By Jurgen Moser and Eduard J. Zehnder
ISBN-10: 0821835777
ISBN-13: 9780821835777
This booklet is an creation to the sphere of dynamical structures, particularly, to the distinctive classification of Hamiltonian platforms. The authors aimed toward protecting the necessities of mathematical thoughts minimum yet giving distinctive proofs and plenty of examples and illustrations from physics and celestial mechanics. in the end, the celestial $N$-body challenge is the starting place of dynamical structures and gave upward push long ago to many mathematical advancements. Jürgen Moser (1928-1999) was once a professor on the Courant Institute, big apple, after which at ETH Zurich. He served as president of the overseas Mathematical Union and got many honors and prizes, between them the Wolf Prize in arithmetic. Jürgen Moser is the writer of numerous books, between them good and Random Motions in Dynamical structures. Eduard Zehnder is a professor at ETH Zurich. he's coauthor with Helmut Hofer of the e-book Symplectic Invariants and Hamiltonian Dynamics. Titles during this sequence are copublished with the Courant Institute of Mathematical Sciences at long island collage.
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By considering the processes which affect the cells on the lattice (proliferation, movement, phenotypic switching and death), and by assuming independence of the lattice sites we can derive master equations for the occupation probabilities of P- and M-cells. By taking the appropriate continuum limit we arrive at the following system of coupled PDEs which describe the density of P- and M-cells respectively: β ∂2 p ∂p = (1 − p − m) 2 + βp(1 − p − m) − (qm + μ) p + q p m ∂t 2 ∂x (1) ∂2 p v ∂ 2m ∂m = ((1 − p) 2 + m 2 ) − (q p + μ)m + qm p.
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