...p">[5]</TD> <TD valign="top"> L. Hörmander, "An introduction to complex analysis in several variables" , North-Holland (1973)</TD></TR></table>
6 KB (880 words) - 16:10, 1 April 2020
...e manifold gives, for a sufficiently smooth manifold, the largest possible global degree of smoothness of the function which is obtained as a result of exten
...ns of several variables and imbedding theorems" S.M. Nikol'skii (ed.) , ''Analysis III'' , ''Encycl. Math. Sci.'' , '''26''' , Springer (1990) pp. 1–140
9 KB (1,435 words) - 08:13, 13 January 2024
...D valign="top">[3]</TD> <TD valign="top"> R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980)</TD></TR><TR><TD valign="top">[4]<
4 KB (681 words) - 03:41, 21 March 2022
If the problem satisfies the global contractivity condition
...having the same sign. This result can be used in the asymptotic stability analysis of Runge–Kutta methods, see [[#References|[a5]]].
9 KB (1,275 words) - 17:43, 1 July 2020
...submersions" , ''Lecture Notes'' , '''40''' , Research Inst. Math., Global Analysis Research Center, Seoul Nat. Univ. (1998)</td></tr><tr><td valign="top">[a5
5 KB (681 words) - 17:43, 1 July 2020
...ighest order) are minimized. However, since the relation between the true (global) error and the local error is generally not known, it is questionable wheth
...D valign="top">[a1]</TD> <TD valign="top"> J.C. Butcher, "The numerical analysis of ordinary differential equations. Runge–Kutta and general linear method
7 KB (1,053 words) - 17:13, 14 February 2020
...ions of representation and approximation of functions, and their local and global properties. The modern theory of functions of a real variable typically inv
...n urgent need for a new critical review of the foundations of mathematical analysis, which was carried out at the end of the 19th century and beginning of the
11 KB (1,738 words) - 18:15, 24 March 2018
...ing analytic set in a local model (cf. [[Analytic set|Analytic set]]). The global dimension is defined by the formula:
The theory of analytic spaces has two aspects: the local and the global aspect. Local analytic geometry is concerned with germs of analytic sets in
22 KB (3,277 words) - 01:53, 19 January 2022
...ion is useful when some functions are not differentiable. Using non-smooth analysis, one can replace derivatives by other objects such as subgradients (see, e.
...0\right\}$. Here $f^0(\theta)=0$ for any $\theta$, hence $\theta^*=0$ is a global minimum. The saddle-point condition requires $U_1=U_1(\theta)\geq 0$ such t
16 KB (2,514 words) - 17:28, 23 October 2017
...ed only for convex and related unimodal functions. The theory of finding a global extremum is still (1989) in the initial phase of development (see [[Multi-e
.../TD> <TD valign="top"> Yu.G. Evtushenko, "Numerical methods for finding global extrema (case of a non-uniform mesh)" ''USSR Comp. Math. Math. Phys.'' , '
13 KB (1,911 words) - 08:00, 6 June 2020
Global stability of the trivial solution of a non-linear system of ordinary differ
then one has global exponential stability:
16 KB (2,300 words) - 08:22, 6 June 2020
...ithms and programs for the computer realization of the discrete models, an analysis of the sensitivity of the model to variations of the parameters, an estimat
...ng of [[Time series|time series]] on a network of measurements, space-time analysis and the compatibility of meteorological fields), and also the use of method
15 KB (2,159 words) - 17:08, 7 February 2011
Another global construction of the Weil bundles on all manifolds $M$ is due to A. Morimoto
...lign="top"> P.W. Michor, A. Kriegl, "The convenient setting of global analysis" , ''Math. Surveys Monogr.'' , '''53''' , Amer. Math. Soc. (1997)</td></tr
12 KB (1,876 words) - 06:30, 15 February 2024
...al structure ( "the very same as Rn" ), this idea admits a whole series of global features typical for manifolds: (non-) orientability, homological [[Poincar
...ion|Morse function]]), etc., which are used for the geometric study of the global structure of manifolds, and, roughly speaking, consist of constructing a po
30 KB (4,462 words) - 07:59, 6 June 2020
briefly, Morse theory 1) is divided into two parts: local and global. The local part is related to the idea of a critical point of a smooth func
The basic results in global Morse theory are as follows. Let $ f $
21 KB (3,095 words) - 08:01, 6 June 2020
...face of any rough plate (see [[#References|[2]]]). In the investigation of global atmospheric processes on an Earth scale, the field of ground pressure and o
...fand, N.Ya. Vilenkin, "Generalized functions. Applications of harmonic analysis" , '''4''' , Acad. Press (1964) (Translated from Russian)</TD></TR><TR><T
9 KB (1,319 words) - 08:09, 6 June 2020
...="top">[3]</TD> <TD valign="top"> B.V. Shabat, "Introduction of complex analysis" , '''1–2''' , Moscow (1976) (In Russian)</TD></TR></table>
...D></TR><TR><TD valign="top">[a7]</TD> <TD valign="top"> S.G. Gindikin, "Analysis on homogeneous domains" ''Russian Math. Surveys'' , '''19''' (1964) pp.
10 KB (1,514 words) - 07:41, 26 March 2023
be a finite-dimensional smooth manifold. Tangent spaces and such provide the global analogues of differential calculus. There is also an "integral calculus on
...nifolds and calculus on manifolds" W. Schiehlen (ed.) W. Wedig (ed.) , ''Analysis and estimation of stochastic mechanical systems'' , Springer (Wien) (1988)
6 KB (827 words) - 22:13, 5 June 2020
...lude numerical integration, optimal recovery (approximation) of functions, global optimization, and solution of integral equations and partial differential e
...average-case setting (see [[Bayesian numerical analysis|Bayesian numerical analysis]]).
12 KB (1,706 words) - 20:29, 9 December 2023
cf. [[Tensor analysis|Tensor analysis]]) on a [[Manifold|manifold]] $ M $
.../TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A. Lichnerowicz, "Global theory of connections and holonomy groups" , Noordhoff (1976) (Translated f
8 KB (1,160 words) - 08:05, 6 June 2020