The Moore Bound for Irregular Graphs

 What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10). Received: June 27, 2000 Final version received: July 3, 2001     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

Synthesis and characteristics of microspheres of polystyrene derivatives

Two sytrene derivatives formylstyrene and styrene sulfonylcholoride, were synthesized. Polymeric microspheres in diameters ranging from 0.1 to 2 μm were synthesized by polymerization of chlormoethylstyrene, formylstyrene, and styrene sulfonylcholoride in organic solvents, in the presence of appropriate surfactants. The kinetics of microsphere formation were studied. The molecular weight distribution of the products was determined by gel permeation chromatography. Conditions for binding various amino ligands to the microspheres were also established.     

Effect of solvents on the electrochemistry of olefins and aromatic molecules

Cyclic voltammetry and electrolysis studies were carried out in dimethyl sulfoxide, diglyme and liquid ammonia. The depolarizers were diethyl fumarate, ethyl cinnamate, stilbene and anthracene. The reduction reactions were carried out in the presence of organic halides, phenol, acids and water. The rates of the reactions were measured. The main solvent effect was noticed with water which reacts 100 times faster in diglyme than in liquid ammonia or DMSO. The results of electrolytic experiments with two reactants simultaneously were compared with those predicted from the kinetic data.     

High-throughput screening of enzyme libraries: thiolactonases evolved by fluorescence-activated sorting of single cells in emulsion compartments

Single bacterial cells, each expressing a different library variant, were compartmentalized in aqueous droplets of water-in-oil (w/o) emulsions, thus maintaining a linkage between a plasmid-borne gene, the encoded enzyme variant, and the fluorescent product this enzyme may generate. Conversion into a double, water-in-oil-in-water (w/o/w) emulsion enabled the sorting of these compartments by FACS, as well as the isolation of living bacteria cells and their enzyme-coding genes. We demonstrate the directed evolution of new enzyme variants by screening >10(7) serum paraoxonase (PON1) mutants, to yield 100-fold improvements in thiolactonase activity. In vitro compartmentalization (IVC) of single cells, each carrying >10(4) enzyme molecules, in a volume of <10 femtoliter (fl), enabled detection and selection despite the fast, spontaneous hydrolysis of the substrate, the very low initial thiolactonase activity of PON1, and the use of difusable fluorescent products.     

Mass spectrometric analysis of ceramic components for solid oxide fuel cells

For the determination of trace impurities in ceramic components of solid oxide fuel cells (SOFCs), some mass spectrometric methods have been applied such as spark source mass spectrometry (SSMS), laser ionization mass spectrometry (LIMS), laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and inductively coupled plasma mass spectrometry (ICP-MS). Due to a lack of suitable standard reference materials for quantifying of analytical results on La _x Sr _y MnO₃ cathode material a matrix-matched synthetic standard-high purity initial compounds doped with trace elements-was prepared in order to determine the relative sensitivity coefficients in SSMS and LA-ICP-MS. Radiofrequency glow discharge mass spectrometry (rf-GDMS) was developed for trace analysis and depth profiling of thick non-conducting layers. Surface analytical techniques, such as secondary ion mass spectrometry (SIMS) and sputtered neutral mass spectrometry (SNMS), were used to determine the element distribution on surfaces (homogeneity) and the surface contaminants of SOFC ceramic layers.Dedicated to Professor Dr. rer. nat. Hubertus Nickel on the occasion of his 65th birthday     

Comparative studies of MCs+-SIMS and e–-beam SNMS for quantitative analysis of bulk materials and layered structures

For the quantification of heterostructure depth profiles the knowledge of relative sensitivity factors (RSF) and the influence of matrix effects on the measured profiles is necessary. Matrix dependencies of the measured ion intensities have been investigated for sputtered neutral mass spectrometry (SNMS) and MCs(+)-SIMS. The use of Cs as primary ions for SNMS is advantageous compared to Ar because the depth resolution is improved without changing RSFs determined under Ar bombardment. No significant amount of molecules has been found in the SNMS spectra under Cs bombardment. Using MCs(+)-SIMS the RSFs are matrix dependent. An improvement of depth resolution can be achieved by biasing the sample against the primary ion beam for SNMS due to a reduction of the net energy of the primary ions and a resulting more gracing impact angle.