mathematics

Roger D. Nussbaum

Roger D. Nussbaum is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Roger D. Nussbaum rather than just read about it. In short: Roger David Nussbaum (born 29 January 1944, in Philadelphia) is an American mathematician, specializing in nonlinear functional analysis and differential equations. Nussbaum graduated in 1965 with a bachelor's degree from Harvard University.

Key takeaways

Roger D. Nussbaum belongs to mathematics; place it in that map before memorising details.
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Reproduce the core statement of Roger D. Nussbaum from memory before moving on to harder problems.

Reference excerpt

Roger David Nussbaum (born 29 January 1944, in Philadelphia) is an American mathematician, specializing in nonlinear functional analysis and differential equations. Nussbaum graduated in 1965 with a bachelor's degree from Harvard University. He received his Ph.D. in 1969 from the University of Chicago with thesis The Fixed Point Index and Fixed Point Theorems for K-Set Contractions supervised by Felix Browder. At Rutgers University Nussbaum became in 1969 an assistant professor, in 1973 an associate professor, and in 1977 a full professor. He retired there as professor emeritus. He was elected in 2012 a Fellow of the American Mathematical Society.

Selected publications

Articles Browder, Felix E.; Nussbaum, Roger D. (1968). "The topological degree for noncompact nonlinear mappings in Banach spaces". Bulletin of the American Mathematical Society. 74 (4): 671–677. doi:10.1090/S0002-9904-1968-11988-3. Nussbaum, Roger D. (1969). "The fixed point index and asymptotic fixed point theorems for k {\displaystyle k} -set-contractions". Bulletin of the American Mathematical Society. 75 (3): 490–496. doi:10.1090/S0002-9904-1969-12213-5. —— (1970). "The radius of the essential spectrum". Duke Mathematical Journal. 37 (3): 473–478. doi:10.1215/S0012-7094-70-03759-2. —— (1970). "Spectral mapping theorems and perturbation theorems for Browder's essential spectrum". Transactions of the American Mathematical Society. 150 (2): 445–455. doi:10.1090/S0002-9947-1970-0265967-9. —— (1971). "The fixed point index for local condensing maps". Annali di Matematica Pura ed Applicata. 89 (1): 217–258. doi:10.1007/BF02414948. ISSN 0373-3114. S2CID 119544692. —— (1971). "Some fixed point theorems". Bulletin of the American Mathematical Society. 77 (3): 360–366. doi:10.1090/S0002-9904-1971-12694-0. —— (1972). "Some asymptotic fixed point theorems". Transactions of the American Mathematical Society. 171: 349–375. doi:10.1090/S0002-9947-1972-0310719-6. —— (1978). "A Hopf global bifurcation theorem for retarded functional differential equations". Transactions of the American Mathematical Society. 238: 139–164. doi:10.1090/S0002-9947-1978-0482913-0. —— (1981). "Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem". In: Fixed point theory. Lecture Notes in Mathematics. Vol. 886. Berlin; Heidelberg: Springer. pp. 309–330. doi:10.1007/BFb0092191. ISBN 978-3-540-11152-8. De Figueiredo D.G.; Lions P.L.; —— (1982). "A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations". In: Costa D. (ed.) Djairo G. de Figueiredo - Selected Papers. Cham, Switzerland: Springer. pp. 133–155. doi:10.1007/978-3-319-02856-9_11. ISBN 978-3-319-02855-2. (over 600 citations) —— (1983). "Some remarks on a conjecture in parameter adaptive control". Systems & Control Letters. 3 (5): 243–246. doi:10.1016/0167-6911(83)90021-X. ISSN 0167-6911. (over 1100 citations) ——; Walsh, Bertram (1998). "Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators". Transactions of the American Mathematical Society. 350 (6): 2367–2391. doi:10.1090/S0002-9947-98-01998-9. Mallet-Paret, John; —— (2011). "Inequivalent measures of noncompactness and the radius of the essential spectrum". Proceedings of the American Mathematical Society. 139 (3): 917–930. doi:10.1090/S0002-9939-2010-10511-7. ——; Priyadarshi, Amit; Verduyn Lunel, Sjoerd (2012). "Positive operators and Hausdorff dimension of invariant sets". Transactions of the American Mathematical Society. 364 (2): 1029–1066. doi:10.1090/S0002-9947-2011-05484-X. Lemmens, Bas; —— (2013). "Continuity of the cone spectral radius". Proceedings of the American Mathematical Society. 141 (8): 2741–2754. arXiv:1107.4532. doi:10.1090/S0002-9939-2013-11520-0.

Books with Bas Lemmens: Nonlinear Perron-Frobenius Theory, Cambridge Tracts in Mathematics, Cambridge University Press 2012 with S. M. Verduyn-Lunel: Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps, Memoirs AMS 1999 with Heinz-Otto Peitgen: Special and Spurious Solutions of x ˙ ( t ) = − α f ( x ( t − 1 ) ) {\displaystyle {\dot {x}}(t)=-\alpha f(x(t-1))} , Memoirs AMS, 1984 with Patrick Fitzpatrick, Jean Mawhin, Mario Martelli: Topological Methods for Ordinary Differential Equations, CIME Lectures, Montecacini Terme 1991, Lecture Notes in Mathematics 1537, Springer Verlag 1993 Hilbert's projective metric and iterated nonlinear maps, 2 vols., AMS 1988 Differential-delay equations with two time lags, Memoirs AMS 1978

References

Worked examples

Example 1 — a first encounter with Roger D. Nussbaum

Start with the simplest possible case. Write down what Roger D. Nussbaum claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Roger D. Nussbaum before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Roger D. Nussbaum ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Roger D. Nussbaum

In research: Roger D. Nussbaum appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Roger D. Nussbaum in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Roger D. Nussbaum is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Roger D. Nussbaum outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Roger D. Nussbaum in 20 minutes

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Frequently asked questions

What is Roger D. Nussbaum in simple terms?

Why does Roger D. Nussbaum matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Roger D. Nussbaum?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Roger D. Nussbaum.