The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

The binding of manganese(II) and zinc(II) to the synthetic oligonucleotide d(C-G-C-G-A-A-T-T-C-G-C-G)2. A 1H NMR study

The interaction of the synthetic oligonucleotide d(C-G-C-G-A-A-T-T-C-G-C-G)2 with two different transition-metal ions has been investigated in aqueous solution by means of 1H NMR spectroscopy. The effects on the DNA due to the presence of manganese(II) or zinc(II) have been monitored by observing the paramagnetic broadening and diamagnetic shifts of the non-exchangeable proton resonance lines, respectively. The 1H NMR spectra acquired during the course of the manganese(II) titration show very distinct broadening effects on certain DNA resonance lines. Primarily, the H8 resonance of G4 is affected, but also the H5 and H6 resonances of C3 are clearly affected by the metal. The results imply that the binding of manganese(II) to DNA is sequence specific. The 1H spectra obtained during the zinc(II) titration reveal diamagnetic shift effects which largely conform with the paramagnetic broadening effects due to the presence of manganese(II), although this picture is somewhat more complex. The H8 resonance of G4 displays a clearly visible high-field shift, while for the other guanosine H8 protons this effect is absent. The H1' and H2' protons of C3 show an effect of similar strength, although in the opposite direction, while H5 and H6 of C3 are only slightly affected. Local differences in the structure of the DNA and the basicities of potential binding sites on different base steps in the sequence might account for the observed sequence selectivity.     

Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

超重元素(新核素)合成研究进展情况分析和展望

本文在介绍和分析国际、国内在超重元素（新核素）合成实验研究与理论研究进展情况的基础上对我国今后如何从理论与实验的结合上开展超重元素（核）合成研究工作提出一些看法和建议，提供讨论。     

Real time ellipsometry for monitoring plasma-assisted epitaxial growth of GaN

GaN is grown on Si-face 4H-SiC(0 0 0 1) substrates using remote plasma-assisted methods including metalorganic chemical vapour deposition (RP-MOCVD) and molecular beam epitaxy (MBE). Real time spectroscopic ellipsometry is used for monitoring all the steps of substrate pre-treatments and the heteroepitaxial growth of GaN on SiC. Our characterization emphasis is on understanding the nucleation mechanism and the GaN growth mode, which depend on the SiC surface preparation.     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Crystal and molecular structure of thiamine monochloride

The crystal and molecular structure of thiamine monochloride (C₁₂H₁₇N₄OSCl) was determined by X-ray diffraction and refined to a finalR value of 0.042. The compound crystallizes in the monoclinic system, space groupP2₁/a, with cell constantsa=18.929(4),b=11.663(2),c=6.376(2) Å and=96.72(8)°. The thiamine molecule is anhydrous and unprotonated, and the torsion angles at the methylene carbon show that it possesses anF conformation. The dihedral angle value of 84.16(6)° between thiazolium and pyrimidine rings is in the normal range found for the thiamine withF conformation, protonated or not, hydrated or not. Thiamine therefore has the same conformation notwithstanding protonation or hydration, with the rings similarly oriented in all the crystal structures containing thiamine.