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
...uler system has been identified, one figures out local conditions that the global cohomology classes $c_L$ satisfy. Then Kolyvagin's descent procedure gives
...orary arithmetic. The interplay between arithmetic and algebraic geometry, analysis (both $p$-adic and complex), number theory, etc. has brought about many int
19 KB (2,901 words) - 17:41, 25 November 2023
...osed with respect to the fundamental operations of arithmetic, algebra and analysis. Finally, an important property of an analytic function is its uniqueness:
...function considered as a whole is generally multi-valued. Many problems in analysis (inversion of a function, the determination of a primitive and the construc
61 KB (9,850 words) - 19:04, 20 January 2022
...i.e. which can be verified at each point of the extremal), there is also a global necessary condition, related to the behaviour of the set of extremals in a
...eory of differential equations and topology. The development of functional analysis made a substantial contribution to the study of qualitative methods. See al
28 KB (4,182 words) - 07:56, 16 April 2023
...automatic control. In particular, one may mention the methods of frequency analysis; methods based on the first approximation to [[Lyapunov stability theory|Ly
There are also various global and necessary-condition-type results especially in the case of analytic sys
43 KB (6,618 words) - 07:32, 26 March 2023
A global problem in many-valued logics is the description of the lattice of closed c
...lay an important role in mathematical logic, model theory and mathematical analysis. For countable-valued logics it has been established that the set of pre-co
34 KB (5,105 words) - 19:20, 16 January 2024
...ign="top">[2]</TD> <TD valign="top"> B.V. Shabat, "Introduction of complex analysis" , '''1–2''' , Moscow (1976) (In Russian) {{MR|}} {{ZBL|0799.32001}} {{ZB
...top">[a1]</TD> <TD valign="top"> L. Hörmander, "An introduction to complex analysis in several variables" , North-Holland (1973) pp. Chapt. 2.4 {{MR|0344507}}
66 KB (9,825 words) - 01:45, 23 June 2022
...its tape, and the position of its head on the tape, provides some kind of global state of the Turing machine. Accordingly, the set $C=\{c_i\}_{i\in I}$ of
...y, M. Suhail Zubairy, "Quantum Computing Devices: Principles, Designs, and Analysis", CRC Press 2010
27 KB (4,213 words) - 18:53, 26 April 2014