Essential collections for equilibrium concepts

The aim of this study is to identify and characterize the parts of an extensive form game that are ??relevant?? to determining whether the outcome of a certain strategy profile is an equilibrium outcome. We formally define what we mean by ??relevant?? and refer to the associated collection of information sets as essential. We apply this idea to a number of classic equilibrium concepts and discuss some implications of our approach.     

Multiscale Approach to the Study of the Electronic Properties of Two Thiophene Curcuminoid Molecules

We studied the electronic and conductance properties of two thiophene–curcuminoid molecules, 2‐thphCCM ( 1 ) and 3‐thphCCM ( 2 ), in which the only structural difference is the position of the sulfur atoms in the thiophene terminal groups. We used electrochemical techniques as well as UV/Vis absorption studies to obtain the values of the HOMO–LUMO band gap energies, showing that molecule 1 has lower values than 2 . Theoretical calculations show the same trend. Self‐assembled monolayers (SAMs) of these molecules were studied by using electrochemistry, showing that the interaction with gold reduces drastically the HOMO–LUMO gap in both molecules to almost the same value. Single‐molecule conductance measurements show that molecule 2 has two different conductance values, whereas molecule 1 exhibits only one. Based on theoretical calculations, we conclude that the lowest conductance value, similar in both molecules, corresponds to a van der Waals interaction between the thiophene ring and the electrodes. The one order of magnitude higher conductance value for molecule 2 corresponds to a coordinate (dative covalent) interaction between the sulfur atoms and the gold electrodes.     

Calcium Carbonate Polyamorphism and Its Role in Biomineralization: How Many Amorphous Calcium Carbonates Are There?

Although the polymorphism of calcium carbonate is well known, and its polymorphs—calcite, aragonite, and vaterite—have been highly studied in the context of biomineralization, polyamorphism is a much more recently discovered phenomenon, and the existence of more than one amorphous phase of calcium carbonate in biominerals has only very recently been understood. Here we summarize what is known about polyamorphism in calcium carbonate as well as what is understood about the role of amorphous calcium carbonate in biominerals. We show that consideration of the amorphous forms of calcium carbonate within the physical notion of polyamorphism leads to new insights when it comes to the mechanisms by which polymorphic structures can evolve in the first place. This not only has implications for our understanding of biomineralization, but also of the means by which crystallization may be controlled in medical, pharmaceutical, and industrial contexts.     

On a parabolic–elliptic chemotactic model with coupled boundary conditions

This paper deals with a nonlinear system of parabolic–elliptic type with a logistic source term and coupled boundary conditions related to pattern formation. We prove the existence of a unique positive global in time classical solution. We also analyze the associated stationary problem. Moreover it is proved, under the assumption of sufficiently strong logistic damping, that there is only one nonzero homogeneous equilibrium, and all the solutions to the nonstationary problem tend to this steady state for large times.     

Flavonoid glycosides from Persea caerulea. Unraveling their interactions with SDS‐micelles through matrix‐assisted DOSY,PGSE, mass spectrometry,and NOESY

Two flavonoid glycosides derived from rhamnopyranoside ( 1 ) and arabinofuranoside ( 2 ) have been isolated from leaves of Persea caerulea for the first time. The structures of 1 and 2 have been established by ¹H NMR, ¹³C NMR, and IR spectroscopy, together with LC–ESI–TOF and LC–ESI–IT MS spectrometry. From the MS and MS/MS data, the molecular weights of the intact molecules as well as those of quercetin and kaempferol together with their sugar moieties were deduced. The NMR data provided information on the identity of the compounds, as well as the α and β configurations and the position of the glycosides on quercetin and kaempferol. We have also explored the application of sodium dodecyl sulfate (SDS) normal micelles in binary aqueous solution, at a range of concentrations, to the diffusion resolution of these two glycosides, by the application of matrix‐assisted diffusion ordered spectroscopy (DOSY) and pulse field gradient spin echo (PGSE) methodologies, showing that SDS micelles offer a significant resolution which can, in part, be rationalized in terms of differing degrees of hydrophobicity, amphiphilicity, and steric effects. In addition, intra‐residue and inter‐residue proton–proton distances using nuclear Overhauser effect build‐up curves were used to elucidate the conformational preferences of these two flavonoid glycosides when interacting with the micelles. By the combination of both diffusion and nuclear Overhauser spectroscopy techniques, the average location site of kaempferol and quercetin glycosides has been postulated, with the former exhibiting a clear insertion into the interior of the SDS‐micelle, whereas the latter is placed closer to the surface. Copyright © 2016 John Wiley & Sons, Ltd.     

First intermolecular cyclopropanation of Fischer dialkylaminocarbene complexes. Synthesis of 1-aminocyclopropanecarboxylic acid derivatives

[reaction: see text] The first cyclopropanation reaction of olefins with Fischer dialkylaminocarbene complexes is presented. The reaction yields 1-aminocyclopropanecarboxylic acid derivatives in a single step, usually with high diastereoselectivity. An approach to the asymmetric version of this reaction is also presented. The synthetic utility of the procedure is exemplified by the synthesis of both cycles of metanoproline in a single step. In addition, the synthesis of the first Fischer carbene containing a halocarbonyl group is reported.     

Fundamental Group for Some Cuspidal Curves

In [1], Hirano gives a method for constructing families of curveswith a large number of singularities. The idea is to consideran abelian covering of P² ramified along three lines in generalposition, and to take the pull-back of a curve C intersectingthe lines non-generically. Similar constructions are used byShimada in [10] and Oka in [8]. We apply this method for thecase where C is a conic, constructing a family of curves withthe following asymptotic behaviour (see [9]): The goal of this paper is to calculate the fundamentalgroup for the curves in this family as well as their Alexanderpolynomial. 1991 Mathematics Subject Classification 14H20, 14H30,14E20.     

A Hahn-Banach theorem for integral polynomials

We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of .

     

Fuzzy nilpotent algebras

We define the concept of fuzzy nilpotent algebra, prove that the homomorphic inverse image of a fuzzy nilpotent algebra is also nilpotent and study the intersection and union of fuzzy nilpotent algebras.     

Improved formal total synthesis of tetrahydrometinoxocrinine

An improved, isomer-free synthesis of Tetrahydrometinoxocrinine ($\text{1}$) is described.