We develop fully polynomial time (Σ,Π)-approximation schemes for stochastic dynamic programs with continuous state and action spaces, when the single-period cost functions are convex Lipschitz-continuous functions that are accessed via value oracle calls. That is, for every given additive error parameter Σ > 0 and multiplicative error factor Π = 1 + > 1, the scheme returns a feasible solution w...

Conditions are found upon satisfaction of which the differential equation x(n)(t)− λx(n)(t− σ) + f(t, x(g(t))) = 0 has solutions which are asymptotically equivalent to the solutions of the equation x(n)(t)− λx(n)(t− σ) = 0. § 0. Introduction We consider the neutral functional differential equation x(n)(t)− λx(n)(t− σ) + f(t, x(g(t))) = 0 (A) under the assumptions that (i) n ≥ 1 is an integer; λ...

We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in R, n ≥ 1, is a σ-limit set for some continuous map.

We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these. §0 Introduction Let (X,B, m, T ) be an invertible, ergodic measure preserving transformation of a σ-finite measure space, then there are no other σ-finite, m-abs...

2 of Lemma 4 and 4 of Proposition 2 in our paper [1] entitled “*Continuous Idempotent Semirings and Their Ideal Completion” are wrong. This note shows counter examples of them. The counter examples are given in linguistic models of *-Continuous Idempotent Semirings. 1 Monodic Tree Languages A ranked set is a couple (Σ, r) of a set Σ of (function) symbols and a mapping r from Σ to the set N of n...