Estimates for the sizes of instability zones for the one-dimensional Schrödinger equation with analytic quasiperiodic potential

We consider a one-dimensional stationary quasiperiodic Schrödinger equation with analytic potential. Using methods of the KAM theory, we construct the boundaries of instability zones and solutions corresponding to these boundaries and estimate the sizes of instability zones. In addition, we consider the case where the potential is a trigonometric polynomial of finite degree.     

Guest‐Adaptable and Water‐Stable Peptide‐Based Porous Materials by Imidazolate Side Chain Control

The peptide‐based porous 3D framework, ZnCar, has been synthesized from Zn²⁺ and the natural dipeptide carnosine (β‐alanyl‐L ‐histidine). Unlike previous extended peptide networks, the imidazole side chain of the histidine residue is deprotonated to afford Zn–imidazolate chains, with bonding similar to the zeolitic imidazolate framework (ZIF) family of porous materials. ZnCar exhibits permanent microporosity with a surface area of 448 m² g^?1, and its pores are 1D channels with 5 Å openings and a characteristic chiral shape. This compound is chemically stable in organic solvents and water. Single‐crystal X‐ray diffraction (XRD) showed that the ZnCar framework adapts to MeOH and H₂O guests because of the torsional flexibility of the main His‐β‐Ala chain, while retaining the rigidity conferred by the Zn–imidazolate chains. The conformation adopted by carnosine is driven by the H bonds formed both to other dipeptides and to the guests, permitting the observed structural transformations.     

Scorpionate‐Type Coordination in MFU‐4l Metal–Organic Frameworks: Small‐Molecule Binding and Activation upon the Thermally Activated Formation of Open Metal Sites

Postsynthetic metal and ligand exchange is a versatile approach towards functionalized MFU‐4l frameworks. Upon thermal treatment of MFU‐4l formates, coordinatively strongly unsaturated metal centers, such as zinc(II) hydride or copper(I) species, are generated selectively. Cu^I‐MFU‐4l prepared in this way was stable under ambient conditions and showed fully reversible chemisorption of small molecules, such as O₂, N₂, and H₂, with corresponding isosteric heats of adsorption of 53, 42, and 32 kJ mol^?1, respectively, as determined by gas‐sorption measurements and confirmed by DFT calculations. Moreover, Cu^I‐MFU‐4l formed stable complexes with C₂H₄ and CO. These complexes were characterized by FTIR spectroscopy. The demonstrated hydride transfer to electrophiles and strong binding of small gas molecules suggests these novel, yet robust, metal–organic frameworks with open metal sites as promising catalytic materials comprising earth‐abundant metal elements.     

5-Ethoxymethylidene-4-thioxo-2-thiazolidinone as Versatile Building Block for Novel Biorelevant Small Molecules with Thiopyrano[2,3-d][1,3]thiazole Core

5-Ethoxymethylidene-4-thioxo-2-thiazolidinone was studied as versatile core building block in the synthesis of new thiopyrano[2,3-d]thiazole derivatives relevant for medicinal chemistry purposes under hetero-Diels–Alder reaction conditions. Promising compounds (6, 10) were identified among synthesized series with high antitumor and moderate antiviral activity.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Reliable determination of the few‐layer graphene oxide thickness using Raman spectroscopy

We report on a reference‐free Raman spectroscopy method for a precise thickness determination of the multilayered graphene oxide flakes. The method is based on the normalization of the total integral intensity of D and G Raman bands to the integral intensity of the second‐order optical phonon peak of the silicon substrate in the Raman spectrum. The normalization provides discrete ratio values corresponding to the number of graphene oxide layers in the respective flakes with the intensity linearly increasing with the number of layers. This provides a fast and robust determination of the thickness of graphene oxide flakes in terms of the layer number up to high values. A comparison with conventional spectrally resolved reflectivity mapping shows similar sensitivity, while selectivity to particular functional chemical groups is a bonus of the Raman‐based method. Copyright © 2015 John Wiley & Sons, Ltd.     

Chemical and Structural Stability of Zirconium‐based Metal–Organic Frameworks with Large Three‐Dimensional Pores by Linker Engineering

The synthesis of metal–organic frameworks with large three‐dimensional channels that are permanently porous and chemically stable offers new opportunities in areas such as catalysis and separation. Two linkers (L1=4,4′,4′′,4′′′‐([1,1′‐biphenyl]‐3,3′,5,5′‐tetrayltetrakis(ethyne‐2,1‐diyl)) tetrabenzoic acid, L2=4,4′,4′′,4′′′‐(pyrene‐1,3,6,8‐tetrayltetrakis(ethyne‐2,1‐diyl))tetrabenzoic acid) were used that have equivalent connectivity and dimensions but quite distinct torsional flexibility. With these, a solid solution material, [Zr₆O₄(OH)₄(L1)_2.6(L2)_0.4]?(solvent)_x, was formed that has three‐dimensional crystalline permanent porosity with a surface area of over 4000 m² g^?1 that persists after immersion in water. These properties are not accessible for the isostructural phases made from the separate single linkers.     

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.     

2,3-unsubstituted chromones and their enaminone precursors as versatile reagents for the synthesis of fused pyridines

A divergent and regioselective approach to fused pyridines was developed through formal [3 + 3] cyclocondensations from simple 2,3-unsubstituted chromones or their enaminone precursors.