On certain extension theorems in the mixed Borel setting

AbstractGiven two sequences M1 and M2 of positive numbers, we give necessary and sufficient conditions under which the inclusions Λ{M1}⊂f(j)(0)j∈N0:f∈D{M2}[−1,1],Λ(M1)⊂f(j)(0)j∈N0:f∈D(M2)[−1,1] hold, by means of explicit constructions. This answers a question raised by Chaumat and Chollet (Math. Ann. 298 (1994) 7–40). We also consider the case when [−1,1] is replaced by [−1,1]m as well as the possibility to get ultraholomorphic extensions

Extension properties in intersections of non quasi-analytic classes

Let K be a non empty compact subset of $Rr$.In [3], J. Chaumat and A.-M. Chollet introduce certain sequences of moderate growth,consider the corresponding intersections of non quasi-analytic classes of jets on K and of functions on $Rr$ and give a Whitney type extension theorem in this situation. These results have already been extended by P. Beaugendre in [1]. Here we continue this research, relaxing the conditions on the sequences and obtaining analytic extensions

Analytic extension of ultradifferentiable Whitney jets

Let $\omega$ be a weight and $F$ be a closed proper subset of $\mathbb{R}^n$. Then for every function $f$ on $\mathbb{R}^n$ belonging to the non quasi-analytic ($\omega$)-class of Beurling (resp. Roumieu) type, there is an element $g$ of the same class which is analytic on $\mathbb{R}^n \setminus F$ and such that $D^\alpha f(x) = D^\alpha g(x)$ for every $\alpha\in\mathbb{N}^n_0$ and $x\in F$

A resource planning analysis of district hospital surgical services in the Democratic Republic of the Congo.

BACKGROUND: The impact of surgical conditions on global health, particularly on vulnerable populations, is gaining recognition. However, only 3.5% of the 234.2 million cases per year of major surgery are performed in countries where the world\u27s poorest third reside, such as the Democratic Republic of the Congo (DRC). METHODS: Data on the availability of anesthesia and surgical services were gathered from 12 DRC district hospitals using the World Health Organization\u27s (WHO\u27s) Emergency and Essential Surgical Care Situation Analysis Tool. We complemented these data with an analysis of the costs of surgical services in a Congolese norms-based district hospital as well as in 2 of the 12 hospitals in which we conducted the situational analysis (Demba and Kabare District Hospitals). For the cost analysis, we used WHO\u27s integrated Healthcare Technology Package tool. RESULTS: Of the 32 surgical interventions surveyed, only 2 of the 12 hospitals provided all essential services. The deficits in procedures varied from no deficits to 17 services that could not be provided, with an average of 7 essential procedures unavailable. Many of the hospitals did not have basic infrastructure such as running water and electricity; 9 of 12 had no or interrupted water and 7 of 12 had no or interrupted electricity. On average, 21% of lifesaving surgical interventions were absent from the facilities, compared with the model normative hospital. According to the normative hospital, all surgical services would cost US$2.17 per inhabitant per year, representing 33.3$0.08 per inhabitant per year, and at Kabare Hospital, US$0.69 per inhabitant per year. CONCLUSION: A significant portion of the health problems addressed at Congolese district hospitals is surgical in nature, but there is a current inability to meet this surgical need. The deficient services and substandard capacity in the surveyed district hospitals are systemic in nature, representing infrastructure, supply, equipment, and human resource constraints. Yet surgical services are affordable and represent a minor portion of the total operating budget. Greater emphasis should be made to appropriately fund district hospitals to meet the need for lifesaving surgical services

Locally convex properties of the spaces of continuous functions vanishing on a fixed subset

Schmets Jean. Locally convex properties of the spaces of continuous functions vanishing on a fixed subset. In: Bulletin de la Classe des sciences, tome 70, 1984. pp. 311-326