Longest Paths and Longest Cycles in Graphs with Large Degree Sums

 Let p(G) and c(G) denote the number of vertices in a longest path and a longest cycle, respectively, of a finite, simple graph G. Define σ₄(G)=min{d(x ₁)+d(x ₂)+ d(x ₃)+d(x ₄) | {x ₁,…,x ₄} is independent in G}. In this paper, the difference p(G)−c(G) is considered for 2-connected graphs G with σ₄(G)≥|V(G)|+3. Among others, we show that p(G)−c(G)≤2 or every longest path in G is a dominating path. Received: August 28, 2000 Final version received: May 23, 2002     

Vinyl Triflimides—A Case of Assisted Vinyl Cation Formation

A new concept for selectivity control in carbocation‐driven reactions has been identified which allows for the chemo‐, regio‐, and stereoselective addition of nucleophiles to alkynes—assisted vinyl cation formation—enabled by a Li⁺‐based supramolecular framework. Mechanistic analysis of a model complex (Li₂NTf₂⁺?3 H₂O) confirms that solely the formation of a complex between the incoming nucleophile and the transition state of the alkyne protonation is responsible for the resulting selective N addition to the vinyl cation. Into the bargain, a general, operationally simple synthetic procedure to previously inaccessible vinyl triflimides is provided.     

A decision support method for designing vegetation layers with minimised irrigation need

Annals of Operations Research - Selecting a vegetation layer design goes along with determining its future irrigation need. Therefore, it is essential to take a design decision that is minimising...     

Parahydrogen induced polarization of barbituric acid derivatives: 1H hyperpolarization studies

Homogeneous hydrogenation of barbituric acid derivatives with parahydrogen yields a substantial increase of the (1)H NMR signals of the reaction products. These physiologically relevant compounds were hydrogenated at both ambient and elevated temperatures and pressures using a standard cationic rhodium catalyst. The resulting nonthermal nuclear spin polarization (hyperpolarization) is limited by the spin-lattice relaxation time T(1) of the corresponding nuclei in the products, being shorter than the time constant of the hydrogenation. The signal-to-noise ratio of the NMR spectra could be further increased upon signal averaging the antiphase PHIP signals of 25 successive scans following 30 degrees pulse experiments and a delay of 10 s.     

Abläufe der Ammonolysen der Ammoniumhexafluorometallate des Aluminiums,Galliums und Indiums, (NH4)3MF6 (M = Al,Ga, In)

The Courses of the Ammonolyses of the Ammonium Hexafluorometalates of Aluminum, Gallium, and Indium, (NH₄)₃MF₆ (M = Al, Ga, In) The courses of the ammonolysis reactions of the ammonium hexafluorometalates (NH₄)₃MF₆ (M = Al, Ga, In) were investigated with the aid of in‐situ powder diffractometry and differential thermal analysis. Under these conditions, the reaction of (NH₄)₃AlF₆ with gaseous ammonia yields at about 360 °C AlF₃ via the intermediates NH₄AlF₄, Al(NH₃)₂F₃ and Al(NH₃)F₃. The ammonolysis of (NH₄)₃GaF₆ produces GaN at about 400 °C. Depending upon the actual reaction conditions, the intermediates NH₄GaF₄ and Ga(NH₃)F₃ as well as their ammonia adducts NH₄GaF₄ · NH₃ and Ga(NH₃)₂F₃ and the amide‐ammoniate Ga(NH₃)(NH₂)F₂ are observed. In the case of (NH₄)₃InF₆ the intermediates (NH₄)₃InF₆ · NH₃ and In(NH₃)F₃ may exist; there are also indications for the reduction of In(III) to In(I) and for the existence of In(NH₃)₂F and InF as products of the ammonolysis of (NH₄)₃InF₆.     

The solubility of Co in TiO2 anatase and rutile and its effect on the magnetic properties

Co-doped anatase and rutile bulk-samples prepared by the sol-gel technique are found to be paramagnetic at room-temperature. Only further annealing in Ar/H₂ gas results in a ferromagnetic behavior. X-ray diffraction and electron-microscope studies reveal for low doping levels <4% the formation of Co-doped rutile samples and the formation of CoTiO₃ as a new phase. Co₃O₄ can be detected in anatase samples with Co doping levels ?4%. The observed Co oxides are reduced by Ar/H₂ to Co metal. The room-temperature ferromagnetism can therefore be traced back to a segregation of metallic Co.     

Stepwise Adsorption of Alkoxy-Pyrene Derivatives onto a Lamellar,Non-Porous Naphthalenediimide-Template on HOPG

The development of new strategies for the preparation of multicomponent supramolecular assemblies is a major challenge on the road to complex functional molecular systems. Here we present the use of a non-porous self-assembled monolayer from uC₃₃-NDI-uC₃₃ , a naphthalenediimide symmetrically functionalized with unsaturated 33 carbon-atom-chains, to prepare bicomponent supramolecular surface systems with a series of alkoxy-pyrene ( PyrOR ) derivatives at the liquid/HOPG interface. While previous attempts at directly depositing many of these PyrOR units at the liquid/HOPG interface failed, the multicomponent approach through the uC₃₃-NDI-uC₃₃ template enabled control over molecular interactions and facilitated adsorption. The PyrOR deposition restructured the initial uC₃₃-NDI-uC₃₃ monolayer, causing an expansion in two dimensions to accommodate the guests. As far as we know, this represents the first example of a non-porous or non-metal complex-bearing monolayer that allows the stepwise formation of multicomponent supramolecular architectures on surfaces.     

Biochemical analysis with microfluidic systems

Microfluidic systems are capillary networks of varying complexity fabricated originally in silicon, but nowadays in glass and polymeric substrates. Flow of liquid is mainly controlled by use of electroosmotic effects, i.e. application of electric fields, in addition to pressurized flow, i.e. application of pressure or vacuum. Because electroosmotic flow rates depend on the charge densities on the walls of capillaries, they are influenced by substrate material, fabrication processes, surface pretreatment procedures, and buffer additives. Microfluidic systems combine the properties of capillary electrophoretic systems and flow-through analytical systems, and thus biochemical analytical assays have been developed utilizing and integrating both aspects. Proteins, peptides, and nucleic acids can be separated because of their different electrophoretic mobility; detection is achieved with fluorescence detectors. For protein analysis, in particular, interfaces between microfluidic chips and mass spectrometers were developed. Further levels of integration of required sample-treatment steps were achieved by integration of protein digestion by immobilized trypsin and amplification of nucleic acids by the polymerase chain reaction. Kinetic constants of enzyme reactions were determined by adjusting different degrees of dilution of enzyme substrates or inhibitors within a single chip utilizing mainly the properties of controlled dosing and mixing liquids within a chip. For analysis of kinase reactions, however, a combination of a reaction step (enzyme with substrate and inhibitor) and a separation step (enzyme substrate and reaction product) was required. Microfluidic chips also enable separation of analytes from sample matrix constituents, which can interfere with quantitative determination, if they have different electrophoretic mobilities. In addition to analysis of nucleic acids and enzymes, immunoassays are the third group of analytical assays performed in microfluidic chips. They utilize either affinity capillary electrophoresis as a homogeneous assay format, or immobilized antigens or antibodies in heterogeneous assays with serial supply of reagents and washing solutions.     

Oxidative Pyrrole Exchange and meso Pyrrylation – Unexpected Reactions of Open‐Chain Tetrapyrrolic 2,2′‐Bidipyrrins

A new hydrogen terminated 2,2′‐bidipyrrin ligand was prepared from a bipyrrole dialdehyde and 3,4‐diethylpyrrole by a POCl₃ induced condensation and isolated as the nickel(II) chelate. Unexpectedly a side reaction occured when base‐deficient and aerobic conditions were chosen in the metalation step. This side reaction led to a novel pentapyrrolic nickel(II) complex with one externally bound pyrrole ring. Further studies showed that the reactions of 2,2′‐bidipyrrins with 3,4‐diethyl‐ or 2,3,4‐trimethylpyrrole and an oxidant resulted in a stepwise exchange of the terminal pyrrole moieties and, in the former case, the introduction of one additional pyrrole ring into one of the two meso positions of the open‐chain tetrapyrrole.