Some Notes on the Linear Complexity of Sidel’nikov-Lempel-Cohn-Eastman Sequences

We continue the study of the linear complexity of binary sequences, independently introduced by Sidel’nikov and Lempel, Cohn, and Eastman. These investigations were originated by Helleseth and Yang and extended by Kyureghyan and Pott. We determine the exact linear complexity of several families of these sequences using well-known results on cyclotomic numbers. Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences.     

Quantum chemical investigation of the adsorption of methanol on a cluster model of faujasite

The adsorption of methanol in zeolites of the faujasite type with sodium and calcium counter ions is studied with quantum chemical methods. The zeolite is represented with a cluster model allowing calculations at the Møller-Plesset as well as the DFT level of theory. An adsorption energy of −62.4 kJ/mol is calculated at the MP2/TZVP//BP86/TZVP level of theory for one methanol molecule at one site II sodium cation. Insight into the adsorption process is obtained with a three-body decomposition which reveals a strong destabilisation of the adsorption strength by large, positive three-body terms, which is important for force field development.     

Asymmetric Synthesis of Fully Substituted Cyclopentane‐Oxindoles through an Organocatalytic Triple Michael Domino Reaction

An efficient, highly stereoselective asymmetric synthesis of fully functionalized cyclopentanes bearing an oxindole moiety and several other functional groups in one pot has been developed. Key step is an organocatalytic triple Michael domino reaction forming three C?C bonds and six stereocenters, including a quaternary one. Starting from equimolar amounts of simple substrates, a high molecular complexity can be reached after a Wittig olefination in one pot. The new protocol can easily be scaled up to gram amounts.     

Single electron densities: a new tool to analyze molecular wavefunctions

A new partitioning scheme for the electron density of a many-electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron-electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many-electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.     

Synthesis and Crystal Structure of [Cr(thd)2(OEt)]2

The mixed‐ligand complex [Cr(thd)₂(OEt)]₂ [(thd)^– = anion of H(thd) = C₁₁H₂₀O₂ = 2,2,6,6‐tetramethylheptane‐3,5‐dione] appears as by‐product when EtOH/H₂O is used as solvent during preparation of Cr(thd)₃. [Cr(thd)₂(OEt)]₂ can be difficult to separate from Cr(thd)₃ by sublimation, but separation is easily accomplished by extracting Cr(thd)₃ with acetone. A detailed account for the sublimation behavior of [Cr(thd)₂(OEt)]₂/Cr(thd)₃ mixtures is advanced. Good yields of [Cr(thd)₂(OEt)]₂ are obtained when CrCl₃, H(thd), and Na(EtO) react in absolute EtOH. [Cr(thd)₂(OEt)]₂ is obtained in the form of green needle‐shaped crystals by recrystallization from toluene. The crystal structure is triclinic [a = 10.2919(15), b = 10.6686(16), c = 14.194(3) Å, α = 106.559(2), β = 107.869(2), and γ = 98.326(2)° at 295 K; space group P . The complex contains two crystallographic equivalent chromium atoms, which are bridged by two cis‐configured ethoxy groups, the four remaining sites in the octahedral coordination around each chromium atom being occupied by oxygen atoms from two thd ligands. The bond lengths and angles concur with the findings for related molecular complexes. The temperature dependence of the magnetic susceptibility of [Cr(thd)₂(OEt)]₂ follows Curie–Weiss law with Weiss constant θ ≈? –65 K and μ_p = 3.87 μ_B.     

Elucidating the origin of diastereoselectivity in a self-replicating system: selfishness versus altruism

We have investigated a diastereoselective self‐replicating system based on a cycloaddition of a fulvene derivative and a maleimide using a two‐pronged approach of combining NMR spectroscopy with computational modelling. Two diastereomers are formed with identical rates in the absence of replication. When replication is enabled, one diastereomer takes over the resources as a “selfish” autocatalyst, while exploiting the competitor as a weak “altruist”, resulting in a diastereoselectivity of 16:1. We applied 1D and 2D NMR spectroscopic techniques supported by ab initio chemical shifts as well as ab initio molecular dynamics simulations to study the structure and dynamics of the underlying network. This powerful combination allowed us to decipher the energetic and structural rationale behind the observed behaviour, while static computational methods currently used in the field did not.     

Biosynthesis of a fluorescent protein with extreme pseudo-Stokes shift by introducing a genetically encoded non-natural amino acid outside the fluorophore

A novel kind of fluorescent protein relying on the intramolecular interplay between two different fluorophores, one of chemical origin and one of biological origin, was developed. The fluorescent non-natural amino acid l-(7-hydroxycoumarin-4-yl)ethylglycine was site-specifically incorporated into the recombinant enhanced cyan fluorescent protein (eCFP) at a permissible surface position ～20 ? away from the protein fluorophore using amber suppression in Escherichia coli with an engineered cognate Methanococcus jannaschii tRNA synthetase. The resulting eCFP(Cou) exhibited almost quantitative intramolecular Fo?rster resonance energy transfer (FRET) between its two fluorophores, showing brilliant cyan emission at 476 nm upon excitation in the near-UV at 365 nm (a wavelength easily accessible via conventional laboratory UV sources), in contrast to its natural counterpart. Thus, this fluorescent protein with unprecedented spectroscopic properties reveals an extreme apparent Stokes shift of ～110 nm between the absorption wavelength of the coumaryl group and the emission wavelength of eCFP.     

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.