Sentence examples for mathematical interpretations are from inspiring English sources

Such mathematical interpretations are not meaning explanations.

The mathematical interpretation is an inherited characteristic from the topology of the system.

(The first argument on mathematical interpretations, above, is essentially the same as this one).

On other, more widespread views, the set of logical truths of a language of that kind can be identified with the set of sentences that are valid across a certain range of mathematical interpretations (where validity is something related to but different from the condition that all the sentences that are replacement instances of its form be true too; see below, section 2.3).

A mathematical expression of this interpretation is the law of large numbers.

While PCA provides a convenient small set of mathematical descriptors of shape, their interpretation is difficult due to the sheer complexity of the shape variation across lines (see Figure S1).

Mao points out that a reasonable mathematical interpretation for the noise is the so-called white noise (dot{B}(t)), which is formally regarded as the derivative of the Brownian motion (B t)), i.e., (dot{B}(t) = dB t)/dt) (see Ref. [6]).

But then A′ cannot be a meaning explanation of A. It would therefore be a mistake to see in mathematical interpretations of intuitionistic systems ways to make the Proof Interpretation "rigorous" or "precise".

Moreover, the shape function and its construction method of a multiscale eigenelement method (MEM) are presented, and the results of SEEM and MEM are compared with that of CEEM and the mathematical homogenization method (MHM) whose physical interpretation is revealed for the first time.

However, this interpretation is based on mathematical derivation and published biological studies in small samples, and not measurements in these national cohorts.

The basic mathematical interpretation of this concept is presented below.