...op">[a6]</TD> <TD valign="top"> R. Horst, P.M. Pardalos, "Handbook of global optimization" , Kluwer Acad. Publ. (1995)</TD></TR><TR><TD valign="top">[a
10 KB (1,422 words) - 14:35, 19 May 2024
...see, e.g., [[Metric space|Metric space]]; [[Functional analysis|Functional analysis]]).
...her geometers. As a result of the interaction of geometry with algebra and analysis there followed the appearance of special calculi, which are conveniently us
20 KB (2,829 words) - 18:41, 11 December 2020
Apart from the lack of global convergence of Newton's method, the use of Hessian matrices is a disadvanta
...letcher, "An overview of unconstrained optimization" ''Dundee Numerical Analysis Report'' , '''NA/149''' (1993)</td></tr><tr><td valign="top">[a9]</td> <td
12 KB (1,897 words) - 19:37, 9 February 2024
...the general framework of the theory of connections. As a device of tensor analysis, covariant differentiation is widely used in theoretical physics, particula
...></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> A. Lichnerowicz, "Global theory of connections and holonomy groups" , Noordhoff (1955) (Translated
15 KB (2,257 words) - 17:31, 5 June 2020
...]) and mathematical [[Cybernetics|cybernetics]] and their study aims at an analysis and formalization of the concept of an algorithm and at modelling real devi
Other models combine local and global storage.
18 KB (2,656 words) - 04:11, 6 June 2020
...(ed.) A. Kishimoto (ed.) I. Ojima (ed.) , ''Quantum and Non-Commutative Analysis'' , ''Math. Phys. Stud.'' , Kluwer Acad. Publ. (1993) pp. 239–251</TD><
...Kotake (ed.) S. Nishikawa (ed.) R. Schoen (ed.) , ''Geometry and Global Analysis (Rept. First MSJ Internat. Res. Inst. (July 12-23, 1993), Tôhoku Univ.'' ,
16 KB (2,356 words) - 19:53, 13 January 2018
...$\mathbb{Z}$, a positive solution to Hilbert's tenth problem; cf. [[Local-global principles for the ring of algebraic integers]].
...orm|Quadratic form]]) reduces the classification of quadratic forms over a global field to that over local fields. This represents the historically first ins
29 KB (4,109 words) - 19:54, 18 March 2018
...oximation on Banach manifolds" S.-S. Chern (ed.) S. Smale (ed.) , ''Global analysis'' , ''Proc. Symp. Pure Math.'' , '''14''' , Amer. Math. Soc. (1970) pp. 213
12 KB (1,758 words) - 00:29, 13 January 2017
...g to the theorem on the resolution of singularities of algebraic surfaces, global methods of the theory of schemes may be applied to the local study of singu
is known. The existence of a global moduli variety of an algebraic surface has been proved only for certain cas
26 KB (3,736 words) - 13:08, 8 February 2020
.... Abraham, "Bumpy metrics" S.-S. Chern (ed.) S. Smale (ed.) , ''Global analysis'' , ''Proc. Symp. Pure Math.'' , '''14''' , Amer. Math. Soc. (1970) pp. 1
13 KB (1,911 words) - 17:44, 4 June 2020
...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