Projective planes over rings of stable rank 2

This paper gives an axiomatic characterization of projective planes over rings of stable rank 2. These rings, which are known from algebraic K-theory, beautifully reflect simple geometric properties. The basic relations in the plane are incidence and the neighbor relation. The axioms consist of a number of axioms expressing elementary relations between points and lines such as, e. g., the existence of a unique line joining any two non-neighboring points, and a couple of axioms ensuring the existence of transvections and dilatations.     

A Stereocontrolied Entry to Racemic Eremophilane and Valencane Sesquiterpenes via an Intramolecular Diels-Alder Reaction

A stereocontrolied route to racemic eremophilane and valencane sesquiterpenes is described via a common intermediate 15 , accessible from an intramolecular Diels-Alder reaction. ¹³ C - NMR .-shift assignments of the bicyclic intermediates and products are presented.     

An EKR-theorem for finite buildings of type $$D_{\ell }$$

We define optimal EKR-sets in finite buildings. This definition is motivated by various contributions on optimal EKR-sets in finite projective spaces and polar spaces. Our main result is the classification of optimal EKR-sets of type \(\{ \ell , \ell -1\}\) in finite building of type \(D_{\ell }\) with \(\ell \) even. As it is the case for most of the known optimal EKR-sets in finite buildings, our EKR-sets have a natural center. This provides some evidence that the EKR-problem for finite buildings and Tits center conjecture are closely related.     

Miklós–Manickam–Singhi conjectures on partial geometries

In this paper we give a proof of the Miklós–Manickam–Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, several specific partial geometries that are counterexamples to the conjecture are described.     

Efficient charge transport along phenylene-vinylene molecular wires

We have studied the motion of charge carriers along isolated phenylene-vinylene (PV) chains using a combination of experimental and theoretical methods. The conductive properties of positive charges along PV chains in dilute solution were studied by using the pulse-radiolysis time-resolved microwave conductivity (TRMC) technique. This technique enables the measurement of high-frequency (tens of GHz) charge carrier mobilities along isolated PV chains without the use of electrodes. The charge carrier mobility along PV chains with finite and infinite length was studied theoretically by charge transport simulations with parameters from density functional theory (DFT) calculations. The high-frequency charge carrier mobility is found to depend strongly on the conjugation length of the PV chains and is found to increase both with increasing length of the PV chain and with increasing conjugation fraction. The experimental results are in good agreement with the calculated results. On the basis of this combined experimental and theoretical study an intrachain charge carrier mobility of a few tens of cm2/Vs is expected for an infinitely long PV chain without conjugation breaks.     

Activation and Photoinduced Release of Alkynes on a Biomimetic Tungsten Center: The Photochemical Behavior of the W−S-Phoz System

The synthesis and structural determination of four tungsten alkyne complexes coordinated by the bio-inspired S,N-donor ligand 2-(4′,4′-dimethyloxazoline-2′-yl)thiophenolate (S-Phoz) is presented. A previously established protocol that involved the reaction of the respective alkyne with the bis-carbonyl precursor [W(CO)₂(S-Phoz)₂] was used for the complexes [W(CO)(C₂R₂)(S-Phoz)₂] (R=H, 1 a ; Me, 1 b ; Ph, 1 c ). Oxidation with pyridine-N-oxide gave the corresponding W-oxo species [WO(C₂R₂)(S-Phoz)₂] (R=H, 2 a ; Me, 2 b ; Ph, 2 c ). All W-oxo-alkyne complexes ( 2 a , b , c ) were found to be capable of alkyne release upon light irradiation to afford five-coordinate [WO(S-Phoz)₂] ( 3 ). The photoinduced release of the alkyne ligand was studied in detail by in situ ¹H NMR measurements, which revealed correlation of the photodissociation rate constant ( 2 b>2 a>2 c ) with the elongation of the alkyne C≡C bond in the molecular structures. Oxidation of [WO(S-Phoz)₂] ( 3 ) with pyridine-N-oxide yielded [WO₂(S-Phoz)₂] ( 4 ), which shows highly fluxional behavior in solution. Variable-temperature ¹H NMR spectroscopy revealed three isomeric forms with respect to the ligand arrangement versus each other. Furthermore, compound 4 rearranges to tetranuclear oxo compound [W₄O₄(μ-O)₆(S-Phoz)₄] ( 5 ) and dinuclear [{WO(μ-O)(S-Phoz)}₂] ( 6 ) over time. The latter two were identified by single-crystal X-ray diffraction analyses.     

Kaleidoscope of life: A 24-neighbourhood outer-totalistic cellular automaton

One of the challenges of cellular automaton research is finding models with a low complexity and at the same time a rich dynamics. A measure of low complexity is the number of states in the model and the number of transition rules to switch between those states. In this paper, we propose a 2-dimensional 2-state cellular automaton that-though governed by a single simple transition rule-has a sufficiently rich dynamics to be computationally universal. According to the transition rule, a cell’s state is determined by the sum of the states of the cells at orthogonal or diagonal distances one or two from the cell (distance-2 Moore neighbourhood), but not by the previous state of the cell itself. Notwithstanding its simplicity, this model is able to generate a great variety of patterns, including several types of stable configurations, oscillators and patterns that move over cellular space (gliders). We prove the computational universality of the model by constructing a universal set of logic gates (NOT and AND) from these patterns. A key element in this proof is the shifting of phases and positions of signals such that they meet the input requirements of the logic gates. Similarities of the model with classical spin systems are also discussed.