Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Titrimetrische Bestimmung von Zink mit Äthylendiamintetraessigsäure in Gegenwart von Palladium(II)

Zusammenfassung Komplexometrische Methoden zur Bestimmung von Zink in Gegenwart von Palladium(II) wurden ausgearbeitet. Dabei wird Palladium(II) mit Kaliumcyanid getarnt und der Zinkgehalt entweder bei p_H 5,8 oder nach Demaskierung mit Chloralhydrat bei p_H 10 mit ÄDTA gegen Methylthymolblau titriert. Diese Zinkbestimmung läßt sich auch in Anwesenheit einer Mischung von Palladium(II), Kupfer(II), Nickel und Kobalt(II) durchführen.

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Summary Complexometric methods have been developed for determining zinc in the presence of palladium(II). In these procedures, Pa(II) is masked with potassium cyanide and the zinc content is titrated either at p_H 5.8 or after demasking with chloralhydrate is titrated with EDTA at p_H 10 in the presence of methylthymol blue. This zinc determination may also be conducted in the presence of a mixture of palladium(II), copper(II), nickel(II),and cobalt(II).

     

Novel method for the preparation of anionic surfactant-selective electrodes

A simple one-step synthesis is described for the functionalization of poly(vinyl chloride) used for the preparation of anionic surfactant-selective membrane electrodes. The method is based on the nucleophilic substitution of a fraction of the chlorine atoms bound to the poly(vinyl chloride) backbone by trimethylamine. The prepared slightly charged polymer gave rise to high-quality surfactant-selective electrode membranes, which had a Nernstian response, short response time, and appropriate stability.     

“Integer-making” theorems

Let X = {x₁, x₂,…} be a finite set and associate to every x_i a real number α_i. Let f(n) [g (n)] be the least value such that given any family $\text{F}$ of subsets of X having maximum degree n [cardinality n], one can find integers α_i, i=1,2,… so that α_i ? α_i|<1 and

$\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{a}{}_{\mathrm{i}}\text{?}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{α}{}_{\mathrm{i}}\text{≤?(n)}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{a}{}_{\mathrm{i}}\text{?}\text{∑}\text{x}{}_{\mathrm{i\; ?\; E}}\text{α}{}_{\mathrm{i}}\text{≤}\text{g(n)}$

for all $\text{E ?}\text{F}$. We prove

$\text{f(n)≤n ? 1 and g(n)≤c(n}\text{log}\text{n)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

.     

Finitely additive states and completeness of inner product spaces

For any unit vector in an inner product space S, we define a mapping on the system of all -closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. Finally, the result will be generalized to general inner product spaces.     

Synthesis of Benzopyran Derivatives,XIV: New Procedure for the Preparation of 2,2-Dimethyl-2H-chromenes

2,2-Dimethyl-4-methoxychromans (1–12) have been converted into 2,2-dimethyl-2H-chromenes (13–24) in acidic media.     

Identification of lipophilic bioproduct portfolio from bioreactor samples of extreme halophilic archaea with HPLC-MS/MS

Extreme halophilic archaea are a yet unexploited source of natural carotenoids. At elevated salinities, however, material corrosivity issues occur and the performance of analytical methods is strongly affected. The goal of this study was to develop a method for identification and downstream processing of potentially valuable bioproducts produced by archaea. To circumvent extreme salinities during analysis, a direct sample preparation method was established to selectively extract both the polar and the nonpolar lipid contents of extreme halophiles with hexane, acetone and the mixture of MeOH/MTBE/water, respectively. Halogenated solvents, as used in conventional extraction methods, were omitted because of environmental considerations and potential process scale-up. The HPLC-MS/MS method using atmospheric pressure chemical ionization was developed and tuned with three commercially available C₄₀ carotenoid standards, covering the wide polarity range of natural carotenoids, containing different number of OH-groups. The chromatographic separation was achieved on a C₃₀ RP-HPLC column with a MeOH/MTBE/water gradient. Polar lipids, the geometric isomers of the C₅₀ carotenoid bacterioruberin, and vitamin MK-8 were the most valuable products found in bioreactor samples. In contrast to literature on shake flask cultivations, no anhydrous analogues of bacterioruberin, as by-products of the carotenoid biosynthesis, were detected in bioreactor samples. This study demonstrates the importance of sample preparation and the applicability of HPLC-MS/MS methods on real samples from extreme halophilic strains. Furthermore, from a biotechnological point-of-view, this study would like to reveal the relevance of using controlled and defined bioreactor cultivations instead of shake flask cultures in the early stage of potential bioproduct profiling.     

Total Syntheses of (−)-Minovincine and (−)-Aspidofractinine through a Sequence of Cascade Reactions

We report 8-step syntheses of (−)-minovincine and (−)-aspidofractinine using easily available and inexpensive reagents and catalyst. A key element of the strategy was the utilization of a sequence of cascade reactions to rapidly construct the penta- and hexacyclic frameworks. These cascade transformations included organocatalytic Michael-aldol condensation, a multistep anionic Michael-S_N2 cascade reaction, and Mannich reaction interrupted Fischer indolization. To streamline the synthetic routes, we also investigated the deliberate use of steric effect to secure various chemo- and regioselective transformations.     

A New Oxygen Containing Pyclen-Type Ligand as a Manganese(II) Binder for MRI and 52Mn PET Applications: Equilibrium,Kinetic, Relaxometric,Structural and Radiochemical Studies

A new pyclen-3,9-diacetate derivative ligand (H₂3,9-OPC2A) was synthesized possessing an etheric O-atom opposite to the pyridine ring, to improve the dissociation kinetics of its Mn(II) complex (pyclen = 3,6,9,15-tetraazabicyclo(9.3.1)pentadeca-1(15),11,13-triene). The new ligand is less basic than the N-containing analogue (H₂3,9-PC2A) due to the non-protonable O-atom. In spite of its lower basicity, the conditional stability of the [Mn(3,9-OPC2A)] (pMn = −log(Mn(II)), c_L = c_Mn(II) = 0.01 mM. pH = 7.4) remains unaffected (pMn = 8.69), compared to the [Mn(3,9-PC2A)] (pMn = 8.64). The [Mn(3,9-OPC2A)] possesses one water molecule, having a lower exchange rate with bulk solvents (k_ex²⁹⁸ = 5.3 ± 0.4 × 10⁷ s⁻¹) than [Mn(3,9-PC2A)] (k_ex²⁹⁸ = 1.26 × 10⁸ s⁻¹). These mild differences are rationalized by density-functional theory (DFT) calculations. The acid assisted dissociation of [Mn(3,9-OPC2A)] is considerably slower (k₁ = 2.81 ± 0.07 M⁻¹ s⁻¹) than that of the complexes of diacetates or bisamides of various 12-membered macrocycles and the parent H₂3,9-PC2A. The [Mn(3,9-OPC2A)] is inert in rat/human serum as confirmed by ⁵²Mn labeling (nM range), as well as by relaxometry (mM range). However, a 600-fold excess of EDTA (pH = 7.4) or a mixture of essential metal ions, propagated some transchelation/transmetalation in 7 days. The H₂3,9-OPC2A is labeled efficiently with ⁵²Mn at elevated temperatures, yet at 37 °C the parent H₂3,9-PC2A performs slightly better. Ultimately, the H₂3,9-OPC2A shows advantageous features for further ligand designs for bifunctional chelators.