A counterexample to the reconstruction of <Emphasis Type="Italic">ω</Emphasis>-categorical structures from their endomorphism monoid

We present an example of two countable ω-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids—in other words, no isomorphism between these monoids is a homeomorphism. For the same two structures, the automorphism groups and polymorphism clones are isomorphic, but not topologically isomorphic. In particular, there exists a countable ω-categorical structure in a finite relational language which can neither be reconstructed up to first-order biinterpretations from its automorphism group, nor up to existential positive bi-interpretations from its endomorphism monoid, nor up to primitive positive bi-interpretations from its polymorphism clone.     

Data Analysis: Keeping Pace with Extraordinary Change

It is a very exciting time in the field of macromolecular crystallography for those of us who are fortunate enough to be involved in the development of instrumentation and software methods. The driver for much of this change has been the remarkable developments in synchrotron light sources and beamline instrumentation over the last two decades. In the 1990s, the ESRF, APS, and SPring-8 set the tone for many of these developments and the 2000s capitalized on them by seeding a host of medium-energy national light sources around the world.     

Regioselectivity in the Intramolecular Heck Reaction of a Series of Cyclic Sulfonamides: An Experimental and Computational Study

Regioselectivity in the intramolecular Heck reaction of a series of N‐sulfonyl‐2,5‐dihydro‐3‐substituted pyrroles was studied. These substrates are unbiased in terms of the formed ring size of the new heterocycle. Results indicate that high levels of regioselectivity are observed under a range of conditions, and that there is an underlying propensity for carbon–carbon bond formation at the most hindered end of the alkene. For two examples (3‐Me and 3‐tBu), DFT calculations were performed and indicate that in both cases, the modelled transition state for carbopalladation is energetically lower for the experimentally preferred isomer.     

Expanding the Chemistry of Molecular U2+ Complexes: Synthesis,Characterization, and Reactivity of the {[C5H3(SiMe3)2]3U}− Anion

The synthesis of new molecular complexes of U²⁺ has been pursued to make comparisons in structure, physical properties, and reactivity with the first U²⁺ complex, [K(2.2.2‐cryptand)][Cp′₃U], 1 (Cp′=C₅H₄SiMe₃). Reduction of Cp′′₃U [Cp′′=C₅H₃(SiMe₃)₂] with KC₈ in the presence of 2.2.2‐cryptand or 18‐crown‐6 generates [K(2.2.2‐cryptand)][Cp′′₃U], 2‐K(crypt) , or [K(18‐crown‐6)(THF)₂][Cp′′₃U], 2‐K(18c6) , respectively. The UV/Vis spectra of 2‐K and 1 are similar, and they are much more intense than those of U³⁺ analogues. Variable temperature magnetic susceptibility data for 1 and 2‐K(crypt) reveal lower room temperature χ_MT values relative to the experimental values for the 5f³ U³⁺ precursors. Stability studies monitored by UV/Vis spectroscopy show that 2‐K(crypt) and 2‐K(18c6) have t_1/2 values of 20 and 15 h at room temperature, respectively, vs. 1.5 h for 1 . Complex 2‐K(18c6) reacts with H₂ or PhSiH₃ to form the uranium hydride, [K(18‐crown‐6)(THF)₂][Cp′′₃UH], 3 . Complexes 1 and 2‐K(18c6) both reduce cyclooctatetraene to form uranocene, (C₈H₈)₂U, as well as the U³⁺ byproducts [K(2.2.2‐cryptand)][Cp′₄U], 4 , and Cp′′₃U, respectively.     

Finding common RNA pseudoknot structures in polynomial time

This paper presents the first polynomial time algorithm for finding common RNA substructures that include pseudoknots and similar structures. While a more general problem is known to be NP-hard, this algorithm exploits special features of RNA structures to match RNA bonds correctly in polynomial time. Although the theoretical upper bound on the algorithm?s time and space usage is high, the data-driven nature of its computation enables it to avoid computing unnecessary cases, dramatically reducing the actual running time. The algorithm works well in practice, and has been tested on sample RNA structures that include pseudoknots and pseudoknot-like tertiary structures.     

Plane-strain deformation near a slot extended under load: Some observations using grain-orientated 312per cent silicon-iron

Experiments were performed using grain-orientated $\text{3}\text{1}\text{2}$per cent silicon-iron. Plane-strain deformation can be obtained in thin plates of this material and, also, the plastic deformation that occurs can be revealed by etching. In some experiments the slot was extended while the specimen was under load and the plastic deformation was then observed. The distribution and density of the resulting slip-lines agrees qualitatively with J. R. Rice's (1968) model of the deformation at the tip of a crack growing in a continuum. In Rice's model, irreversible plastic deformation prevents complete focusing of the slip-lines at a crack tip; and in the present work an analogous effect was observed, the major difference being that in the present experiments the slip-lines are fixed by the crystal structure of the material. A qualitative explanation of the observations is given in terms of the interaction that exists between dislocations and a crack.