Discrete systems on infinite intervals

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...

Some Boundary Value Problems on Infinite Intervals for Functional Differential Systems

< +∞. (3) Earlier, these problems were studied only in the cases, where f1 and f2 are either the Nemytski’s operators ([3], [4], [5]), or the linear operators ([1], [2], [6]). Below, we will present new, and in a certain sense, unimprovable conditions which guarantee, respectively, the solvability and well-posedness of (1), (2) and (1), (3). Throughout the paper, the following notation will be ...

Discrete Morse Inequalities on Infinite Graphs

The goal of this paper is to extend to infinite graphs the knownMorse inequalities for discrete Morse functions proved by R. Forman in the finite case. In order to get this result we shall use a special kind of infinite subgraphs on which a discrete Morse function is monotonous, namely, decreasing rays. In addition, we shall use this result to characterize infinite graphs by the number of criti...

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....