...J.A. Thorpe, "The curvature of 4-dimensional Einstein spaces" , ''Global Analysis (In Honour of K. Kodaira)'' , Univ. Tokyo Press (1969) pp. 355–365</TD>
15 KB (2,270 words) - 08:28, 26 March 2023
The simplest ordinary differential equation is already encountered in analysis: The problem of finding the primitive function of a given continuous functi
...[Eigen value|Eigen value]]) and also with the [[Spectral analysis|spectral analysis]] of ordinary differential operators.
33 KB (4,933 words) - 01:50, 23 January 2022
...e involving the idea of descent in the space of controls and of successive analysis of variants (of the type of [[Dynamic programming|dynamic programming]]).
...rical solution of optimal control problems is based on the idea of optimal analysis of variants [[#References|[10]]], [[#References|[11]]], [[#References|[12]]
23 KB (3,462 words) - 08:27, 6 June 2020
...e method for the construction of geometry and its foundations. This deeper analysis of the foundations of geometry was enhanced by the discovery in 1826 of the
...cular, to justify methods of analysis in geometry and geometric methods in analysis.
25 KB (3,631 words) - 19:39, 5 June 2020
...tion of subspaces, on the contrary, one obtains quite general results of a global nature. Thus, if
...ping) has been constructed [[#References|[2]]], and is a universal (in the global sense) deformation for any compact analytic subspace of
41 KB (5,916 words) - 11:24, 26 March 2023
...opological decompositions of operator algebras" A. Salam (ed.) , ''Global analysis and its applications (Trieste, 1972)'' , '''3''' , IAEA (1974) pp. 305–
17 KB (2,631 words) - 19:37, 19 January 2024
...>[5]</TD> <TD valign="top"> L.V. [L.V. Ovsyannikov] Ovsiannikov, "Group analysis of differential equations" , Acad. Press (1982) (Translated from Russian)
...valign="top"> K. Uhlenbeck, "Conservation laws and their application in global differential geometry" B. Srinivasan (ed.) J. Sally (ed.) , ''Emmy Noethe
16 KB (2,336 words) - 08:02, 6 June 2020
...or studying many problems in contemporary algebra, geometry, topology, and analysis.
...nsion (over $\Z$) of a space, the algebraic dimension of a variety and the global dimension of a ring. The description given by Grothendieck of the spectral
26 KB (4,342 words) - 15:06, 15 July 2014
...etrical forms, mainly with curves and surfaces, by methods of mathematical analysis. In differential geometry the properties of curves and surfaces are usually
...ometry. Many geometrical concepts were defined prior to their analogues in analysis. For instance, the concept of a tangent is older than that of a derivative,
33 KB (5,039 words) - 11:46, 26 March 2023
2) to investigate the question of the local and global solvability and subellipticity of equations (see [[#References|[12]]]); and
.../TR><TR><TD valign="top">[11]</TD> <TD valign="top"> J. Leray, "Lagrangian analysis and quantum mechanics" , M.I.T. (1981) (Translated from French) {{MR|064626
24 KB (3,360 words) - 19:39, 5 June 2020
A term denoting a number of problems related to research on extremals and global minima of functionals in the $ k $-dimensional volume $ \mathop{\rm vo
...roblems in variational calculus, topology, algebraic geometry, and complex analysis that give rise to the following situation: One is given a manifold $ M ^
29 KB (4,259 words) - 11:43, 3 March 2022
Symbolic dynamics is also used for the analysis of chaotic behaviour of dynamical systems (cf. [[Chaos|Chaos]]; [[Fractals|
...3)</TD></TR><TR><TD valign="top">[a25]</TD> <TD valign="top"> M. Shub, "Global stability of dynamical systems" , Springer (1987) (Translated from French
15 KB (2,197 words) - 08:48, 29 April 2023
...general, a Cartier divisor on a ringed space $(X,\c O_X)$ is defined as a global section of the sheaf $M_X^*/\c O_X^*$ of germs of divisors. Here $M_X$ deno
|valign="top"|{{Ref|We2}}||valign="top"| R.O. Wells jr., "Differential analysis on complex manifolds", Springer (1980) {{MR|0608414}} {{ZBL|0435.32004}}
16 KB (2,805 words) - 02:18, 6 January 2022
''analysis of variance''
MANOVA (multivariate analysis of variance) is the multivariate generalization of ANOVA. Its model equatio
56 KB (8,477 words) - 17:45, 1 July 2020
...$, there is duality between the $k$-space $H^i(X, \calF)$ and the space of global Ext's
...eory for non-closed sets" , ''General topology and its relations to modern analysis and algebra (Proc. Symp. Prague)'' , Acad. Press (1961) pp. 123–132 {{MR|
64 KB (9,418 words) - 12:44, 8 February 2020
An analysis of the lower bound for $ L ( n) $
...usually the simpler, since for its solution it is sufficient in the final analysis to construct just one scheme, whereas the second requires a survey in some
27 KB (4,142 words) - 14:55, 7 June 2020
...ave re-animated those directions of commutative algebra that can be called global commutative algebra. These relate to the theory of invariants (cf. [[Invari
16 KB (2,400 words) - 17:45, 4 June 2020
Numerous investigations have been devoted to the study of global properties of concrete systems of differential equations. In connection wit
...of the elementary catastrophes, see [[#References|[a2]]]. Furthermore, the analysis of trajectories near an equilibrium can be restricted to the ones forming a
29 KB (4,392 words) - 08:08, 6 June 2020
...to algorithms for solving simple problems of a standard structure (modular analysis of algorithms). There is as yet no rigorous foundation for such an approach
...accuracy on smooth solutions which is usually of order three at most and a global accuracy of order one at most (because of the low accuracy of the finite-di
28 KB (3,843 words) - 19:41, 5 June 2020
...$\int f ( \theta , \phi ) d \phi$, an important advantage for statistical analysis.
...e inverse gives a large-sample variance of $\theta ^ { * }$ in statistical analysis. The supplemented EM [[#References|[a19]]] and supplemented ECM [[#Referenc
26 KB (3,861 words) - 17:03, 1 July 2020