It is a well-known and elementary fact in complex analysis that a bounded and [[Holomorphic function|holomorphic function]] on the who
...al differential geometry, involving geometric measure theory and nonlinear analysis (cf. also [[Plateau problem|Plateau problem]]).
10 KB (1,518 words) - 21:22, 14 January 2021
...tems and algebraic curves" M. Grmela (ed.) J.E. Marsden (ed.) , ''Global analysis'' , ''Lect. notes in math.'' , '''755''' , Springer (1979) pp. 83–200</
5 KB (759 words) - 22:10, 5 June 2020
...gular solutions of these boundary value problems. Profound applications to global problems of classical differential geometry were done on the basis of these
...nsional hyperbolic Monge–Ampère equations. The solution of a few important global problems for saddle surfaces was obtained as an application of these result
17 KB (2,601 words) - 08:01, 6 June 2020
of) the derived functors of the global section functor $ F \mapsto F( 1) $(
...TD valign="top"> I. Moerdijk, G.E. Reyes, "Models for smooth infinitesimal analysis" , Springer (1990) {{MR|1083355}} {{ZBL|0715.18001}} </TD></TR><TR><TD vali
8 KB (1,216 words) - 18:08, 14 November 2023
...zation of formal moduli, I" D.C. Spencer (ed.) S. Iyanaga (ed.) , ''Global analysis (papers in honor of K. Kodaira)'' , Princeton Univ. Press (1969) pp. 21–7
6 KB (837 words) - 07:19, 14 November 2023
is generated by two elements. The global [[Homological dimension|homological dimension]] of $ A _ {n} ( K) $
...ces|[a8]]] for a survey of this. The result (a1) was proved by micro-local analysis in [[#References|[a40]]]. An algebraic proof was found later in [[#Referenc
28 KB (4,182 words) - 19:30, 19 January 2024
...ties. This structure/non-structure dichotomy is known as the main gap. The analysis discussed so far (1990) suffices to establish (Shelah, late 1970's) the Mor
...type. B.I. Zil'ber initiated the use of this geometric structure to obtain global information about the models of $ T $.
11 KB (1,671 words) - 11:38, 22 December 2019
...ctions on an open set $\Omega \subset D ^ { n }$ can be represented by the global cohomology group $H _ { \Omega } ^ { n } ( U , \widetilde { \mathcal O } )$
...ordinary hyperfunctions. The case $K = D ^ { n }$ corresponds to that for global Fourier hyperfunctions, given at the beginning.
26 KB (3,903 words) - 17:01, 1 July 2020
It can perform a bifurcation analysis of (a1). It can compute branches of stable and unstable periodic orbits and
...al systems equations. Several other packages, notably Global Manifolds 1D, Global Manifolds 2D, GAIO and BOV-method compute invariant manifolds. See [[#Refer
13 KB (1,928 words) - 17:00, 1 July 2020
...><TR><TD valign="top">[16]</TD> <TD valign="top"> D. Neumann, T. O'Brien, "Global structure of continuous flows on 2-manifolds" ''J. Diff. Eq.'' , '''22''' :
10 KB (1,474 words) - 20:08, 12 January 2024
...e that as suggested by the presence of chaotic solutions and by a Painlevé analysis [[#References|[a7]]] (cf. also [[Painlevé test|Painlevé test]]), the Kura
...inertial manifold, which exponentially absorbs solutions and contains the global attractor [[#References|[a10]]], [[#References|[a4]]]. On restricting the p
21 KB (3,050 words) - 17:43, 1 July 2020
...eddies symmetrically staggered, as in Fig.a1. However, a linear stability analysis with respect to small disturbances shows that the first configuration is al
...], the velocity induced on each vortex by all the others, and the eventual global displacement velocity of the sheets using the complex potential formulation
19 KB (3,002 words) - 17:46, 1 July 2020
...ximation of local solutions to the homogeneous equation $P ( D ) u = 0$ by global solutions. The space of solutions to a linear homogeneous ordinary differen
.../tr><tr><td valign="top">[a6]</td> <td valign="top"> L. Hörmander, "The analysis of linear partial differential operators II" , ''Grundl. Math. Wissenschaft
8 KB (1,264 words) - 05:21, 19 March 2022
...ization of formal moduli I" D.C. Spencer (ed.) S. Iyanaga (ed.) , ''Global analysis (papers in honor of K. Kodaira)'' , Univ. Tokyo Press (1969) pp. 21–72 {{
7 KB (1,008 words) - 07:42, 20 March 2024
...e [[#References|[a5]]], [[#References|[a11]]] for examples and references. Global analyses of these equations are merely of mathematical interest because the
...="top">[a4]</TD> <TD valign="top"> P.G. Ciarlet, V. Lods, "Asymptotic analysis of linearly elastic shells I. Justification of membrane shell equations" '
8 KB (1,209 words) - 08:28, 6 June 2020
...utation of the input data is equally likely. For biased distributions, the analysis becomes significantly more complicated, and for arbitrary distributions the
...e behaviour is not identical to the worst-case behaviour — an average-case analysis makes sense. A precise complexity estimation has been given for many Boolea
21 KB (3,198 words) - 18:47, 11 December 2020
...1–56</TD></TR><TR><TD valign="top">[a15b]</TD> <TD valign="top"> D. Rand, "
Global phase space universality, smooth conjugacies and renormalisation: the <img
12 KB (1,685 words) - 08:27, 6 June 2020
...fand, N.Ya. Vilenkin, "Generalized functions. Applications of harmonic analysis" , '''4''' , Acad. Press (1968) (Translated from Russian)</TD></TR><TR><T
...top"> S. Albeverio, R. Høegh-Krohn, B. Zegarlinski, "Uniqueness and global Markov property for Euclidean fields: the case of general polynomial intera
7 KB (970 words) - 08:09, 6 June 2020
...\Gamma \backslash X ) , \widetilde { M } )$ and what is the image of the "global" cohomology $H ^ { \bullet } ( \Gamma \backslash X , \tilde { \mathcal{M}
giving a global class. The only difficulty is that this sum need not converge. Hence the fo
12 KB (1,817 words) - 15:30, 1 July 2020
is generated by global sections; for any analytic sheaf $ {\mathcal F} $
...><TD valign="top">[1]</TD> <TD valign="top"> R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980) {{MR|0608414}} {{ZBL|0435.32004}} <
7 KB (1,004 words) - 08:07, 6 June 2020
...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
...0/e035550178.png" />. II" W.L. Baily jr. (ed.) T. Shioda (ed.) , ''Complex Analysis and Algebraic geometry'' , Cambridge Univ. Press & Iwanami Shoten (1977
15 KB (2,046 words) - 05:46, 13 June 2022
...tence criteria for global solutions (1983). In many cases the existence of global solutions is assumed beforehand (this is natural in many applications) and
...Lavrent'ev, "Some improperly posed problems of mathematical physics and analysis" , Amer. Math. Soc. (1986) (Translated from Russian)</TD></TR><TR><TD val
19 KB (2,714 words) - 13:11, 13 January 2024
...gn="top">[2]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...estimate of the local error. However, since the relation between the true (global) error and the local error is generally not known, and because the local er
16 KB (2,467 words) - 15:35, 4 June 2020
A global a priori estimate for an elliptic operator $ A $
...n the elliptic operator in question turns out to be invertible, and in the global a priori estimate of the type (1) the last term (the low norm at the right-
12 KB (1,764 words) - 05:06, 24 February 2022
...als, quadrature formulas, moment problems, and other problems of classical analysis (see [[#References|[7]]]–). The origin of the study of the rows of the Pa
...icients of a power series) for their construction, they allow one to study global properties of the corresponding analytic function (analytic continuation, t
15 KB (2,227 words) - 13:32, 11 November 2023
recommendation, he was appointed Professor of Analysis and Mechanics
statistical analysis " always to collect a large number of elements,
13 KB (1,947 words) - 18:43, 4 March 2024
...heory of topological characteristics of nonlinear operators II" , ''Global analysis: Studies and Applications IV'' , ''Lecture Notes Math.'' , '''1453''' , Spr
16 KB (2,462 words) - 06:56, 15 February 2024
...tional-differential, as well as more complicated equations in mathematical analysis are all equations of the type (1), as are also systems of algebraic equatio
...>[2]</TD> <TD valign="top"> F. Riesz, B. Szökefalvi-Nagy, "Functional analysis" , F. Ungar (1955) (Translated from French)</TD></TR><TR><TD valign="top"
19 KB (2,803 words) - 19:40, 5 June 2020
...lso weighs the relative importance of the criteria in order to arrive at a global judgement. Moreover, in a group of decision makers each member faces the qu
...top">[a8]</td> <td valign="top"> F.A. Lootsma, "Multi-criteria decision analysis via ratio and difference judgement" , Kluwer Acad. Publ. (1999)</td></tr><
18 KB (2,526 words) - 15:30, 1 July 2020
...ne { \partial }$-problem]]), the prescribed curvature equation, and global analysis, [[#References|[a1]]], [[#References|[a7]]], [[#References|[a10]]].
10 KB (1,540 words) - 17:43, 1 July 2020