In this paper we introduce and study a regularising one-to-one mapping Υ0 from the class of one-dimensional Lévy measures into itself. This mapping appeared implicitly in our previous paper [BT2], where we introduced a one-to-one mapping Υ from the class ID(∗) of one-dimensional infinitely divisible probability measures into itself. Based on the studies of Υ0 in the present paper, we also deduc...

A probability measure μ on Rd is called weakly unimodal if there exists a constant κ ≥ 1 such that for all r > 0, (0.1) sup a∈Rd μ(B(a, r)) ≤ κμ(B(0, r)). Here, B(a, r) denotes the `∞-ball centered at a ∈ Rd with radius r > 0. In this note, we derive a sufficient condition for weak unimodality of a measure on the Borel subsets of Rd. In particular, we use this to prove that every symmetric infi...

The core of games arising from semi-infinite transportation situations with infinitely divisible goods is studied. In these situations one aims at maximizing the profit from transporting a good from a finite number of suppliers to an infinite number of demanders. This good is infinitely divisible. It is shown that the underlying primal and dual infinite programs have no duality gap. Further, th...

We extend the Lévy-Khintchine representation for an infinitely divisible distribution to define a driving process in the context of the bond price framework developed earlier. We describe a methodology using subordination to construct such processes and we develop some examples in detail.

We study in a constructive manner some problems of topology related to the set Irr of irrational reals. The constructive approach requires a strong notion of an irrational number ; constructively, a real number is irrational if it is clearly different from any rational number. We show that the set Irr is one-to-one with the set Dfc of infinite developments in continued fraction (dfc). We define...

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each r...

It is good to be able to pass on the best wishes of the International Institute of Refrigeration (IIR) and to remind you that the IIR will be holding its Gustav Lorentzen Memorial Conference in Glasgow next year. I hope that the IIR conference will be as well supported and as valuable as this CIBSE/ASHRAE conference. You are warmly invited to attend the Gustav Lorentzen conference in Glasgow, w...

When a natural gas pipeline ruptures, the adjacent automatic line control valves (ALCVs) should close quickly to prevent leakage or explosion. The differential pressure set point (DPS) at each valve location is the main criteria for value setting in ALCV action. If the DPS is not properly adjusted, the ALCV may mistakenly close or it may not take any action at proper time. This study focused on...

and accessory rods at PSO level. Testing evaluated (1) accessory Study Design. In vitro cadaveric biomechanical study. Objective. To assess effects of 4-rod reconstruction, rod material, and anterior column support on motion and surface rod strain in a pedicle subtraction osteotomy model. Summary of Background Data. Pedicle subtraction osteotomy (PSO) can correct significant sagittal deformity ...