In [2, Chapter VII (p. 133)], Ritt shows an example of two irreducible differential variety of differential dimension 2 in U whose intersection consists of a single point: the origin. The details below follow Ritt’s exposition using more modern language and notation. The first part is taken from my tutorial paper [3], with some change in notation. That paper provides the basic background needed...

In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...

Social comparisons are known to increase individual work morale, but because they could foster competition, may also negatively impact how well co-workers together. This paper uses a novel experiment explore this potential tradeoff. The varies whether members of reference group receive relative performance information on knowledge task and measures affects the willingness subsequently help prod...

Archibald, Beal, Birkhoff, Blichfeldt, B. H. Camp, Cole, Crum, Dantzig, Dodd, Douglas, Fine, Fiske, Fite, M. C. Foster, Philip Franklin, Fry, Gafafer, Gill, Gronwall, Hazlett, Hebbert, E. R. Hedrick, Hille, Huntington, Joffe, Kellogg, Kircher, Kuhn, Lamson, MacDuffee, Mathewson, Meder, Mirick, Molina, Mullins, Northcott, Oglesby, Osgood, Pell, Pfeiffer, Raynor, Reddick, R. G. D. Richardson, Rit...

This paper focuses on effectivity aspects of the Lüroth’s theorem in differential fields. Let F be a differential field of characteristic 0 and F〈u〉 be the field of differential rational functions generated by a single indeterminate u. Let be given non constant rational functions v1, . . . , vn ∈ F〈u〉 generating a subfield G ⊆ F〈u〉. The differential Lüroth’s theorem proved by Ritt in 1932 state...

We study the following questions: (1) What are all solutions to f ◦f̂ = g◦ĝ with f, g, f̂ , ĝ ∈ C(X) being complex rational functions? (2) For which rational functions f(X) and g(X) with rational coefficients does the equation f(a) = g(b) have infinitely many solutions with a, b ∈ Q? We utilize various algebraic, geometric and analytic results in order to resolve both (1) and a variant of (2) in ...