...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