Graph polynomials from principal pivoting

The recursive computation of the interlace polynomial introduced by Arratia, Bollobás and Sorkin is defined in terms of a new pivoting operation on undirected simple graphs. In this paper, we interpret the new pivoting operation on graphs in terms of standard pivoting (on matrices). Specifically, we show that, up to swapping vertex labels, Arratia et al.'s pivoting operation on a graph is equivalent to a principal pivot transform on the graph's adjacency matrix, provided that all computations are performed in the Galois field F₂. Principal pivoting on adjacency matrices over F₂ has a natural counterpart on isotropic systems. Thus, our view of the interlace polynomial is closely related to the one by Aigner and van der Holst.The observations that adjacency matrices of undirected simple graphs are skew-symmetric in F₂ and that principal pivoting preserves skew-symmetry in all fields suggest to extend Arratia et al.'s pivoting operation to fields other than F₂. Thus, the interlace polynomial extends to polynomials on gain graphs, namely bidirected edge-weighted graphs whereby reversed edges carry non-zero weights that differ only by their sign. Extending a proof by Aigner and van der Holst, we show that the extended interlace polynomial can be represented in a non-recursive form analogous to the non-recursive form of the original interlace polynomial, i.e., the Martin polynomial.For infinite fields it is shown that the extended interlace polynomial does not depend on the (non-zero) gains, as long as they obey a non-singularity condition. These gain graphs are all supported by a single undirected simple graph. Thus, a new graph polynomial is defined for undirected simple graphs. The recursive computation of the new polynomial can be done such that all ends of the recursion correspond to independent sets. Moreover, its degree equals the independence number. However, the new graph polynomial is different from the independence polynomial.     

Superhydrophobic behaviour of plasma modified electrospun cellulose nanofiber-coated microfibers

In this work, a method is presented for production of a textile cellulose fiber with non-wetting properties suitable for applications ranging from wound care and tissue engineering to clothing and other textile applications. Non-wettability is achieved by coating a textile cellulose microfiber with electrospun cellulose nanofibers, creating a large and rough surface area that is further plasma treated with fluorine plasma. High surface roughness and efficient deposition of covalently bound fluorine groups results in the fiber exhibiting non-wetting properties with contact angle measurements indicating superhydrophobicity (>150° water contact angle). It is an environmentally friendly method and the flexibility of the electrospinning process allows for careful design of material properties regarding everything from material choice and surface chemistry to fiber morphology and fiber assembly, pointing to the potential of the method and the developed fibers within a wide range of applications.     

Deuteron breakup by low-energy α-particles

An investigation of the ²H(α, αp)n reaction at a lab energy of 15 MeV has been performed. Results from kinematically complete measurements at eleven angular combinations are presented and analyzed in terms of a semiphenomenological impulse approximation. It is found that if contributions from three-nucleon transfer reactions and n-p final state interactions as well as sequential reactions via states in ⁶Li are included, it is possible to reach qualitative agreement with the data.     

Georgiĭ Borisovich Bokiĭ (On the occasion of his 100th birthday)

Memorial Data

Georgiĭ Borisovich Bokiĭ (On the occasion of his 100th birthday)     

Deuteron breakup by α-particles at 13,15 and 18 MeV

Kinematically complete measurements on the D(α, αp)n reaction have been made at three low energies for the incident α-particle and for a number of coplanar angular combinations at each energy. The experimental data, which thus cover a substantial phase space volume, provide material for a severe test of low-energy reaction theories. The data have been analysed in a three-body model, which relies on the numerical solution of the Faddeev equations in momentum space. Rank-one separable two-body potentials for the alpha-nucleon and nucleon-nucleon systems have served as the input information.Agreement between calculated and measured cross sections ranges from excellent to rather poor. Due to the strong effect of the Coulomb correction, which at present is quite uncertain, the appearance of cases with excellent agreement may be fortuitous. The variation of on-shell properties of the two-body potentials produce small changes in the cross sections, implying that more refined models must be employed to achieve good agreement, for instance, the explicit inclusion of effects due to the Pauli principle. However, before firm conclusions in this respect can be drawn, much greater confidence has to be gained in how to treat the Coulomb interaction in few-body breakup reactions.