For any h ∈ IN , a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → ZZ h − {0} such that the induced vertex set labeling l : V (G) → ZZ h defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h ∈ IN for which G admits a zero-sum h-magic labeling. In this pap...

The 1°gAg nuclear magnetic resonance line in a sample of polycrystalline AgF is observed to broaden substantially when the 19F spins are irradiated near the magic angle in their rotating frame. This is due to the reduction of 19F-19 F dipolar coupling, which normally causes fluctuations in the 19F-l°9Ag interactions (Abragam and Winter), inducing an exchange narrowing analogous to classical mot...

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and q ≪ n (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number qc. For a magic number (n ...

Background: Polymer gel dosimeters combined with magnetic resonance imaging (MRI) can be used for dose verification of advanced radiation therapy techniques. However, the uncertainty of dose map measured by gel dosimeter should be known. The purpose of this study is to investigate the uncertainty related to calibration curve and MRI protocol for MAGIC (Methacrylic and Ascorbic acid in Gelatin I...

B. Reduction in Saddle-Type Coil Size 5 C. Solenoidal Coils and Magic Angle Spinning 5 D. Microcoils 6 E. Microfabrication 7 F. Direct Comparisons of Probe Sensitivity 8 V. Microliter-Volume Static NMR Spectroscopy 9 A. Natural Product Extracts 9 B. Analysis of Combinatorial Chemistry Products 10 VI. Nanoliter-Volume Static NMR Spectroscopy 10 VII. NMR Detection of Capillary Separations 12 A. F...

Recent experimental results concerning interaction cross sections (σI) are reviewed. σI values have been measured by a transmission method using the fragment separator at GSI. The σI values for B, C, N, O, and F isotopes are presented. By using Glauber-model analysis, the effective matter radii for light neutron-rich nuclei can be deduced. The recently shown magic number, N = 16, near the neutr...

We introduce a family of magic squares, called linear magic squares, and show that any parallel linear sudoku solution of sufficiently large order can be relabeled so that all of its subsquares are linear magic. As a consequence, we show that if n has prime factorization p1 1 · · · p kt t and q = min{p k j j | 1 ≤ j ≤ t}, then there is a family of q(q − 1) mutually orthogonal magic sudoku solut...

Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, “magic” optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transit...

For any kEN, a graph G = (V, E) is said to be ;:z k-magic if there exists a labeling Z: E( G) --+ ;:z k {OJ such that the induced vertex set labeling Z+: V (G) --+ ;:z k defined by Z+(v) = L Z(uv) uvEE(G) is a constant map. For a given graph G, the set of all kEN for which G is ;:z k-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper we will consider the func...

Since 2004, the MAGIC γ-ray telescope has newly discovered 6 TeV blazars. The total set of 13 MAGIC-detected active galactic nuclei includes well-studied objects at other wavelengths like Markarian 501 and the giant radio galaxy M 87, but also the distant the flat-spectrum radio quasar 3C 279, and the newly discovered TeV γ-ray emitter S5 0716+71. In addition, also long-term and multi-wavelengt...