The Hopf maximum principle is a maximum principle in the theory of second order elliptic partial differential equations and has been described as the...

integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) that is one of the most important...

sinusoidal functions. Maximum modulus principle Hopf maximum principle Protter, Murray H.; Weinberger, Hans Felix (1984). Maximum principles in differential...

important tool in the proof of the maximum principle and in the theory of partial differential equations. The Hopf lemma has been generalized to describe...

partial differential equation Parabolic partial differential equation Hopf maximum principle Elliptic complex Ultrahyperbolic wave equation Semi-elliptic operator...

are now regarded as fundamental to the field, such as his strong maximum principle for second-order parabolic partial differential equations and the...

mathematical symbols, read mathematical books and papers (notably those of Heinz Hopf, J. H. C. Whitehead, and Hassler Whitney) to him, and later worked as his...

Crandall and Pierre-Louis Lions. By extending the strong maximum principle of Eberhard Hopf to his notion of viscosity solutions, Calabi was able to use...

between entropy generation and the robustness of biological systems. The Hopf decomposition states that dynamical systems can be decomposed into a conservative...

manifold M: any holomorphic function on it is constant by the maximum modulus principle. Now if we had a holomorphic embedding of M into Cn, then the...

to a two-dimensional sphere of constant curvature 4. The Hopf fibration S3 → S2 is a principle bundle with structure group U(1). Furthermore, relative...

Svetlana; Levendorski, Sergei (2013). "Efficient Laplace inversion, Wiener-Hopf factorization and pricing lookbacks". International Journal of Theoretical...

{\displaystyle \operatorname {diam} (M,d_{g})=\sup\{d_{g}(p,q):p,q\in M\}.} The Hopf–Rinow theorem shows that if ( M , d g ) {\displaystyle (M,d_{g})} is complete...

physical principle that could be described in terms of the use of energy by a system, a concept later developed by Howard T. Odum as the maximum power principle...

Potts model, it is often noted that it can be derived following a maximum entropy principle: For a given set of sample covariances and frequencies, the Potts...

Euclidean space whose boundary forms a closed curve of given length The Hopf conjectures relating the curvature and Euler characteristic of higher-dimensional...

{z} _{k}\end{aligned}}} The above system is known as the inverse Wiener-Hopf factor. The backward recursion is the adjoint of the above forward system...

continuum. Other minor results from his early career include a proof of a maximum principle for the gradient of a minimizing function in the field of calculus...

Michel Barbaza, David Geddes, Jean-Louis Vernet, Miguel Llongueras & Maria Hopf (1982). "Prehistoric Human Adaptations in Catalonia (Spain)", Journal of...

bogie and body inertia on the nonlinear wheel-set hunting recognized by the hopf bifurcation theory". Int J Auto Engng: 186–196. Iwnicki, Simon (2006). Handbook...

Genet. 10 (11): 783–796. doi:10.1038/nrg2664. PMID 19834483. Bernstein H, Hopf FA, Michod RE (1987). "The Molecular Basis of the Evolution of Sex". Molecular...

3390/life11080777. ISSN 2075-1729. PMC 8401828. PMID 34440521. Bernstein H, Byerly HC, Hopf FA, Michod RA, Vemulapalli GK. (1983) The Darwinian Dynamic. Quarterly Review...

result, which can be proved using the Gauss–Bonnet theorem, is the Poincaré-Hopf index theorem for vector fields on M which vanish at only a finite number...

H.-J.; Eichwede, F.; Födisch, M.; Taccone, F.S.; Wöbker, G.; Schwab, T.; Hopf, H.-B.; Tonner, P.; Hachimi-Idrissi, S. (Aug 2010). "Safety and feasibility...

801–810. doi:10.1111/brv.12367. PMID 28913952. S2CID 4764175. Bernstein H, Hopf FA, Michod RE (1987). "The molecular basis of the evolution of sex". Molecular...

uranium would be used at least 60 times more efficiently than today. James Hopf, a nuclear engineer writing for American Energy Independence in 2004, believes...

studies took off in the 1960s, particularly following the work of Maria Hopf and Hans Helbæk, and later Willem van Zeist, Gordon Hillman, Jack Harlan...

(Fields medallist 1982) describe the mathematical underlying structure (the Hopf algebra) of renormalization, and its link to the Riemann-Hilbert problem...

Literacy Project. 2015-08-24. Retrieved 2021-07-09. Daniel Zohary; Maria Hopf; Ehud Weiss (2012). Domestication of Plants in the Old World: The Origin...

{\displaystyle \leq _{\text{pre}}} ". However, just removing the potent induction principle from that axiomatization does not leave a workable algebraic theory. Indeed...