The influence of substrate surface roughness on microstrip transmission line loss using conventional analyses and length‐scale fractal analysis

Two components of conductor topography can impact conductor loss for signals in the GHz frequency range: conductor–ceramic interface roughness and conductor edge angle. This study is an experimental investigation of the influence of these conductor topographies on conductor loss in microstrip circuits produced by thick‐film technology. The aluminum nitride ceramic substrates have different surface roughnesses due to different surface finish processes. The substrate surfaces were characterized using conventional and length‐scale fractal analysis. The conductor–ceramic interface was measured with a contact profilometer. The conductor edge angle and conductor edge profile were measured optically. It was found that there is a direct correlation between conductor loss and conductor edge angle, whereas there is an inverse correlation between loss and substrate roughness or relative length of the conductor–ceramic interface. This is the opposite result to the conventional expectation of surface roughness effects on conductor loss. There is also a negative correlation between conductor edge angle and surface roughness or relative length. The loss behavior can be explained by the interaction of the conductor paste with the surfaces during processing. The paste tends to spread more on the smoother surfaces, and thus creates an elongated edge of diminishing cross‐section and a small edge angle. This leads to greater conductor loss. Copyright © 2009 John Wiley & Sons, Ltd.     

Isomorph-Free Exhaustive Generation

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists. In one form of our technique, no explicit isomorphism testing is required. In the other form, isomorph testing is restricted to within small subsets of the entire set of objects. A variety of different examples are presented, including the generation of graphs with some hereditary property, the generation of Latin rectangles and the generation of balanced incomplete block designs. The technique can also be used to perform unbiased statistical analysis, including approximate counting, of sets of objects too large to generate exhaustively.     

Weak approximation over function fields

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction. Mathematics Subject Classification (2000) 14M20, 11G35, 14G05     

Mono‐, di‐ and trimethylated homologues of isoprenoid tetraether lipid cores in archaea and environmental samples: mass spectrometric identification and significance

Higher homologues of widely reported C₈₆ isoprenoid diglycerol tetraether lipid cores, containing 0–6 cyclopentyl rings, have been identified in (hyper)thermophilic archaea, representing up to 21% of total tetraether lipids in the cells. Liquid chromatography‐tandem mass spectrometry confirms that the additional carbon atoms in the C_87‐88 homologues are located in the etherified chains. Structures identified include dialkyl and monoalkyl (‘H‐shaped’) tetraethers containing C_40‐42 or C_81‐82 hydrocarbons, respectively, many representing novel compounds. Gas chromatography‐mass spectrometric analysis of hydrocarbons released from the lipid cores by ether cleavage suggests that the C₄₀ chains are biphytanes and the C₄₁ chains 13‐methylbiphytanes. Multiple isomers, having different chain combinations, were recognised among the dialkyl lipids. Methylated tetraethers are produced by Methanothermobacter thermautotrophicus in varying proportions depending on growth conditions, suggesting that methylation may be an adaptive mechanism to regulate cellular function. The detection of methylated lipids in Pyrobaculum sp. AQ1.S2 and Sulfolobus acidocaldarius represents the first reported occurrences in Crenarchaeota. Soils and aquatic sediments from geographically distinct mesotemperate environments that were screened for homologues contained monomethylated tetraethers, with di‐ and trimethylated structures being detected occasionally. The structural diversity and range of occurrences of the C_87‐89 tetraethers highlight their potential as complementary biomarkers for archaea in natural environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Benzylic Functionalization of Anthrones via the Asymmetric Ring Opening of Oxabicycles Utilizing a Fourth‐Generation Rhodium Catalytic System

While anthrones exist as privileged scaffolds in bioactive molecules, the enantioselective functionalization of anthrones is surprisingly scarce in the literature, with no asymmetric transition metal catalyzed example to date. Herein, we report the first asymmetric transition metal catalyzed benzylic functionalization of anthrones through the rhodium(I) catalyzed desymmetrization of oxabicycles. As previously developed rhodium(I) systems were found to be unsuitable for this substrate, a new robust fourth‐generation [Rh(cod)OH]₂ based catalytic system was developed to address synthetic challenges in this protocol.     

Koszulity of some path categories

We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.     

Indium triflate mediated tandem acetalisation-acetal exchange reactions under solvent-free conditions

Acyclic acetals and ketals undergo exchange reactions in the presence of catalytic quantities of indium(III) triflate and diols to generate the corresponding cyclic acetals and ketals in excellent yield. The protocol is rapid, employs mild conditions and can be adapted to employ solvent-free reaction conditions. We have further developed this methodology to encompass a tandem acetalisation-acetal exchange protocol which provides facile access to cyclic ketals from unreactive ketones also under very mild, solvent-free reaction conditions.