Vergleichende Morphinbestimmungen

Ohne Zusammenfassung     

Zur Erkennung terti?rer Alkohole

Ohne Zusammenfassung     

List Homomorphisms and Circular Arc Graphs

G , H, and lists , a list homomorphism of G to H with respect to the lists L is a mapping , such that for all , and for all . The list homomorphism problem for a fixed graph H asks whether or not an input graph G together with lists , , admits a list homomorphism with respect to L. We have introduced the list homomorphism problem in an earlier paper, and proved there that for reflexive graphs H (that is, for graphs H in which every vertex has a loop), the problem is polynomial time solvable if H is an interval graph, and is NP-complete otherwise. Here we consider graphs H without loops, and find that the problem is closely related to circular arc graphs. We show that the list homomorphism problem is polynomial time solvable if the complement of H is a circular arc graph of clique covering number two, and is NP-complete otherwise. For the purposes of the proof we give a new characterization of circular arc graphs of clique covering number two, by the absence of a structure analogous to Gallai's asteroids. Both results point to a surprising similarity between interval graphs and the complements of circular arc graphs of clique covering number two. Received: July 22, 1996/Revised: Revised June 10, 1998     

A heterogeneous catalytic method for the conversion of nitriles into amides using molecular sieves modified with copper(II)

A heterogenous catalytic method is developed for the hydration of nitriles into amides with acetaldoxime. Copper(II) supported on 4 Å molecular sieves is an efficient catalyst for this reaction.     

Red‐Emitting Rhodamine Dyes for Fluorescence Microscopy and Nanoscopy

Fluorescent markers emitting in the red are extremely valuable in biological microscopy since they minimize cellular autofluorescence and increase flexibility in multicolor experiments. Novel rhodamine dyes excitable with 630 nm laser light and emitting at around 660 nm have been developed. The new rhodamines are very photostable and have high fluorescence quantum yields of up to 80 %, long excited state lifetimes of 3.4 ns, and comparatively low intersystem‐crossing rates. They perform very well both in conventional and in subdiffraction‐resolution microscopy such as STED (stimulated emission depletion) and GSDIM (ground‐state depletion with individual molecular return), as well as in single‐molecule‐based experiments such as fluorescence correlation spectroscopy (FCS). Syntheses of lipophilic and hydrophilic derivatives starting from the same chromophore‐containing scaffold are described. Introduction of two sulfo groups provides high solubility in water and a considerable rise in fluorescence quantum yield. The attachment of amino or thiol reactive groups allows the dyes to be used as fluorescent markers in biology. Dyes deuterated at certain positions have narrow and symmetrical molecular mass distribution patterns, and are proposed as new tags in MS or LC‐MS for identification and quantification of various substance classes (e.g., amines and thiols) in complex mixtures. High‐resolution GSDIM images and live‐cell STED‐FCS experiments on labeled microtubules and lipids prove the versatility of the novel probes for modern fluorescence microscopy and nanoscopy.     

Linear-time certifying algorithms for near-graphical sequences

A sequence 〈d₁,d₂,…,d_n〉 of non-negative integers is graphical if it is the degree sequence of some graph, that is, there exists a graph G on n vertices whose ith vertex has degree d_i, for 1≤i≤n. The notion of a graphical sequence has a natural reformulation and generalization in terms of factors of complete graphs.If H=(V,E) is a graph and g and f are integer-valued functions on the vertex set V, then a (g,f)-factor of H is a subgraph G=(V,F) of H whose degree at each vertex v∈V lies in the interval [g(v),f(v)]. Thus, a (0,1)-factor is just a matching of H and a (1, 1)-factor is a perfect matching of H. If H is complete then a (g,f)-factor realizes a degree sequence that is consistent with the sequence of intervals 〈[g(v₁),f(v₁)],[g(v₂),f(v₂)],…,[g(v_n),f(v_n)]〉.Graphical sequences have been extensively studied and admit several elegant characterizations. We are interested in extending these characterizations to non-graphical sequences by introducing a natural measure of “near-graphical”. We do this in the context of minimally deficient (g,f)-factors of complete graphs. Our main result is a simple linear-time greedy algorithm for constructing minimally deficient (g,f)-factors in complete graphs that generalizes the method of Hakimi and Havel (for constructing (f,f)-factors in complete graphs, when possible). It has the added advantage of producing a certificate of minimum deficiency (through a generalization of the Erdös-Gallai characterization of (f,f)-factors in complete graphs) at no additional cost.     

Two-photon near- and far-field fluorescence microscopy with continuous-wave excitation

We report on scanning far- and near-field two-photon microscopy of cell nuclei stained with DAPI and bisbenzimidazole Hoechst 33342 (BBI-342) with the 647-nm laser line of a cw ArKr mixed-gas laser. Two-photon-excited fluorescence images are obtained for 50-200 mW of average power at the sample. A nearly quadratic dependence of fluorescence intensity on laser power confirmed the two-photon effect. The nonlinearity was further supported by evidence of three-dimensional sectioning in a scanning far-field microscope. We find that the cw two-photon irradiation sufficient for imaging within typically 5 s does not significantly impair cell cycling of BBI-342-labeled live cells. Finally, high-resolution imaging in scanning near-field microscopy with good contrast is demonstrated.