A complementary thermodynamic limit for classical Coulomb matter

The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale _inh. For a system ofN positive andN negative particles, _inh and the characteristic length scale of correlations _corr (=Debye screening length) are related via _inh=(2N)^1/2 _corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, _corr fixed. Its complementary limit is characterized byN, _inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature.     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve

In comparison with direct measurements of unsaturated hydraulic conductivity, the methods of calculations from the moisture retention curve are attractive for their fast and simple use and low cost. These are the main reasons for their increasing use, mainly in spatial variability studies. On the other hand, it is known that their applicability is limited. The possibility of the use of the retention curve to indirectly determine hydraulic conductivities is analyzed as follows. The theoretical derivation of the relationK(h) – (h) is briefly discussed with regards to potential sources of inaccuracy. The sensitivity of the algorithm forK(h) calculation is studied as a response to possible inaccuracies in the retention curve determination. Conclusions about the usability of calculated hydraulic conductivities are drawn.     

α—氨基酸的快原子轰击质谱

本文研究了１８种α－氨基酸的快原子轰击质谱，发现添加三氟乙酸溶液能显著提高灵敏度，改善谱图。特征碎片主要有中性丢失ＣＯ２Ｈ２，Ｈ２Ｏ，ＮＨ３的离子以及Ｒ＾＋离子。侧链的性质决定了碎片的产生和离子的强弱。     

Multielemental characterisation of cobalt by glow discharge quadrupole mass spectrometry

Multielemental determination and the assessment of purity of cobalt metal used in the preparation of Ni-based super-alloys have been carried out by glow discharge quadrupole mass spectrometry (GD-QMS). Relative sensitivity factors (RSF) generated from certified iron matrix reference samples (NIST 663 and 664 low alloy steel pin standards) could be used for the determination of different trace element constituents of the sample. Different wet chemical procedures were also carried out for the determination of the trace constituents in the sample. The GD-QMS results are in reasonably good agreement with those obtained from wet chemical procedures, validating the use of the RSF values generated on low alloy steel standards for the computation of trace element concentrations in cobalt metal. A variety of molecular ions formed through the reaction of cobalt (matrix) with the discharge gas (argon) were also detected.     

Extension of the measuring range of balances

The basic principle of comparing the sample mass with the mass of a reference body in equilibrium gives the equal-armed beam balance a unique accuracy. Main parameters characterising the suitability of the instrument are measuring range, resolution and relative sensitivity (resolution/maximum load). The historical development of the values of these parameters achieved depended strongly on the practical need in those times. Technically unfavourable scales of the oldest Egyptian dynasties (~3000 BC) could resolve mass differences of 1 g and had a relative sensitivity of at least 10^–3. More sophisticated instruments from the 18^th Dynasty (~1567–1320 BC) achieved a relative sensitivity of 10^–4 independent of the size of the instrument. In 350 BC Aristotle clarified the theory of the lever and at about 250 BC Archimedes used the balance for density determinations of solids. The masterpiece of a hydrological balance was Al Chazini’s 'Balance of Wisdom’ built about 1120. Its relative sensitivity was 2⋅10^–5. Real progress took place when scientists like Lavoisier (1743–1794) founded modern chemistry. At the end of the 19^th century metrological balances reached a relative sensitivity of 10^–9 with a maximum load of several kilogrammes. That seems to be the high end of sensitivity of the classical mechanical beam balance with knife edges. Improvements took place by electrodynamic compensation (Emich, Gast). In 1909 Ehrenhaft and Millikan could weigh particles of 10^–15 g by means of electrostatic suspension. In 1957 Sauerbrey invented the oscillating quartz crystal balance. By observing the frequency shift of oscillating carbon nanotubes or of silica nanorods, masses or mass changes in the attogram or zeptogram have been observed recently.     

Fourier interferometric stimulation (FIS) in biology and medicine

A continuously scanning Michelson interferometer was developed to modulate an intensive light source spectrally. The interferogram is used as a stimulus to investigate spectral sensitivities in insects and man. The FIS-method is fast and precise and shows many advantages which are partly based on the advantages of Fourier spectroscopy. The existing applications are summarized.     

原子转移自由基聚合原位合成温敏性微球

以过硫酸钾为引发剂、丙酮-水[V(丙酮)∶V(水)＝4∶6]的混合溶剂为反应介质, 在少量二乙烯苯存在的条件下使苯乙烯(St)和对氯甲基苯乙烯(CMSt)进行无皂乳液共聚反应, 得到了粒径大小均匀的交联型聚苯乙烯(PSt)微球, 由X射线光电子能谱对表面组分测定发现: CMSt上的氯原子在聚合过程中富集于交联微球的表面. 以此交联型PSt微球为原子转移自由基聚合(ATRP)的引发剂, 在22 ℃下引发N-异丙基丙烯酰胺(NIPAAm)进行原位ATRP反应, 得到了表面原子转移自由基聚合接枝的交联聚苯乙烯(PNIPAAm-g-PSt)温敏性微球. 借助傅立叶变换红外光谱、差示扫描量热仪、扫描电子显微镜及激光光散射仪等对PNIPAAm-g-PSt的结构、相转变温度、形态及不同温度下的粒径变化进行了测定, 结果表明NIPAAm单体成功地原位ATRP接枝在交联PSt微球的表面, 接枝微球的球形更规整, 在水中的相转变温度约为32 ℃, 具有明显的温度敏感性.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.