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punctilio    
n. 细节,拘泥形式,拘束

细节,拘泥形式,拘束

punctilio
n 1: a fine point of etiquette or petty formality
2: strict observance of formalities


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    One participant provides an example involving the tangent bundle of the 2-sphere to illustrate how the integral of the curvature form relates to the first Chern class and the Euler characteristic
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    The operator norm of the integral operator \ ( T \) defined on \ ( H = L^2 (0,1) \) by \ ( Tf (s) = \int_0^1 (5s^2t^2 + 2) (f (t))dt \) is calculated using the relation \ ( ||T|| \leq \sqrt {\frac {50} {6}} \) By taking \ ( f = 1 \), the equality \ ( ||T|| = \frac {\sqrt {65}} {3} \) is established The operator \ ( T \) is self-adjoint due to its symmetric kernel \ ( k (s,t) = 5s^2t^2 + 2
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    The discussion focuses on evaluating the surface integral ∫∫S F · dS for the vector field F (x, y, z) = xy i + yz j + zx k over the surface S defined by the paraboloid z = 3 - x² - y², constrained within the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 The user attempted to convert the integral into polar coordinates but faced confusion regarding the correct application of the surface integral





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