The number oft-wise balanced designs

We prove that the number oft-wise balanced designs of ordern is asymptotically , provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by and above by for constants c₂>c₁>0.     

Comparability invariance of the fixed point property

We show that the fixed point property is comparability invariant for finite ordered sets; that is, if P and Q are finite ordered sets with isomorphic comparability graphs, then P has the fixed point property if and only if Q does. In the process we give a characterization of comparability invariants which can also be used to give shorter proofs of some known results.     

Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.     

Choosability of planar graphs

A graph G = G(V, E) with lists L(v), associated with its vertices v V, is called L-list colourable if there is a proper vertex colouring of G in which the colour assigned to a vertex v is chosen from L(v). We say G is k-choosable if there is at least one L-list colouring for every possible list assignment L with L(v) = k v V(G).

Now, let an arbitrary vertex v of G be coloured with an arbitrary colour f of L(v). We investigate whether the colouring of v can be continued to an L-list colouring of the whole graph. G is called free k-choosable if such an L-list colouring exists for every list assignment L (L(v) = k v V(G)), every vertex v and every colour f L(v). We prove the equivalence of the well-known conjecture of Erd s et al. (1979): “Every planar graph is 5-choosable” with the following conjecture: “Every planar graph is free 5-choosable”.     

Development of a HS-LIF-system for Lagrangian correlation measurement

Within the presented work, a key assumption for a combustion noise model is validated. Heat release fluctuations are the main reason for the noise emission of turbulent premixed flames. Within the combustion noise model of Hirsch et al. [31st Symposium (Int.) on Combustion, pp 1435–1441, 2006], the heat release is computed in the wavenumber domain and transferred into the frequency domain, subsequently. The transformation of the spectra requires a power law dependence of the scalar spectra upon the wavenumber proportional to and upon the frequency proportional to f ⁻² in the inertial subrange. The validation of the latter assumption requires a measurement system, which allows time dependent recording of fluid properties, e.g. the progress variable. These are provided by a HS-LIF-system, which supports a repetition rate of 1 kHz with sufficient energy to detect OH-radicals. From the high speed video data, the motion of the flame front is reconstructed. The presented study shows the set up of the HS-LIF-system as well as the various image post processing steps, including data binarization, flame front tracking and finally, computation of the lagrangian correlation for the progress variable. It can be shown that the spectral distribution of the progress variable in the Lagrangian frame is as assumed by the above mentioned combustion noise model.     

Size determination of metallic iron particles by temperature dependent Mössbauer and ferromagnetic resonance studies

The thermal decomposition products of NaX·Fe(CO)₅ after various steps of heat treatment, in vacuum as well as under gas atmosphere (Ar, H₂), have been investigated by temperature-dependent Mössbauer and ferromagnetic resonance measurements. The measured spectra of both techniques consistently are analyzed using superparamagnetic relaxation behavior of magnetic particles. From this analysis information concerning composition and size of magnetic iron particles is derived.     

Strict Kinetic Treatment of the Electron Response to Spatial Field Disturbances in Nonequilibrium Plasmas

In generalization of former approaches for the simplified solution of the inhomogeneous electron Boltzmann equation a higher order solution technique has been developed. This technique is based on a multi-term expansion of the electron velocity distribution function and allows a strict study of the electron kinetics in plasmas acted upon by space-dependent electric fields. This solution technique is used to investigate the response of the plasma electrons to spatially limited disturbances of the electric field in weakly ionized plasmas of helium and mercury. By solving the kinetic equation with increasing order of the multi-term expansion the convergent solution of the kinetic problem and thus the strict spatial behaviour of the velocity distribution and of significant macroscopic properties of the electrons has been determined and analysed. Furthermore, the impact of higher order terms of the expansion has been revealed and the falsification of the velocity distribution and of related macroscopic properties has been evaluated when instead of the multi-term solution the simpler two-term solution of the kinetic equation is used.     

Extremal cover times for random walks on trees

Let C_ν(T) denote the “cover time” of the tree T from the vertex v, that is, the expected number of steps before a random walk starting at v hits every vertex of T. Asymptotic lower bounds for C_ν(T) (for T a tree on n vertices) have been obtained recently by Kahn, Linial, Nisan and Saks, and by Devroye and Sbihi; here, we obtain the exact lower bound (approximately 2n In n) by showing that C_ν(T) is minimized when T is a star and v is one of its leaves. In addition, we show that the time to cover all vertices and then return to the starting point is minimized by a star (beginning at the center) and maximized by a path (beginning at one of the ends).     

Total synthesis of pamamycin-649B

The first total synthesis of the macrodiolide antibiotic pamamycin-649B (1) was achieved by using sultone methodology. The diethyl substituted larger hydroxy acid fragment was constructed in a concise fashion through domino elimination/alkoxide-directed 1,6-additions of ethyllithium to sultones derived from intramolecular Diels-Alder reaction of furan-containing vinylsulfonates. Intermolecular Yamaguchi esterification of the two hydroxy acid building blocks and subsequent Yamaguchi cyclization eventually provided the target macrocycle 1. Since the final lactonization with formation of the ester linkage between C1' and the C8 oxygen proceeded with complete C2' epimerization, the more readily available C2' epimeric smaller fragment could be used to streamline the synthetic sequence.     

Core, shell, and surface-optimized dendrimers for blue light-emitting diodes

We present a novel core-shell-surface multifunctional structure for dendrimers using a blue fluorescent pyrene core with triphenylene dendrons and triphenylamine surface groups. We find efficient excitation energy transfer from the triphenylene shell to the pyrene core, substantially enhancing the quantum yield in solution and the solid state (4-fold) compared to dendrimers without a core emitter, while TPA groups facilitate the hole capturing and injection ability in the device applications. With a luminance of up to 1400 cd/m(2), a saturated blue emission CIE(xy) = (0.15, 0.17) and high operational stability, these dendrimers belong to the best reported fluorescence-based blue-emitting organic molecules.