Ramsey’s theorem for colors from a metric space

The Ramsey theorem says that for any countably infinite undirected clique whose edges are colored by a finite number of colors, there is an infinite subclique whose edges are colored by a single color. In this note, we generalize the theorem to a situation where the colors form a compact metric space.     

Weak radiative decays of the B meson and bounds on $$M_{H^\pm }$$ in the Two-Higgs-Doublet Model

In a recent publication (Abdesselam et al. arXiv:1608.02344), the Belle collaboration updated their analysis of the inclusive weak radiative B-meson decay, including the full dataset of \((772 \pm 11)\times 10^6~B\bar{B}\) pairs. Their result for the branching ratio is now below the Standard Model prediction (Misiak et al. Phys Rev Lett 114:221801, 2015, Czakon et al. JHEP 1504:168, 2015), though it remains consistent with it. However, bounds on the charged Higgs boson mass in the Two-Higgs-Doublet Model get affected in a significant manner. In the so-called Model II, the 95% C.L. lower bound on \(M_{H^\pm }\) is now in the 570–800 GeV range, depending quite sensitively on the method applied for its determination. Our present note is devoted to presenting and discussing the updated bounds, as well as to clarifying several ambiguities that one might encounter in evaluating them. One of such ambiguities stems from the photon energy cutoff choice, which deserves re-consideration in view of the improved experimental accuracy.     

Bromine adsorption on Ge(001) surface: comparative study for coverages of 0.25, 0.5, 0.75 and 1 monolayer

We present theoretical analysis of bromine adsorption on the Ge(001)-p(1×2) surface. Bromine adsorbs dissociatively at the Ge(001) surface and the adlayer of bromine develops ordered structures of adatoms bound to substrate dimers. We analyse atomic configurations of the Ge(001) surface covered by 0.25, 0.5, 0.75 and 1 monolayer of bromine. Various stable surface structures, found in calculations, are presented and their energies are compared. Simulated STM images are also discussed for the considered configurations.      

Shape memory ionomers

This review is focused on the use of ionomers in shape memory polymers. Ionomers are polymers that contain less than ∼15% ionic groups. The incompatibility between the ion-pairs and the polymer backbone drives microphase separation producing dispersed ionic aggregates, which can physically crosslink the polymer. Shape memory polymers are responsive materials that can be deformed to program a temporary shape and then recovered on application of an external stimulus. Through the review of the main types of ionomers used in shape memory polymers, polyurethanes and polyester ionomers, polyolefin and polyaromatic ionomers, and perfluorosulfonic acid ionomers (i.e., Nafion^®) it will be shown that ionomers can produce robust thermoplastic shape memory polymers and in many cases impart unique properties which allow advanced shape memory materials to be obtained including antibacterial, high temperature, and multishape memory polymers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1389–1396     

Model Calculations and Experimental Studies as a Route Toward Simplification of the Kinetic Mechanism of the H2O2–NaSCN–NaOH–CuSO4 Homogeneous Oscillator

Oscillatory chemical reactions are usually characterized by complicated kinetic mechanisms in which the source of instability is combined with the parallel dissipative process. One of such systems is the H₂O₂–NaSCN–NaOH–CuSO₄ homogeneous oscillator, in which dynamic instabilities are associated with the irreversible oxidation of thiocyanate ions with hydrogen peroxide. Following our previous studies on this system, we now propose further intuitive and substantial simplification of its kinetic mechanism toward the scheme involving only five intermediates. Its compatibility with our previous, nine‐variable model is verified in terms of model calculations, compared with experimental potentiometric and spectrophotometric data. In particular, supercritical nature of a Hopf bifurcation as a route toward oscillations born out of a single steady state upon increasing catalyst (copper species) concentration was observed in the model and an analogous type of bifurcation is suggested by available experimental data. Our work is a step toward final reduction of the mechanism of the studied system to the “minimum oscillator,” the concept used earlier, e.g., for the Belousov–Zhabotinsky reaction, of however remarkably different kinetic mechanism.     

Reaction of 5,5-diphenyl-2-thiohydantoin with 1,3-dibromopropane under phase transfer catalytic conditions : Crystal and molecular structure of 2,3,4,5-tetrahydro-7,7-diphenylimidazo-[2,1-b]-thiazine -6(7H)-one

The reaction of the potassium salt of 5,5-diphenyl-2-thiohydantoin with 1,3-dibromopropane and triethylamine carried out under phase transfer catalytic conditions gave almost quantitatively two isomeric diphenylimidazothiazine 2 and 3 in a ratio ca 1:2. 2,3,4,5-Tetrahydro-7,7-diphenylimidazo- [2,1-b]-thiazine-6(7H)-one (3) crystallises from DMSO in the space group P2₁2₁2₁ with a = 8.488(3), b = 11.682(4), c = 15.522(5)Å. The 6-membered thiazine ring in 3 adopts a sofa conformation.     

Acyclic and cyclic aminophosphonic acids: asymmetric syntheses mediated by chiral sulfinyl auxiliary

Aminophosphonic acids have become increasingly important in different fields of chemistry, medicine and agriculture. This account outlines the results obtained in the author’s laboratory on the asymmetric synthesis of acyclic and cyclic aminophosphonic acids mediated by chiral sulfinyl auxiliary. A key reaction in the synthesis of enantiopure α- and β-aminoalkanephosphonic acids involving a highly diastereoselective addition of phosphite anions or α-phosphonate carbanions to enantiopure sulfinimines is discussed. The asymmetric cyclopropanation of enantiopure α-phosphorylvinyl sulfoxides with sulfur ylides is presented as a platform for developing a new approach to optically active β-aminocyclopropanephosphonic acids. It is exemplified by the total synthesis of enantiopure β-amino-γ-phenylcyclopropanephosphonic acid - a constrained analogue of the GABA_B antagonist phaclofen.     

A metrizable X with Cp(X) not homeomorphic to Cp(X) × Cp(X)

We give an example of an infinite metrizable space X such that the space C_p(X), of continuous real-valued functions on X endowed with the pointwise topology, is not homeomorphic to its own square C_p(X) × C_p(X). The space X is a zero-dimensional subspace of the real line. Our result answers a long-standing open question in the theory of function spaces posed by A. V. Arhangel’skii.