length

SearchAdvancedHelp

(0.001 seconds)

11—19 of 19 matching pages

11: 28.33 Physical Applications

… ►We shall derive solutions to the uniform, homogeneous, loss-free, and stretched elliptical ring membrane with mass $\rho$ per unit area, and radial tension $\tau$ per unit arc length. … ►If the parameters of a physical system vary periodically with time, then the question of stability arises, for example, a mathematical pendulum whose length varies as $\cos \left(2\omega t\right)$. …

12: 21.9 Integrable Equations

… ►Particularly important for the use of Riemann theta functions is the Kadomtsev–Petviashvili (KP) equation, which describes the propagation of two-dimensional, long-wave length surface waves in shallow water (Ablowitz and Segur (1981, Chapter 4)): …

13: 19.24 Inequalities

… ►Approximations and one-sided inequalities for $R_G(0,y,z)$ follow from those given in §19.9(i) for the length $L(a,b)$ of an ellipse with semiaxes $a$ and $b$, since ►

19.24.7 $$L(a,b)=8R_G(0,a^2,b^2).$$

ⓘ

Symbols:

$R_G(x,y,z)$: symmetric elliptic integral of second kind and $L(a,b)$: length

Permalink:

http://dlmf.nist.gov/19.24.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §19.24(i), §19.24 and Ch.19

…

14: 1.2 Elementary Algebra

… ►A column vector of length $n$ is an $n\times 1$ matrix …and the corresponding transposed row vector of length $n$ is … ►Column vectors $𝐮$ and $𝐯$ of the same length $n$ have a scalar product … ►Special cases are the Euclidean length or $l^2$ norm … ►Unless otherwise indicated, matrices are assumed square, of order $n$; and, when vectors are combined with them, these are of length $n$. …

15: 34.4 Definition: $\mathit{6}j$ Symbol

… ►Except in degenerate cases the combination of the triangle inequalities for the four $\mathit{3}j$ symbols in (34.4.1) is equivalent to the existence of a tetrahedron (possibly degenerate) with edges of lengths $j_1,j_2,j_3,l_1,l_2,l_3$; see Figure 34.4.1. …

16: 1.6 Vectors and Vector-Valued Functions

… ►then the length of a path for $a\le t\le b$ is …

17: Bibliography B

… ►

On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (4), pp. 1119–1178.

ⓘ

External Links:

ISSN 0894-0347, FullText, MathReview (David J. Aldous), ZentralBlatt

Referenced by:

§32.14.

Encodings:

BibTeX

… ►

A monotonicity property involving ${}_3{}^{}F_2^{}$ and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2), pp. 403–419.

ⓘ

External Links:

ISSN 1095-7154, Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§19.9(i), §19.9(i).

Encodings:

BibTeX

…

18: 1.4 Calculus of One Variable

… ►For historical reasons, $w(x)$ is also sometimes referred to as a density, as, for example, the mass per unit length at point $x$, see Shohat and Tamarkin (1970, p vii). …

19: 18.39 Applications in the Physical Sciences

… ►Thus the overall degeneracy of the solutions (18.39.29) (the number of independent eigenfunctions corresponding to a single eigenvalue (18.39.31) for all values of $l$ and $m_l$) consistent with each $n$ is $n^2$, which controls the lengths of the rows in the Periodic Table. …