Balázs–Shepard Operators on Infinite Intervals, II

Monoidal intervals of clones on infinite sets

Let X be an infinite set of cardinality κ. We show that if L is an algebraic and dually algebraic distributive lattice with at most 2 completely join irreducibles, then there exists a monoidal interval in the clone lattice on X which is isomorphic to the lattice 1 + L obtained by adding a new smallest element to L. In particular, we find that if L is any chain which is an algebraic lattice, and...

On Infinite Cycles II

We adapt the cycle space of a finite or locally graph to graphs with vertices of infinite degree, using as cycles the homeomorphic images of the unit circle S in the graph together with its ends. We characterize the spanning trees whose fundamental cycles generate this cycle space, and prove infinite analogues to the standard characterizations of finite cycle spaces in terms of edge-decompositi...

On infinite dimensional Volterra type operators

Since Lotka and Volterra’s seminal and pioneering works (see [10]) many decades ago, modeling of interacting, competing species have received considerable attention in the fields of biology, ecology, mathematics (for example, see [3, 9]). In their remarkably simple deterministic model, Lotka and Volterra considered two coupled nonlinear differential equations that mimic the temporal evolution o...

Boundary Value Problems for Functional Difference Equations on Infinite Intervals

The Possibility of Tschebycheff Quadrature on Infinite Intervals.

Numbers,' in Bull. Nat. Res. Council (Washington, D. C.), Vol. 5, Part 3, No. 28, pp. 21-25 (1923). 8 This result is due to the writer; cf. E. Landau, Vorlesungen uber Zahlentheorie, Bd. 3, Verlag von S. Hirzel Leipzig (1927), pp. 327, 328. 9 Berlin Abhandlungen, Mathematisch-Physikalische Klasse, 61-65 (1857). 10 J. fur die Math., 128, 45-68 (1905). 11 Lehmer, D. H. and Emma, Bull. Amer. Math....