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Il y a 1 jour · The winding number (corresponding to an integer of π 1 (S 1) = Z) can be used to prove the fundamental theorem of algebra, which states that every non-constant complex polynomial has a zero. [43] The fact that π n −1 ( S n −1 ) = Z implies the Brouwer fixed point theorem that every continuous map from the n -dimensional ball to itself has a fixed point.
Il y a 4 heures · Zermelo’s Theorem says that all finite-horizon two-player zero-sum games of perfect information are determined: one of the players i, j has a winning strategy. The key to its proof is the following recursive definition of the positions in the game tree where player i has a winning strategy.
Il y a 4 heures · The elevation of the ladder forms an angle of 75.5° with the ground. The height at which the ladder touches the wall can be found using the Pythagorean Theorem: a2 +b2 b2 b2 b2 b = (4a)2 = (4a)2 −a2 = 16a2 −a2 = 15a2 = a 15−−√. Thus, the ladder touches the wall at a 15−−√ feet from the ground. Media.
Il y a 4 heures · On the other hand, we show the case (ii) in Theorem 1.3 for σ<s0 assuming the existence of a solution in Hs0 ≥0(T) (not in H σ ≥0(T)). Namely, Theorem 1.3 asserts non-existence of a continuous extension of the flow map in Hs0 ≥0(T) to H σ ≥0(T) for σ<s0. In order to prove Theorem 1.3, we show that a similar situation arises
Il y a 4 heures · RED (Instrumental Mix) by Iriser, released 26 July 2024
Il y a 4 heures · The heat treatment temperature must precisely meet the required profile to ensure the quality of the workpiece. The model of the heat treatment furnace is not precisely known because it is nonlinear and complex. Considering this aspect, model-free temperature control methods are proposed, which are not based on a model of the process, but only on the input and output data acquired from the ...
Il y a 1 jour · In the case of a high [dOHb] in the voxel and a low [dOHb] in the inflow, the initial high rate of signal intensity decline falls off exponentially as the difference in inflow and outflow of contrast declines to zero. The time constant of this exponential is MTT. Thus, model Fig. 2A describes the central volume theorem where MTT = CBV/CBF.
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