...oblems and has opened new possibilities for the application of geometry to analysis. It is Riemannian geometry which was used by A. Einstein to realize the ide
...the development of the geometry of infinite-dimensional manifolds — global analysis.
30 KB (4,323 words) - 19:35, 5 June 2020
...of the subdomains. In spectral methods, the domain is not subdivided, but global basis functions of high order are used. Accuracy is gained by increasing th
...pectral methods are, in general, more complicated to code and require more analysis to be done prior to coding than simpler methods.
9 KB (1,381 words) - 16:55, 1 July 2020
...ed by a system of differential equations such as (1). On the other hand, a global (i.e. suitable for all states of the dynamical system) and invariant (i.e.
...alitative picture of the behaviour of all trajectories in the phase space (global theory) or at least in some part of it (local theory). In the theory of dyn
27 KB (4,058 words) - 19:36, 5 June 2020
...eral content. In its most general meaning it is considered nowadays as the analysis of connections in principal fibre spaces or fibre spaces associated to them
<TR><TD valign="top">[a2]</TD> <TD valign="top"> A. Lichnerowicz, "Global theory of connections and holonomy groups" , Noordhoff (1976) (Translated
7 KB (1,108 words) - 19:43, 13 August 2023
as numerical functions and to apply to them the methods of analysis. In general, the value of a field quantity at a point depends on the choice
...></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> A. Lichnerowicz, "Global theory of connections and holonomy groups" , Noordhoff (1976) (Translated
7 KB (1,075 words) - 16:43, 4 June 2020
.../math> is the projectivization of the kernel of the natural restriction of global sections
...ument is that it implicitly assumes that the restriction <math>r</math> of global sections is ''surjective'', which isn't the case in general.
14 KB (2,200 words) - 18:27, 23 October 2017
...opology was the [[Compact-open topology|compact-open topology]]. A careful analysis of topologies on $\mathcal{C} ( Y , X )$ in relation to the exponential law
...lign="top"> A. Kriegl, P.W. Michor, "The convenient setting of global analysis" , ''Math. Surveys and Monographs'' , '''53''' , Amer. Math. Soc. (1997)</
10 KB (1,545 words) - 18:18, 20 January 2021
...op">[a8]</td> <td valign="top"> R. Illner, H. Lange, P.F. Zweifel, "Global existence and asymptotic behaviour of solutions of the Wigner–Poisson and
7 KB (1,053 words) - 16:59, 1 July 2020
...topology|differential topology]] and [[Mathematical analysis|mathematical analysis]]. It is rooted in the fundamental work of L. Kronecker [[#References|[a5]]
...roach, but Brouwer created and used new simplicial techniques to define a (global) degree $d [ f , M , N ]$ for continuous mappings $f : M \rightarrow N$ bet
12 KB (1,815 words) - 17:42, 1 July 2020
...with and having many applications in [[Mathematical analysis|mathematical analysis]]. It has been extensively studied by G.G. Lorentz in [[#References|[a13]]]
...lign="top">[a9]</TD> <TD valign="top"> H.H. Gonska, Xin-Long Zhou, "A global inverse theorem on simultaneous approximation by Bernstein–Durrmeyer oper
10 KB (1,438 words) - 07:53, 26 March 2023
...ang–Mills theory leads to global questions incorporating both topology and analysis, as opposed to the purely local theory of classical differential geometry.
7 KB (1,013 words) - 16:45, 1 July 2020
...encyclopediaofmath.org/legacyimages/d/d032/d032600/d032600193.png" />-adic analysis stimulated the development of the theory of Diophantine approximations in t
...ers by their approximation properties, etc. The corresponding methods are "global" (continued fractions, etc.). The metric approach involves the description
54 KB (7,359 words) - 18:32, 31 March 2017
...gn="top">[1]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods:
analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...al orders, that is, the order of accuracy after just one step; the actual (
global) order at a fixed node <img align="absmiddle" border="0" src="https://www.e
32 KB (4,604 words) - 16:55, 7 February 2011
...(see [[Lie group, local|Lie group, local]]). Systematic research into the global structure of Lie groups was first begun by E. Cartan and H. Weyl. The first
==The global structure of Lie groups.==
26 KB (3,980 words) - 17:06, 13 June 2020
...these fields by the [[Galerkin method|Galerkin method]] through objective analysis (interpolation, extrapolation, smoothing) of empirical data on these fields
...ear mechanics, related to the van der Pol method, in a multiple time scale analysis. An example of this is the quasi-geostrophysic series, filtering fast waves
13 KB (1,880 words) - 08:03, 6 June 2020
''Diophantine analysis''
...for these two types of fields [[#References|[3]]], which are usually named global fields. This analogy is especially noticeable if the algebraic functions st
24 KB (3,602 words) - 11:48, 26 March 2023
...aofmath.org/legacyimages/m/m063/m063460/m063460167.png" /> is defined as a
global section of <img align="absmiddle" border="0" src="https://www.encyclopediao
..."top">[5]</TD> <TD valign="top"> L. Hörmander, "An introduction to complex
analysis in several variables" , North-Holland (1973) {{MR|0344507}} {{ZBL|0271.3200
44 KB (5,974 words) - 22:47, 29 November 2014
...mmodated in the method of utilization and interpretation of the results of analysis.
...compact convex set. By expanding the space of products the problem of the analysis of the efficient methods here may be reduced to the case where $ Z $
37 KB (5,562 words) - 11:11, 7 January 2024
.... D. Moore [[#References|[a8]]], [[#References|[a9]]] showed by asymptotic analysis that a singularity could develop along the sheet at finite time starting fr
...r><td valign="top">[a4]</td> <td valign="top"> J. Duchon, R. Robert, "Global vortex sheet solutions of Euler equations in the plane" ''J. Diff. Eqs.''
8 KB (1,185 words) - 17:00, 1 July 2020
...n that of Abelian varieties, some results involving Drinfel'd modules over global function fields $L$ can be proved, whose analogues over number fields $L$ a
...hic representations. This can partially be achieved and leads to (local or global) reciprocity laws between representations of $\GL(r)$ and Galois representa
19 KB (3,204 words) - 20:11, 14 April 2012