``long-run", or ``global" statistical dependence in the Earth sciences.
peculiar method of analysis that follows very
9 KB (1,398 words) - 20:37, 22 September 2016
...r equipments, and computer networks), which is oriented to the qualitative analysis and synthesis of such systems (discovering deadlocks or conflict situations
...conducted along two lines. The mathematical theory is advanced by a formal analysis of their properties. The most interesting problems include recognizing dead
6 KB (897 words) - 19:23, 16 August 2016
...theory is based on the implicit-function theorem in non-linear functional analysis and on the general theory of linear problems of corresponding type.
The global theory of non-linear problems is less completely developed, and then only f
30 KB (4,331 words) - 16:42, 20 January 2022
.... Subsequently, fundamental results were obtained by methods of functional analysis and by algebraic methods, concerning the homotopy invariance of classes and
...ying the topological invariants, provided by $K$-theory. Multi-dimensional global problems of the calculus of variations on manifolds proved to be more diffi
9 KB (1,298 words) - 14:59, 30 August 2014
...ture of the boundary conditions or any supplementary conditions). Such a "global" character of variational calculus in the large proper is stressed by the
...#References|[12]]]). Variational calculus in the large is also employed in global [[Differential geometry|differential geometry]] [[#References|[13]]].
14 KB (2,052 words) - 08:27, 6 June 2020
..., "Anosov diffeomorphisms" S.-S. Chern (ed.) S. Smale (ed.) , ''Global analysis'' , ''Proc. Symp. Pure Math.'' , '''14''' , Amer. Math. Soc. (1970) pp. 6
...300</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> M. Shub, "Global stability of dynamical systems" , Springer (1986)</TD></TR><TR><TD valign=
9 KB (1,321 words) - 07:59, 21 June 2014
...nnected the theory of variational inequalities to [[Convex analysis|convex analysis]], especially to the notion of subdifferentiability, and to the theory of m
...R><TD valign="top">[a10]</TD> <TD valign="top"> V.K. Le, K. Schmitt, "Global bifurcation in variational inequalities" , Springer (1997)</TD></TR><TR><T
5 KB (737 words) - 20:35, 18 March 2024
...b C$ and $f,g: U \to \mathbb C$ are differentiable in the sense of complex analysis (cf. [[Analytic function]]). Then the formula reads as \eqref{e:rule}.
Global derivatives are maps from $C^1 (M)$ to $C^0 (M)$ satisfying the (analog of)
5 KB (757 words) - 10:34, 11 December 2013
...D valign="top">[4]</TD> <TD valign="top"> R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980)</TD></TR><TR><TD valign="top">[5]<
4 KB (543 words) - 22:15, 5 June 2020
...integral formulas is one of the most important tools in classical complex analysis (cf. also [[Boundary value problems of analytic function theory|Boundary va
In applications involving the construction of global holomorphic functions satisfying special properties, and in order to solve
15 KB (2,167 words) - 16:10, 11 February 2024
...p">[5]</TD> <TD valign="top"> L. Hörmander, "An introduction to complex analysis in several variables" , North-Holland (1973)</TD></TR></table>
6 KB (880 words) - 16:10, 1 April 2020
...e manifold gives, for a sufficiently smooth manifold, the largest possible global degree of smoothness of the function which is obtained as a result of exten
...ns of several variables and imbedding theorems" S.M. Nikol'skii (ed.) , ''Analysis III'' , ''Encycl. Math. Sci.'' , '''26''' , Springer (1990) pp. 1–140
9 KB (1,435 words) - 08:13, 13 January 2024
...D valign="top">[3]</TD> <TD valign="top"> R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980)</TD></TR><TR><TD valign="top">[4]<
4 KB (681 words) - 03:41, 21 March 2022
If the problem satisfies the global contractivity condition
...having the same sign. This result can be used in the asymptotic stability analysis of Runge–Kutta methods, see [[#References|[a5]]].
9 KB (1,275 words) - 17:43, 1 July 2020
...submersions" , ''Lecture Notes'' , '''40''' , Research Inst. Math., Global Analysis Research Center, Seoul Nat. Univ. (1998)</td></tr><tr><td valign="top">[a5
5 KB (681 words) - 17:43, 1 July 2020
...ighest order) are minimized. However, since the relation between the true (global) error and the local error is generally not known, it is questionable wheth
...D valign="top">[a1]</TD> <TD valign="top"> J.C. Butcher, "The numerical analysis of ordinary differential equations. Runge–Kutta and general linear method
7 KB (1,053 words) - 17:13, 14 February 2020
...ions of representation and approximation of functions, and their local and global properties. The modern theory of functions of a real variable typically inv
...n urgent need for a new critical review of the foundations of mathematical analysis, which was carried out at the end of the 19th century and beginning of the
11 KB (1,738 words) - 18:15, 24 March 2018
...ing analytic set in a local model (cf. [[Analytic set|Analytic set]]). The global dimension is defined by the formula:
The theory of analytic spaces has two aspects: the local and the global aspect. Local analytic geometry is concerned with germs of analytic sets in
22 KB (3,277 words) - 01:53, 19 January 2022
...ion is useful when some functions are not differentiable. Using non-smooth analysis, one can replace derivatives by other objects such as subgradients (see, e.
...0\right\}$. Here $f^0(\theta)=0$ for any $\theta$, hence $\theta^*=0$ is a global minimum. The saddle-point condition requires $U_1=U_1(\theta)\geq 0$ such t
16 KB (2,514 words) - 17:28, 23 October 2017
...ed only for convex and related unimodal functions. The theory of finding a global extremum is still (1989) in the initial phase of development (see [[Multi-e
.../TD> <TD valign="top"> Yu.G. Evtushenko, "Numerical methods for finding global extrema (case of a non-uniform mesh)" ''USSR Comp. Math. Math. Phys.'' , '
13 KB (1,911 words) - 08:00, 6 June 2020