Asymptotic stability of the polynomial or dynamical system is strongly
which can be directly used in asymptotic stability investigations for
4 KB (607 words) - 02:33, 14 September 2022
...progression]] with denominator $q$, while the value $-\ln q$ is called the asymptotic rate of convergence.
...gn="top">[1]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
2 KB (287 words) - 12:05, 13 August 2014
A method for formally finding high-frequency asymptotic approximations of solutions of problems in the theory of diffraction and pr
...lied and one must use more complicated expansions, for example some unique asymptotic approximation or some version of the boundary-layer method (the most import
7 KB (1,036 words) - 05:39, 19 March 2022
denotes the asymptotic variance of an estimator $ T $
on (the asymptotic version of) the estimator $ T $.
5 KB (759 words) - 08:12, 6 June 2020
relations, asymptotic relations''
All formulas of the above type are called asymptotic estimates; they are especially interesting for infinitely-small and infinit
5 KB (805 words) - 17:44, 31 March 2020
Asymptotic expansions have been obtained. The case where the functions $ f $
There is also an asymptotic series for $ V _ {x ^ {0} } ( \lambda ) $ (for the formulas of the cont
8 KB (1,104 words) - 08:08, 4 March 2022
By the analysis of E. Wigner [[#References|[a2]]], [[#References|[a3]]], all states which d
...^ { i ( p ^ { 0 } - \omega ) t } \mathcal{F} ( f _ { l } ) )$, one defines asymptotic fields by their action on the vacuum vector $\Omega$:
9 KB (1,385 words) - 20:57, 8 February 2024
...ious properties, and yields solutions the form of which coincides with the asymptotic part of the solutions of transport equations. For improved forms of the dif
...olume of the medium is large. The method has been successfully used in the analysis of the optical fibre oximeter of blood. The use of the so-called Henyey–G
2 KB (336 words) - 17:10, 7 February 2011
...ation form. The area has close connections with statistics and time-series analysis, and also offers a very wide spectrum of applications.
...he random variable $\hat { \theta } _ { N }$. The covariance matrix of the asymptotic (normal) distribution of the estimate takes the typical form
7 KB (1,131 words) - 14:45, 16 December 2023
Viewed from a modern perspective, Karamata theory is the study of asymptotic relations of the form
Perhaps the most important application of Karamata theory to analysis is Karamata's Tauberian theorem (or the Hardy–Littlewood–Karamata theor
6 KB (794 words) - 22:14, 5 June 2020
which is asymptotic for small $ \mu $
...nsitions (5), (6), studies were conducted with the purpose of obtaining an asymptotic expansion of its solution. In the regular case the solution of the initial
18 KB (2,607 words) - 18:34, 5 June 2020
...on spaces $\mathcal{V}$. A further approach uses analytic continuation and asymptotic series of distributions.
...nd D. Laugwitz [[#References|[a10]]] in their foundations of infinitesimal analysis.
12 KB (1,717 words) - 17:43, 1 July 2020
...[#References|[3]]]), in the problem of Hardy and Ramanujan on obtaining an asymptotic formula for the number of "unbounded partitions" of a natural number.
...<TD valign="top"> T.M. Apostol, "Modular functions and Dirichlet series in analysis" , Springer (1976) {{ZBL|0332.10017}}</TD></TR>
2 KB (368 words) - 07:06, 29 March 2024
D. Zagier [[#References|[a5]]] investigated the asymptotic growth for the number of solutions to the Markov equation ($a=n=3$) below a
...</TD> <TD valign="top"> A. Hurwitz, "Über eine Aufgabe der unbestimmten Analysis" ''Archiv. Math. Phys.'' , '''3''' (1907) pp. 185–196 (Also: Mathemat
4 KB (641 words) - 16:51, 14 August 2023
An important question is the asymptotic (for $ \epsilon \rightarrow 0 $)
...as been calculated by A.D. Dorodnitsyn [[#References|[7]]] by constructing asymptotic approximations, for $ \lambda \rightarrow \infty $,
13 KB (1,854 words) - 12:59, 13 January 2024
It can be shown that the asymptotic behaviour as $ N \rightarrow \infty $
...TR><TD valign="top">[3]</TD> <TD valign="top"> T.M. Anderson, "Statistical analysis of time series" , Wiley (1971) {{MR|0283939}} {{ZBL|0225.62108}} </TD></TR>
5 KB (740 words) - 19:58, 16 January 2024
...rized by a Voss net, a [[Ruled surface|ruled surface]] has a semi-geodesic asymptotic net, etc. The theory of nets is closely related to aspects of mapping surfa
...mathematics, physics and mechanics (for example, [[Tensor analysis|tensor analysis]], the [[Cartan method of exterior forms|Cartan method of exterior forms]],
9 KB (1,331 words) - 08:25, 6 June 2020
If the symbol of the given pseudo-differential operator has an asymptotic expansion in positive homogeneous functions $ a _ \alpha ( x, \xi ) $ (
...TR><TR><TD valign="top">[4]</TD> <TD valign="top"> L.V. Hörmander, "The analysis of linear partial differential operators" , '''3''' , Springer (1985)</TD>
3 KB (388 words) - 06:28, 22 February 2022
...plications in survival analysis (cf. also [[Regression analysis|Regression analysis]]).
...]: [[Martingale|Martingale]]), conditions may be given for consistency and asymptotic normality of the estimators $\widehat { \beta }$ and $\widehat { A } ( t |
8 KB (1,222 words) - 07:18, 12 February 2024
...ethod|Schauder method]], as well as other methods of non-linear functional analysis, are applied in investigations of this equation.
Questions of stability of solutions, eigen-function expansions, asymptotic expansions in a small parameter, etc., can be studied for integro-different
5 KB (685 words) - 19:38, 12 January 2024