Delayed renewal process and delayed renewal reward process are introduced in the framework of uncertainty theory and their uncertainty distributions are provided. Furthermore, delayed renewal theorem on the limit value of the expected renewal rate of the process and delayed renewal reward theorem on the limit value of the long-run expected reward per unit time are presented. At last, some examp...

Knot modification of B-spline curves is extensively studied in the past few years. Altering one knot value, curve points move on well-defined paths, the limit of which can be computed if the knot value tends to infinity. Symmetric alteration of two knot values can also be studied in a similar way. The extension of these limit theorems for general synchronized modification of two knots is discus...

We apply the private core and the private value to a dynamic economy and study the evolution of private core and private value allocations as individuals acquire information Ž . learn through time. In particular, a realized agreement in each period generates information that changes the underlying information structure in the economy. Since the private Ž . core value depends on the distribution...

Let B be a one-dimensional Brownian motion and f : R → R be a Borel function that is locally integrable on R \ {0} . We present necessary and sufficient conditions (in terms of the function f ) for the existence of the limit lim ε↓0 ∫ t 0 f(Bs) I(|Bs| > ε) ds in probability and almost surely. This limit (if it exists) can be called the principal value of the integral ∫ t 0 f(Bs) ds . The obtain...

A concept of “limit of sequence of subsets” is defined here. This article contains the following items: 1. definition of the superior sequence and the inferior sequence of sets, 2. definition of the superior limit and the inferior limit of sets, and additional properties for the sigma-field of sets, 3. definition of the limit value of a convergent sequence of sets, and additional properties for...

We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is α-stable Lévy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and α-sta...

We study the Cauchy initial-value problem for the Benjamin-Ono equation in the zero-dispersion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate analogue of the method invented by Lax and Levermore to analyze the corresponding limit for the Korteweg–de Vries equation. © 2010 Wiley Periodicals, Inc.

OBJECTIVE To investigate the interprotocol agreement of oxygen uptake efficiency slope (OUES). METHODS 16 Japanese children and adolescents (10 boys and six girls) underwent two sessions of maximal exercise testing according to the following two treadmill protocols: the standard Bruce protocol and the rapidly increasing staged (RIS) protocol. Maximal oxygen uptake (VO2max), the ventilatory an...