The strong chromatic index of complete cubic Halin graphs

A complete cubic Halin graph is a cubic Halin graph whose characteristic tree is a complete cubic tree, in which all leaves are at the same distance from the root vertex. In this work, we determine the strong chromatic index of the complete cubic Halin graph.     

On Weighted Kernels of Two Posets

A recent result of Aharoni Berger and Gorelik (Order 31(1), 35–43, 2014) is a weighted generalization of the well-known theorem of Sands Sauer and Woodrow (Theory Ser. B 33(3), 271–275, 1982) on monochromatic paths. The authors prove the existence of a so called weighted kernel for any pair of weighted posets on the same ground set. In this work, we point out that this result is closely related to the stable marriage theorem of Gale and Shapley (Amer. Math. Monthly 69(1), 9–15, 1962), and we generalize Blair’s theorem by showing that weighted kernels form a lattice under a certain natural order. To illustrate the applicability of our approach, we prove further weighted generalizations of the Sands Sauer Woodrow result.     

On a problem of Bourgain concerning the $$L_p$$ norms of exponential sums

For \(n \ge 1\) let

$$\begin{aligned} {\mathcal {A}}_n := \bigg \{ P: P(z) = \sum \limits _{j=1}^n{z^{k_j}}: 0 \le k_1 < k_2 < \cdots < k_n, k_j \in {\mathbb {Z}} \bigg \}, \end{aligned}$$

that is, \({\mathcal {A}}_n\) is the collection of all sums of \(n\) distinct monomials. These polynomials are also called Newman polynomials. Let

$$\begin{aligned} M_{p}(Q) := \left( \int _{0}^{1}{\left| Q(e^{i2\pi t}) \right| ^p\,dt} \right) ^{1/p}, \qquad p > 0. \end{aligned}$$

We define

$$\begin{aligned} S_{n,p} := \sup _{Q \in {\mathcal {A}}_n}{\frac{M_p(Q)}{\sqrt{n}}} \qquad \text{ and } \qquad S_p := \liminf _{n \rightarrow \infty }{S_{n,p}} \le \Sigma _p := \limsup _{n \rightarrow \infty }{S_{n,p}}. \end{aligned}$$

We show that

$$\begin{aligned} \Sigma _p \ge \Gamma (1+p/2)^{1/p}, \qquad p \in (0,2). \end{aligned}$$

The special case \(p=1\) recaptures a recent result of Aistleitner [1], the best known lower bound for \(\Sigma _1\).

     

Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations

We show the existence of a subcritical Hopf bifurcation in thedelay-differential equation model of the so-called regenerative machine toolvibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the specialalgebraic structure of the delayed terms in the nonlinear part of the equation,the computation results in simple analytical formulas. Numerical simulationsgave excellent agreement with the results.     

Intramolecular 1,3-dipolar cycloadditions of norbornadiene-tethered nitrile oxides.

Efficient routes to the synthesis of norbornadiene-tethered nitrile oxides have been developed, and their intramolecular 1,3-dipolar cycloadditions were studied. The cycloadditions occurred in good yields for a variety of substrates and were found to be highly regio- and stereoselective, giving single regio- and stereoisomers in most cases.     

A note on parity constrained orientations

This note extends a result of Frank, Jordán, and Szigeti [3] on parity constrained orientations with connectivity requirements. Given a hypergraph H, a non-negative intersecting supermodular set function p, and a preferred in-degree parity for every node, a formula is given on the minimum number of nodes with wrong in-degree parity in an orientation of H covering p.     

Study of FeOx/Au inverse model catalysts by in situ sum frequency generation vibrational spectroscopy

In this work a complex experimental setup is described which was developed by connecting an ultra-high vacuum multi-technique surface analysis system and a sum frequency generation vibrational spectrometer. This arrangement provides a unique environment to study interfaces under in situ conditions by a combination of complementary techniques. Preliminary results of CO adsorption experiments on gold and iron oxide thin layers grown on gold are presented as application examples of the experimental setup.