Sentence examples for generalized number from inspiring English sources

The types of number sequences, in order of increasing sophistication, are (1) initial number sequences (INS), (2) tacitly nested number sequences (TNS), (3) explicitly nested number sequences (ENS), and (4) generalized number sequences (GNS).

If we define the so-called generalized number system based on m in the following way: M_{0}:=1,quadquad M_{k+1}:=m_{k}M_{k} quad (kin mathbb{N} ), then every (nin mathbb{N} ) can be uniquely expressed as (n=sum_{j=0}^{infty}n_{j}M_{j}), where (n_{j}in Z_{m_{j}}) ((jin mathbb{N} _)) and only a finite number of the (n_{j}) differ from zero.

To examine the effect of iron deficiency on seizure manifestation/semiology, we compared the type (focal or generalized), number (including recurrences after admission) and duration (proportion with status epilepticus) of seizures in cases with and without iron deficiency.

Generalized number sequence.

In Section 3, we establish some identities involving G n ( k ), the Stirling numbers, the generalized Stirling numbers, the higher order Bernoulli numbers and the Cauchy numbers.

Our results can be applied to any linear recurrence sequences by using a similar method; for example, Lucas numbers, Pell numbers, Horadam numbers, generalized Fibonacci p-numbers.

In the paper, by the Faà di Bruno formula, the authors establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the restricted hexagonal numbers.

By the Faà di Bruno formula and some properties of the Bell polynomials of the second kind, we establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the restricted hexagonal numbers.

For example, we get the bounds for the spectral norms of geometric circulant matrices involving the generalized Fibonacci number and Lucas numbers [10].

Here we aim at presenting further interesting identities about certain interesting finite series associated with binomial coefficients, harmonic numbers and generalized harmonic numbers.

Applying this inverse relation to the identities in Section 2, we obtain many formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers asserted by the following corollary.