Smooth extensions of functions on separable Banach spaces

Let $X$ be a Banach space with a separable dual $X^{*}$. Let $Y\subset X$ be a closed subspace, and $f:Y\to\mathbb{R}$ a $C^{1}$-smooth function. Then we show there is a $C^{1}$ extension of $f$ to $X$.Comment: 19 pages. This version fixes a gap in the previous proof of Theorem 1 by providing a sharp version of Lemma

Social Support and Health: A Theoretical Formulation Derived from King's Conceptual Framework

This article describes the development and initial empirical testing of a theoretical formulation of social support, family, health, and child health derived from Imogene King's conceptual framework for nursing. A correlational design was used to test the formulation with 103 families who have children with diabetes mellitus. Three hypotheses were sup ported : parents' social support had a direct and positive effect on family health, parents' social support and child's social support were positively related, and illness factors had a direct and negative effect on child health. Both the supported and unsupported hypotheses are discussed in terms of the present substantive knowledge base and evidence of validity for King's framework. Direction for further theory development and research are identified.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68995/2/10.1177_089431848900200309.pd

Is American Public Administration Detached From Historical Context?: On the Nature of Time and the Need to Understand It in Government and Its Study

The study of public administration pays little attention to history. Most publications are focused on current problems (the present) and desired solutions (the future) and are concerned mainly with organizational structure (a substantive issue) and output targets (an aggregative issue that involves measures of both individual performance and organizational productivity/services). There is much less consideration of how public administration (i.e., organization, policy, the study, etc.) unfolds over time. History, and so administrative history, is regarded as a “past” that can be recorded for its own sake but has little relevance to contemporary challenges. This view of history is the product of a diminished and anemic sense of time, resulting from organizing the past as a series of events that inexorably lead up to the present in a linear fashion. To improve the understanding of government’s role and position in society, public administration scholarship needs to reacquaint itself with the nature of time.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Study of doubly strange systems using stored antiprotons

Bound nuclear systems with two units of strangeness are still poorly known despite their importance for many strong interaction phenomena. Stored antiprotons beams in the GeV range represent an unparalleled factory for various hyperon-antihyperon pairs. Their outstanding large production probability in antiproton collisions will open the floodgates for a series of new studies of systems which contain two or even more units of strangeness at the P‾ANDA experiment at FAIR. For the first time, high resolution γ-spectroscopy of doubly strange ΛΛ-hypernuclei will be performed, thus complementing measurements of ground state decays of ΛΛ-hypernuclei at J-PARC or possible decays of particle unstable hypernuclei in heavy ion reactions. High resolution spectroscopy of multistrange Ξ−-atoms will be feasible and even the production of Ω−-atoms will be within reach. The latter might open the door to the |S|=3 world in strangeness nuclear physics, by the study of the hadronic Ω−-nucleus interaction. For the first time it will be possible to study the behavior of Ξ‾+ in nuclear systems under well controlled conditions

EuFe2_2As2_2 under high pressure: an antiferromagnetic bulk superconductor

We report the ac magnetic susceptibility $\chi_{ac}$ and resistivity $\rho$ measurements of EuFe$_2$As$_2$ under high pressure $P$. By observing nearly 100% superconducting shielding and zero resistivity at $P$ = 28 kbar, we establish that $P$-induced superconductivity occurs at $T_c \sim$~30 K in EuFe$_2$As$_2$. $\rho$ shows an anomalous nearly linear temperature dependence from room temperature down to $T_c$ at the same $P$. $\chi_{ac}$ indicates that an antiferromagnetic order of Eu$^{2+}$ moments with $T_N \sim$~20 K persists in the superconducting phase. The temperature dependence of the upper critical field is also determined.Comment: To appear in J. Phys. Soc. Jpn., Vol. 78 No.