Proof complexity of propositional default logic

Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen??s system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti??s enhanced calculus for skeptical default reasoning.     

On the structure and dynamics of duplex GNA

Glycol nucleic acid (GNA), with a nucleotide backbone comprising of just three carbons and the stereocenter derived from propylene glycol (1,2-propanediol), is a structural analog of nucleic acids with intriguing biophysical properties, such as formation of highly stable antiparallel duplexes with high Watson-Crick base pairing fidelity. Previous crystallographic studies of double stranded GNA (dsGNA) indicated two forms of backbone conformations, an elongated M-type (containing metallo-base pairs) and the condensed N-type (containing brominated base pairs). A herein presented new crystal structure of a GNA duplex at 1.8 ? resolution from self-complementary 3'-CTC(Br)UAGAG-2' GNA oligonucleotides reveals an N-type conformation with alternating gauche-anti torsions along its (O3'-C3'-C2'-O2') backbone. To elucidate the conformational state of dsGNA in solution, molecular dynamic simulations over a period of 20 ns were performed with the now available repertoire of structural information. Interestingly, dsGNA adopts conformational states in solution intermediate between experimentally observed backbone conformations: simulated dsGNA shows the all-gauche conformation characteristic of M-type GNA with the higher helical twist common to N-type GNA structures. The so far counterintuitive, smaller loss of entropy upon duplex formation as compared to DNA can be traced back to the conformational flexibility inherent to dsGNA but missing in dsDNA. Besides extensive interstrand base stacking and conformational preorganization of single strands, this flexibility contributes to the extraordinary thermal stability of GNA.     

Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 2 – Development of an experimental procedure for the determination of the molar mass of silicon using MC-ICP-MS

The isotopic abundances and thus molar mass M(Si) of a silicon crystal material with natural isotopic abundances have been measured for the first time using multicollector-ICP-mass spectrometry (MC-ICP-MS) in combination with a novel concept of a modified isotope dilution mass spectrometry (IDMS)-method. This experimental work is the further development of part 1 of this series of papers. While part 1 describes the theoretical background and the mathematical derivation of the novel concept in detail, the measurements presented here serve to validate the novel concept and give experimental proof of its capability. Moreover, the also new method for the analytical calculation of calibration factors needed in the determination of absolute isotope amount ratios has been tested successfully. Silicon isotopic abundances have been measured directly from an aqueous alkaline matrix following a new sample preparation protocol developed within the framework of this study. A molar mass of M(Si) = 28.08548(13) g/mol with an associated relative uncertainty of u_rel = 4.6 × 10^?6 (k = 1) has been measured. This is in excellent agreement with the current IUPAC value for the molar mass of natural silicon M(Si_nat) = 28.08550(15) g/mol with u_rel = 5.3 × 10^?6 (k = 1). An uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was calculated to assess the presented results and to validate the novel concept with the help of experimental data. The development of a new experimental procedure is presented in detail and the contributions to the uncertainty are discussed in comparison to part 1 of this work.     

A non-miquelian Laguerre plane satisfying a theorem of miquelian type

This note shows that a theorem of miquelian type known as (M2) holds in a certain non miquelian Laguerre plane of shear type as defined by Löwen and Pfüller[1].Dedicated to Professor H. Karzel on the occasion of his 70th birthday     

Gruppen mit reduziblem Subnormalteilerverband

Ohne Zusammenfassung     

Konstruktion von Fundamentallösungen für Convolutoren

We introduce a constructive method for finding fundamental solutions of convolutors in general distribution spaces where a generalized Fourier transform exists and where the topology of the space of test functions can be described by means of an analytic uniform structure in the sense of Ehrenpreis. For convolutors f in a space of Beurling distributions we obtain solutions of unbounded order (resp. of bounded order; resp. of exponential growth) if the Fourier transform of f is slowly (resp. very slowly; resp. extremely slowly) decreasing. These results include constructive proofs of the known existence theorems of Ehrenpreis and Hörmander. For families of convolutors our method yields solutions which depend continuously on parameters.     

A matrix optimization problem

A minimization problem for a matrix-valued matrix function is considered. A duality theorem is proved. Some examples illustrate its applicability.