On partitioning two matroids into common independent subsets

Let M₁ and M₂ be two matroids on the same ground set S. We conjecture that if there do not exist disjoint subsets A₁,A₂,…,A_k+1 of S, such that _isp_M1(A_i)≠Ø, and similarly for M₂, then S is partitioned into k sets, each independent in both M₁ and M₂. This is a possible generalization of König's edge-coloring theorem. We prove the conjecture for the case k=2 and for a regular case, in which both matroids have the same rank d, and S consists of k·d elements. Finally, we prove another special case related to a conjecture of Rota.     

A Type of Auxiliary for Native Chemical Peptide Ligation beyond Cysteine and Glycine Junctions

Native chemical ligation enables the chemical synthesis of proteins. Previously, thiol‐containing auxiliary groups have been used to extend the reaction scope beyond N‐terminal cysteine residues. However, the N‐benzyl‐type auxiliaries used so far result in rather low reaction rates. Herein, a new N^α‐auxiliary is presented. Consideration of a radical fragmentation for cleavage led to the design of a new auxiliary group which is selectively removed under mildly basic conditions (pH 8.5) in the presence of TCEP and morpholine. Most importantly and in contrast to previously described auxiliaries, the 2‐mercapto‐2‐phenethyl auxiliary is not limited to Gly‐containing sites and ligations succeed at sterically demanding junctions. The auxiliary is introduced in high yield by on‐resin reductive amination with commercially available amino acid building blocks. The synthetic utility of the method is demonstrated by the synthesis of two antimicrobial proteins, DCD‐1L and opistoporin‐2.     

On uncountable hypersimple unidimensional theories

We extend the dichotomy between 1-basedness and supersimplicity proved in Shami (J Lond Math Soc 83(2):309–332, 2011). The generalization we get is to arbitrary language, with no restrictions on the topology [we do not demand type-definabilty of the open set in the definition of essential 1-basedness from Shami (J Lond Math Soc 83(2):309–332, 2011)]. We conclude that every (possibly uncountable) hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the language is countable.     

Hybrid silver nanoparticle and transparent conductive oxide structure for silicon solar cell applications

Transparent conductive oxides (TCOs) have been widely used as electrodes for various solar cell structures. For heterojunction silicon wafer solar cells, the front TCO layer not only serves as a top electrode (by enhancing the lateral conductance of the underlying amorphous silicon film), but also as an antireflection coating. These requirements make it difficult to simultaneously achieve excellent conductance and transparency, and thus, only high‐quality indium tin oxide (ITO) has as yet found its way into industrial heterojunction silicon wafer solar cells. In this Letter, we present a cost‐effective hybrid structure consisting of a TCO layer and a silver nano‐particle mesh. This structure enables the separate optimization of the electrical and optical requirements. The silver nanoparticle mesh provides high electrical conductance, while the TCO material is optimized as an antireflection coating. Therefore, this structure allows the use of cost‐effective (and less conductive) TCO materials, such as aluminium‐doped zinc oxide. The performance of the hybrid structure is demonstrated to achieve a similar visible transmission (～86% in the 380–780 nm range) as an 80 nm thick ITO layer, but with 10 times better lateral conductance. The presented hybrid structure thus seems well suited for a variety of photovoltaic devices. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Intersection of Two Infinite Matroids

Conjecture: Let M and N be two matroids (possibly of infiniteranks) on the same set S. Then there exists a set I independentin both M and N, which can be partitioned as I=HK, where sp_M(H)sp_N(K)=S.This conjecture is an extension of Edmonds' matroid intersectiontheorem to the infinite case. We prove the conjecture when oneof the matroids (say M) is the sum of countably many matroidsof finite rank (the other matroid being general). For the proofwe have also to answer the following question: when does thereexist a subset of S which is spanning for M and independentin N?     

On Serial Symmetric Exchanges of Matroid Bases

We study some properties of a serial (i.e., one‐by‐one) symmetric exchange of elements of two disjoint bases of a matroid. We show that any two elements of one base have a serial symmetric exchange with some two elements of the other base. As a result, we obtain that any two disjoint bases in a matroid of rank 4 have a full serial symmetric exchange