI 540 (91%).
The pie chart showing the world consumption of corrosion inhibitors on a value basis is given in Figure 13[63].
Each organization interested in receiving data on a regular basis is given the opportunity to use the data upon request to the Ministry for the Interior.
A more appropriate basis is given by the Prolate Spheroidal Wave functions (PSWFs) [15].
(It is noteworthy that in Laws, the principal speaker an unnamed visitor from Athens proposes that laws should be accompanied by "preludes" in which their philosophical basis is given as full an explanation as possible.
A suggestion how to represent perceptual memory computationally with respect to its neuro-cognitive basis is given in Section 4. For facilitating perception and resolving ambiguous perceptual information, knowledge stored in the semantic memory is needed.
The scientific basis is given by applying the concept of visual variables described in the scientific discipline of information visualization.
In our example, the maximal incoherence associated to the Fourier basis is given by the canonical or spike basis φ k (t) = δ(t -- k).
