An eulerian trail traversing specified edges in given order

The following results are proved in this paper. Let G be a 2k-edge-connected eulerian graph. (i) For every set {e₁, e₂, ?, e_2k+1} ? E(G) there is an eulerian trail T of the form e₁, e₂, ?, e_2k+1, ?. (ii) For every set E* = {e₁, e₂, ?, e_k} ? E(G) there is an eulerian trail T = e₁, ?, e₂, ?, e_k, ? in which the elements of E* are traversed in accordance with a prescribed orientation. © 1995 John Wiley & Sons, Inc.     

Über ESR-spektroskopische untersuchungen am radikaldianion des lophins und seine cyclisierung zu 2-phenyl-phenanthroimidazol

Treating lophine with potassium at ?50° in an inert solvent yields the radical dianion 6 of this compound. The solution being warmed to room temperature, the radical rearranges to a red diamagnetic intermediate 7. In presence of potassium then the radical dianion 3 of 2-phenyl-4,5,(9′,10′)-phenanthrimidazole is formed which has been described earlier.ESR-spectroscopical investigations show, that the spin density in the 2-phenyl ring of radical 6 vanishes. According to spin density calculations 2-phenyl residue and heterocycle are strongly distorted.     

Controlled anodic generation of the catalyst in kinetic continuous flow analysis

Controlled anodic dissolution of copper in a separate generator cell yields well-defined concentrations of catalyst, depending on the voltage applied. This adjustable generation of copper catalyst makes it possible to determine iron over a wide range of concentration (10–1500 μg Fe³⁺ ml^-1) via the iron(III)—thiosulphate reaction. By the copper(II)-catalyzed hydrogen peroxide—hydroquinone reaction, EDTA can be determined as an inhibitor (0.5–5 μg ml^-1) and cadmium(II) as a reactivator (1–10 μg ml^-1). As zinc(II) forms complexes with 2,2'-bipyridine, which activates copper in this reaction, it can be determined (5–50 μg Zn²⁺ ml^-1) by measuring the decrease in activation. The electrogeneration of silver ion as a catalyst is also described. The sulphanilic acid—peroxodisulphate reaction is catalyzed by silver(I), which is again activated by 2,2'-bipyridine. Zinc(II) can be determined (0.29–2.9 mg Zn²⁺ ml^-1) by the same principle as in the copper(II)-catalyzed reaction.     

Solid-phase synthesis of lipidated peptides

Characteristic partial structures of lipidated proteins embodying different lipid groups as well as additional fluorescent tags or a maleimide for coupling to proteins can be synthesized readily by means of a new solid-phase technique employing the oxidative cleavage of the hydrazide linker as well as on-resin farnesylation and palmitoylation after appropriate deprotection of cysteine thiol groups as the key steps.     

Polymerization in the crystalline state. IX. Relation between the velocity of radiation-induced in-source polymerization and post-polymerization

A general relation is derived between the polymerization velocities to be expected for crystalline monomers during irradiation at a polymerization temperature and the post-polymerization observed in samples irradiated at very low temperatures and subsequently warmed outside the irradiation source. For acrylamide, the experimental data are in satisfactory agreement with the theoretical relationship. The possible reasons for a deviation from this relationship are discussed.     

Electric-field driven director oscillations in a nematic liquid crystal: a NMR investigation

We have investigated the oscillatory behavior of the nematic director for 4-pentyl-4'-cyanobiphenyl (5CB) when it is subjected to a static magnetic field and a sinusoidal electric field. In these experiments the two fields were inclined at about 50 degrees and the frequency of the electric field was varied from several hertz to approximately 1000 Hz. The director orientation was measured using time-resolved deuterium NMR spectroscopy since this has the advantage of being able to determine the state of director alignment in the sample. In fact, for all of the frequencies studied the director is found to remain uniformly aligned. Since the diamagnetic and dielectric anisotropies are both positive the director oscillates in the plane formed by the two fields. These oscillations were observed to continue for many cycles, indicating that the coherence in the director orientation was not lost during this motion. The maximum and minimum angles made by the director with the magnetic field were determined, as a function of frequency, from the NMR spectrum averaged over many thousand cycles of the oscillations. At low frequencies (several hertz) these limiting angles are essentially independent of frequency but as the frequency increases the two angles approach each other and become equal at high frequencies, typically 1000 Hz. Our results are well explained by a hydrodynamic theory in which the sinusoidal time dependence of the electric field is included in the torque-balance equation. This analysis also shows that, for a range of frequencies between the high and low limits, these NMR experiments can give dynamic as well as static information concerning the nematic phase.     

Rapid separation of phenylthiohydantoin amino acids: ambient pressure ion-mobility mass spectrometry (IMMS)

An electrospray ionization (ESI) ambient pressure ion-mobility spectrometer (APIMS) interfaced to an orthogonal reflector time-of-flight mass spectrometer (TOFMS) was evaluated for the first time as a detector for the identification of phenylthiohydantoin (PTH)-derivatized amino acids, the final products in the Edman sequencing process of peptides and proteins. The drift and flight times of the twenty common PTH amino acids were characterized by a well-defined 2-D mobility/mass spectral pattern. The combination of mobility/mass modes of analysis gave rise to a unique trend-line formation for the series of PTH amino acids. In addition, each PTH amino acid had a unique reduced mobility constant K(o), thus enabling the differentiation of all the amino acid derivatives including the PTH-leucine and PTH-isoleucine isomers. More importantly it was shown that it was possible to resolve a complete reference mixture of PTH amino acids in a single experimental run in less than 1 min. Detection limits for the PTH amino acids were found to range from 1.04 to 3.52 ng; indicating that the limits of detection were less than 17.0 pmol for all of the PTH amino acids.     

How constant are Ritchie's "constant selectivity relationships"? A general reactivity scale for n-, pi-, and sigma-nucleophiles

The kinetics of 82 reactions of benzhydrylium ions (Ar(2)CH(+)) with n-nucleophiles has been determined at 20 degrees C. Evaluation by the equation log k = s(N + E) delivered the reactivity parameters N and s for 15 n-nucleophiles (water, hydroxide, amines, etc.). All nucleophiles except water (s = 0.89) and (-)SCH(2)CO(2)(-) (s = 0.43) have closely similar slope parameters (0.52 < s < 0.71), indicating that the reactions of most n-nucleophiles approximately follow Ritchie's constant selectivity relationship (s = constant). The different slope parameter for water is recognized as the main reason for the deviations from the Ritchie relationship reported in 1986. Correlation analysis of the rate constants for the reactions of benzhydrylium ions with the n-nucleophiles (except H(2)O) on the basis of Ritchie's equation log k = N(+) + log k(0) yields a statistically validated set of N(+) parameters for Ritchie-type nucleophiles and log k(0) parameters for benzhydrylium ions. The N and s parameters of the n-nucleophiles derived from their reactions with benzhydrylium ions were combined with literature data for the reactions of these nucleophiles with other carbocations to yield electrophilicity parameters E for tritylium, tropylium, and xanthylium ions. While the E parameters for tropylium and xanthylium ions appear to be generally applicable, it is demonstrated that the E parameters of tritylium ions can be used to predict reactivities toward n-nucleophiles as well as hydride transfer rate constants but not rates for the reactions of tritylium ions with pi-nucleophiles. It is now possible to merge the large data sets determined by Ritchie and others with our kinetic data and present a nucleophilicity scale comprising n- (e.g., amines), pi- (e.g., alkenes and arenes), and sigma-nucleophiles (e.g., hydrides).     

Homological domino effects and the first Finitistic Dimension Conjecture

Summary Counterexamples to the first Finitistic Dimension Conjecture are constructed. In fact, for any fieldk and any integerm2, there exist finite dimensionalk-algebras such that the little finitistic dimension of ism, while the big finitistic dimension ism+1. Our examples are monomial relation algebras; within this class of algebras the big and little finitistic dimensions cannot differ by more than 1. The analysis of the examples is based on a sharp picture of arbitrary second syzygies over monomial relation algebras.Oblatum 5-VI-1991 & 28-X-1991This research was partially supported by a grant from the National Science Foundation. It is dedicated to Maurice Auslander on the occasion of his sixtyfifth birthday.