The terminal set M is a closed subset of Rn+1. The admissible control set U is assumed to be the set of piecewise continuous function on [t0, t1]. The performance function J is assumed to be C1. The function V (·, ·) is called the value function and we shall use the convention V (t0, x0) = ∞ if the control problem above admits no feasible solution. We will denote by U(x0, t0), the set of feasib...

The basic model for incompressible two-phase flows with phase transitions is derived from basic principles and shown to be thermodynamically consistent in the sense that the total energy is conserved and the total entropy is nondecreasing. The local well-posedness of such problems is proved by means of the technique of maximal Lp-regularity in the case of equal densities. This way we obtain a l...

i=1 pi(t)Φβi (x(τi(t))) = e(t), t ∈ [t0,∞)T where T is a time scale, t0 ∈ T a fixed number; [t0,∞)T is a time scale interval; Φ∗(u) = |u|∗−1u; the functions r, pi, e : [t0,∞)T → R are right-dense continuous with r > 0 nondecreasing; τk : T → T are nondecreasing right-dense continuous with τk(t) ≤ t , limt→∞ τk(t) = ∞; and the exponents satisfy β1 > · · · > βm > α > βm+1 > · · ·βn > 0. All resul...

We consider the nonlinear degenerate elliptic-parabolic-hyperbolic equation ∂tg(u)−∆b(u)− div Φ(u) = f(g(u)) in (0, T )× Ω, where g and b are nondecreasing continuous functions, Φ is vectorial and continuous, and f is Lipschitz continuous. We prove the existence, comparison and uniqueness of entropy solutions for the associated initial-boundary-value problem where Ω is a bounded domain in RN . ...

Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise...

Lemma A1: If a contract {wt} is self-enforcing, then there is another self-enforcing contract {w′ t} such that: (i) w′ t is nondecreasing in t, (ii) the no-shirking conditions, Ut − U1 ≥ ĉ for all t ≥ 2, do not bind for any t ≥ 2, (iii) firms’expected (discounted) profits are the same under two contracts, V1 = V ′ 1 . Proof. The proof is by construction. We show it in several steps. Step (1) (c...

The use of supervised learning techniques for fitting weights and/or generator functions of weighted quasi-arithmetic means – a special class of idempotent and nondecreasing aggregation functions – to empirical data has already been considered in a number of papers. Nevertheless, there are still some important issues that have not been discussed in the literature yet. In the second part of this...

The traditional zero-one principle for sorting networks states that ”if a network with n input lines sorts all 2n binary sequences into nondecreasing order, then it will sort any arbitrary sequence of n numbers into nondecreasing order.” We generalize this to the situation when a network sorts almost all binary sequences and relate it to the behavior of the sorting network on arbitrary inputs. ...

We show that a real z is polynomial time random if and only if each nondecreasing polynomial time computable function is differentiable at z. This establishes an analog in feasible analysis of a recent result of Brattka, Miller and Nies, who characterized computable randomness in terms of differentiability of nondecreasing computable functions. Further, we show that a Martin-Löf random real z i...