patch-test
发表于 2025-3-21 16:13:05
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Malleable
发表于 2025-3-21 22:32:01
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喧闹
发表于 2025-3-22 00:51:27
Convexity and Extremal Principles strategy for obtaining existence propositions consists in considering convexity instead of compactness. Figure 39.1 shows the logical connections. We place the Hahn-Banach theorem at the pinnacle; in the final analysis this theorem goes back to the central fixed point theorem of Bourbaki and Kneser
起来了
发表于 2025-3-22 07:48:14
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煞费苦心
发表于 2025-3-22 10:37:37
Lagrange Multipliers and Eigenvalue Problemsconditions. Moreover, we will interpret this condition geometrically and explain the connection with manifolds in B-spaces. In this connection, a generalization of the implicit function theorem is the focal point (Theorem 43.C). The central concepts are:
热心
发表于 2025-3-22 13:07:56
Ljusternik-Schnirelman Theory and the Existence of Several Eigenvectorseral eigenvectors for (1) within the generalized context of the Courant maximum-minimum principle. In this connection, in an essential way, we use the fact that . and . are odd potential operators, i.e., . = ., . = ., and .(− .) = − .(.), .(−.) = − .(.) for all . ∈ .. We have already explained the b
BILL
发表于 2025-3-22 19:01:05
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Connotation
发表于 2025-3-22 21:16:44
otential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert‘s paper showed me that this was not obviously so. Suddenly other certainties about Aristotle‘s (appar
环形
发表于 2025-3-23 04:21:07
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REIGN
发表于 2025-3-23 05:43:15
Eberhard Zeidlerotential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert‘s paper showed me that this was not obviously so. Suddenly other certainties about Aristotle‘s (appar