3-Connected {<Emphasis Type="Italic">K</Emphasis><Subscript>1,3</Subscript>, <Emphasis Type="Italic">P</Emphasis><Subscript>9</Subscript>}-Free Graphs are Hamiltonian-Connected

We investigate pairs of forbidden subgraphs that imply a 3-connected graph is Hamiltonian-connected. In particular we show that the pair {K _1,3, P ₉} is such a pair. As it is known that P ₁₀ cannot replace P ₉, this result is best possible. Further, we show that certain other graphs are not possible.     

Photoinduced Barkhausen effect in the ferromagnetic semiconductor (Ga,Mn)As

Magnetization of ferromagnetic materials commonly occurs via random jumps of domain walls between pinning sites, a phenomenon known as the Barkhausen effect. Using strongly focused light pulses of appropriate power and duration we demonstrate the ability to selectively activate single jumps in the domain wall propagation in (Ga,Mn)As, manifesting itself as a discrete photoinduced domain wall creep as a function of illumination time. The propagation velocity can be increased over 7 orders of magnitude varying the illumination power density and the magnetic field.     

Formation of ultracold Rb2 molecules in the v' = 0 level of the a(3)Σ+(u) state via blue-detuned photoassociation to the 1(3)Π(g) state

We report on the observation of blue-detuned photoassociation in Rb(2), in which vibrational levels are energetically above the corresponding excited atomic asymptote. (85)Rb atoms in a MOT were photoassociated at short internuclear distance to levels of the 1(3)Π(g) state at a rate of approximately 5 × 10(4) molecules s(-1). We have observed most of the predicted vibrational levels for all four spin-orbit components; 0(+)(g), 0(-)(g), 1(g), and 2(g), including levels of the 0(+)(g) outer well. These molecules decay to the metastable a(3)Σ(+)(u) state, some preferentially to the v' = 0 level, as we have observed for photoassociation to the v' = 8 level of the 1(g) component.     

Hyphenated Mass Spectrometry versus Real-Time Mass Spectrometry Techniques for the Detection of Volatile Compounds from the Human Body

Mass spectrometry (MS) is an analytical technique that can be used for various applications in a number of scientific areas including environmental, security, forensic science, space exploration, agri-food, and numerous others. MS is also continuing to offer new insights into the proteomic and metabolomic fields. MS techniques are frequently used for the analysis of volatile compounds (VCs). The detection of VCs from human samples has the potential to aid in the diagnosis of diseases, in monitoring drug metabolites, and in providing insight into metabolic processes. The broad usage of MS has resulted in numerous variations of the technique being developed over the years, which can be divided into hyphenated and real-time MS techniques. Hyphenated chromatographic techniques coupled with MS offer unparalleled qualitative analysis and high accuracy and sensitivity, even when analysing complex matrices (breath, urine, stool, etc.). However, these benefits are traded for a significantly longer analysis time and a greater need for sample preparation and method development. On the other hand, real-time MS techniques offer highly sensitive quantitative data. Additionally, real-time techniques can provide results in a matter of minutes or even seconds, without altering the sample in any way. However, real-time MS can only offer tentative qualitative data and suffers from molecular weight overlap in complex matrices. This review compares hyphenated and real-time MS methods and provides examples of applications for each technique for the detection of VCs from humans.     

Phosphaniminato-Komplexe des Zinks mit Hydrido-, Alkinylo-, Alkenylo- und Amido-Liganden

Phosphoraneiminato Complexes of Zinc with Hydrido, Alkynylo, Alkenylo, and Amido Ligands Synthesis and properties of the phosphoraneiminato complexes [ZnCl(NPMe₃)]₄ ( 1 ), [ZnH(NPMe₃)]₄ ( 2 ) as well as of the alkynylo derivatives [Zn(C≡C–SiMe₃)(NPMe₃)]₄ ( 3 ), [Zn(C≡C–C≡C–SiMe₃)(NPR₃)]₄ [R = Me ( 4 a ), R = Et ( 4 b )], [Zn(C≡C–Ph)(NPMe₃)]₄ ( 5 ) and of the alkenylozinc complexes [Zn(CH=CHMe)(NPR₃)]₄ [R = Me ( 6 a ), R = Et ( 6 b )] are described. According to crystal structure analyses of 1 , 3 , and 4 b these complexes possess heterocubane structures with only slightly distorted Zn₄N₄ cubic skeletons. Experiments to substitute the terminal ligands at the zinc atoms by bis(trimethylsilyl)amido groups lead to disintegration of the heterocubanes and formation of the dimeric complex [Zn(μ₂-NPEt₃){N(SiMe₃)₂}]₂ ( 7 ) and of the trinuclear derivative [Zn₃(μ₂-NPMe₃)₄{N(SiMe₃)₂}₂] ( 8 ), in which the central zinc atom is surrounded by the four N atoms of the NPEt₃^– groups in a spiro-cyclic fashion. 7 and 8 are also characterized by crystal structure analyses.     

On k‐ordered graphs

Ng and Schultz [J Graph Theory 1 ( 6 ), 45–57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k‐ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k‐ordered Hamiltonian. We give sum of degree conditions for nonadjacent vertices and neighborhood union conditions that imply a graph is k‐ordered Hamiltonian. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 69–82, 2000     

On p-intersection representations

For a graph G = (V,E) and integer p, a p-intersection representation is a family F = {S_x: × E V} of subsets of a set S with the property that |S_u ∩ S_ν| ≥ p ∩ {u, ν} E E. It is conjectured in [1] that θ_p(G) ≤ θ (K_n/2,n/2) (1 + o(1)) holds for any graph with n vertices. This is known to be true for p = 1 by [4]. In [1], θ (K_n/2,n/2) ≥ (n² + (2p− 1n)n)/4p is proved for any n and p. Here, we show that this is asymptotically best possible. Further, we provide a bound on θp(G) for all graphs with bounded degree. In particular, we prove θp(G) ≤ O(n^1/p) for any graph Gwith the maximum degree bounded by a constant. Finally, we also investigate the value of θ_p for trees. Improving on an earlier result of M. Jacobson, A. Kézdy, and D. West, (The 2-intersection number of paths and bounded-degree trees, preprint), we show that θ₂(T) ≤ O(d√n) for any tree T with maximum-degree d and θ₂(T) ≤ O(n^3/4) for any tree on n vertices. We conjecture that our results can be further improved and that θ₂(T) ≤ O(d√n) as long as Δ(T) ≤ √n. If this conjecture is true, our method gives θ₂(T) ≤ O(n^3/4) for any tree T which would be the best possible. © 1996 John Wiley & Sons, Inc.