Conditional minimum along the scale direction
E2,E4>0 and EV≥0 are energy integrals of one reference shape; Qλ(x)=Q(x/λ), with dimensionless λ. The unique positive stationary scale and positive curvature are analytic results for this family, not a full field solution or nonradial stability.
Based on the final manuscript · Chapter 4
E2,E4>0 and EV≥0 are energy integrals of one reference shape; Qλ(x)=Q(x/λ), with dimensionless λ. The unique positive stationary scale and positive curvature are analytic results for this family, not a full field solution or nonradial stability.
Chapter reference: Final collected manuscript, Chapter 4, Eq. (4.22) and the following analytic root and second derivative (p1374–p1375) · ASD-BOOK-ddbade997b45
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Final collected manuscript, Chapter 4, Eq. (4.22) and the following analytic root and second derivative (p1374–p1375)
Registered equation, symbols and scope checked against the final manuscript; original ID and scientific status preserved.
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- E2,E4>0 and EV≥0 are energy integrals of one reference shape; Qλ(x)=Q(x/λ), with dimensionless λ. The unique positive stationary scale and positive curvature are analytic results for this family, not a full field solution or nonradial stability.
Source locators: p1373–p1375
Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e
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MAT-d1034a344d58 · Ch. 4 (4.22), elementary differentiation with EV=0
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algebraThree-dimensional scaling and analytic stationary radiusASD-WEB-SD-032