Sentence examples for elementary theoretical from inspiring English sources

Furthermore, an elementary theoretical analysis shows that this map φ can preserve many structure-preserving properties, such as the order, the symmetry and the symplecticity.

An elementary number theoretical argument and Lemma 1 yield that p | m ( m + 1 ) and ord p ( 1 p + 2 p + ⋯ + m p m 2 ( m + 1 ) 2 ) = ord p B p + 1 ( m + 1 ) − B p + 1 m 2 ( m + 1 ) 2 ≠ 0. Suppose that p | m, and let d be the smallest positive integer such that B p + 1 ( m + 1 ) − B p + 1 = 1 d f ( m ) m 2 ( m + 1 ) 2, and let f ( X ) ∈ Z [ X ].

Polkinghorne received an additional doctorate in theoretical elementary particle physics from Trinity College in 1974.

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics.

The choice of the species to be eliminated and of the reactions to be aggregated, as well as the calculation of rates of elementary modes have no theoretical justification in these methods and their inappropriate use can alter dynamics (for instance, as Clarke noticed, the stability of limit cycles is not guaranteed).

He was also director of the Laboratory of Theoretical Physics and Elementary Particles at Paris-Sud.

In fact, all the derivations are based on the theoretical expression of the elementary cross-covariances, Σ y (i,l), given in (5) although in practice these elementary cross-covariances are estimated by sample averaging as follows: begin{array}rcl@ widehat{Sigma}_{boldsymbol{y}}(i,l)~=~frac{1}{N}sumlimits_{n=1}^{N}y_{i}(n y_{l}^{H}(n), end{array} (25).

Central to this endeavor is the theoretical construct of an elementary functional neuronal unit above the level of individual neurons and below that of whole brain areas and systems: the distributed neuronal assembly (DNA) or thought circuit (TC).

A number of elementary tests validate the numerical output with theoretical results and the de facto standard in-plane shear test of picture frame has also been validated numerically.

This theoretical model is validated with elementary-aged students and used to investigate whether students' quantitative literacy is related to the use of the Investigations curriculum.

When Dalton spoke of elementary atoms, he did not have a merely theoretical idea in mind but the chemical elements as determined by Lavoisier.