The heart of a convex body

We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\heartsuit(\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\heartsuit(\mathcal{K})$ and the mirror symmetries of $\mathcal{K};$ we show that $\heartsuit(\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\heartsuit(\mathcal{K});$ we also prove an upper estimate for the area of $\heartsuit(\mathcal{K}),$ when $\mathcal{K}$ is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6

Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

Long-term nutrient addition increased CH4 emission from a bog through direct and indirect effects

Peatlands are globally significant sources of atmospheric methane (CH4). While several studies have examined the effects of nutrient addition on CH4 dynamics, there are few long-term peatland fertilization experiments, which are needed to understand the aggregated effects of nutrient deposition on ecosystem functioning. We investigated responses of CH4 flux and production to long-term field treatments with three levels of N (1.6-6.4 g m(-2) yr(-1) as NH4NO3), potassium and phosphorus (PK, 5.0 g P and 6.3 g K m(-2) yr(-1) as KH2PO4), and NPK in a temperate bog. Methane fluxes were measured in the field from May to August in 2005 and 2015. In 2015 CH4 flux was higher in the NPK treatment with 16 years of 6.4 g N m(-2) yr(-1) than in the control (50.5 vs. 8.6 mg CH4 m(-2) d(-1)). The increase in CH4 flux was associated with wetter conditions derived from peat subsidence. Incubation of peat samples, with and without short-term PK amendment, showed that potential CH4 production was enhanced in the PK treatments, both from field application and by amending the incubation. We suggest that changes in this bog ecosystem originate from long-term vegetation change, increased decomposition and direct nutrient effects on microbial dynamics.Peer reviewe

Shape coexistence at the proton drip-line: First identification of excited states in 180Pb

Excited states in the extremely neutron-deficient nucleus, 180Pb, have been identified for the first time using the JUROGAM II array in conjunction with the RITU recoil separator at the Accelerator Laboratory of the University of Jyvaskyla. This study lies at the limit of what is presently achievable with in-beam spectroscopy, with an estimated cross-section of only 10 nb for the 92Mo(90Zr,2n)180Pb reaction. A continuation of the trend observed in 182Pb and 184Pb is seen, where the prolate minimum continues to rise beyond the N=104 mid-shell with respect to the spherical ground state. Beyond mean-field calculations are in reasonable correspondence with the trends deduced from experiment.Comment: 5 pages, 4 figures, submitted to Phys.Rev.

First observation of excited states in 173Hg

The neutron-deficient nucleus 173Hg has been studied following fusion-evaporation reactions. The observation of gamma rays decaying from excited states are reported for the first time and a tentative level scheme is proposed. The proposed level scheme is discussed within the context of the systematics of neighbouring neutron-deficient Hg nuclei. In addition to the gamma-ray spectroscopy, the alpha decay of this nucleus has been measured yielding superior precision to earlier measurements.Comment: 5 pages, 4 figure

Search for Fingerprints of Tetrahedral Symmetry in 156Gd^{156}Gd

Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2-transitions at the bottom of the odd-spin negative parity band in $^{156}Gd$. The present study reports on experiment performed to address this phenomenon. It allowed to determine the intra-band E2 transitions and branching ratios B(E2)/B(E1) of two of the negative-parity bands in $^{156}Gd$.Comment: presented by Q.T. Doan at XLII Zakopane School of Physics: Breaking Frontiers: Submicron Structures in Physics and Biology, May 2008. 5 pages, minor corrections. To be published in the proceeding

Could continuous cover forestry be an economically and environmentally feasible management option on drained boreal peatlands?

Environmental and economic performance of forestry on drained peatlands was reviewed to consider whether continuous cover forestry (CCF) could be a feasible alternative to even-aged management (EM). CCF was regarded feasible particularly because continuously maintaining a tree stand with significant transpiration and interception capacity would decrease the need for ditch network maintenance. Managing CCF forests in such a way that the ground water levels are lower than in clear-cut EM forests but higher than in mature EM forests could decrease greenhouse gas emissions and negative water quality impacts caused both by anoxic redox reactions and oxidation and mineralization of deep peat layers. Regeneration studies indicated potential for satisfactory natural regeneration under CCF on drained peatlands. An economic advantage in CCF over EM is that fewer investments are needed to establish the forest stand and sustain its growth. Thus, even if the growth of trees in CCF forests were lower than in EM forests, CCF could at least in some peatland sites turn out to be a more profitable forest management regime. An advantage of CCF from the viewpoint of socially optimal forest management is that it plausibly reduces the negative externalities of management compared to EM. We propose that future research in drained peatland forests should focus on assessing the economic and environmental feasibility of CCF.Peer reviewe

Level structure of 99Nb

The β decay of 97Sr to 97Y has been investigated using ion-guide on-line mass separation and a 10 Ge-detector array to record γ−γ coincidences to a detection limit well below that of former studies. Similarities are found in the β-decay patterns of 99Zr and of its isotone 97Sr and also in the γ-ray decay rates and branchings of the corresponding levels in their respective daughters 99Nb and 97Y. This indicates a persisting influence of the d5/2 neutron shell closure for 99Nb. The level structure of 99Nb and the β-feeding pattern are discussed in the frame of the interacting boson-fermion plus broken pair model and the microscopic quasiparticle phonon model