Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13C-13C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³C-¹³C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³C-¹³C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.     

In vitro biomolecular interaction studies and cytotoxic activities of copper(II) and zinc(II) complexes bearing ONS donor thiosemicarbazones

Among all the bio‐metals, zinc and copper derivatives of ONS donor thiosemicarbazone have aroused great interest because of their potential biological applications. Multisubstituted thiosemicarbazone ligand H₂dspt (3,5‐dichlorosalicylaldehyde‐N⁴‐phenylthiosemicarbazone) derived new ternary complexes like [Zn(dspt)(phen)]?DMF ( 1 ) and [Cu(dspt)(phen)]?DMF ( 2 ), and another thiosemicarbazone, H₂dsct (3,5‐dichlorosalicylaldehyde‐N⁴‐cyclohexylthiosemicarbazone), derived [Cu(dsct)(bipy)]?DMF ( 3 ). These complexes have been characterized by elemental analysis (CHNS), Fourier transform infrared (FT‐IR), ultraviolet–visible (UV–Vis) and proton nuclear magnetic resonance (¹H‐NMR) spectra. The structures of the complexes were obtained by single‐crystal X‐ray diffraction analysis. Compounds 1 and 2 got crystallized in the monoclinic P2₁/c space group. The complexes showed interesting supramolecular interaction, which in turn stabilizes the complexes. The ground state electronic configurations of the complexes were studied using the B3LYP/LANL2DZ basis set, and ESP plots of complexes were investigated. The interaction of the complexes with calf thymus DNA (CT‐DNA) was studied using absorption and fluorescence spectroscopic methods. A UV study of the interaction of the complexes with calf thymus DNA (CT‐DNA) has shown that the complexes can effectively bind to CT‐DNA, and [Cu(dspt)(phen)]·DMF ( 2 ) exhibited the highest binding constant to CT‐DNA (K_b = 3.7 × 10⁴). Fluorescence spectral studies also indicated that Complex 2 binds relatively stronger with CT DNA through intercalative mode, exhibiting higher binding constant (K_q = 4.7 × 10⁵). The DNA cleavage result showed that the complexes are capable of cleaving the DNA without the help of any external agent. Molecular docking studies were carried out to understand the binding of complexes with the molecular target DNA. Complex 2 exhibited the highest cytotoxicity against human breast cancer cell line MD‐MBA‐231 (IC₅₀ = 23.93 μg/mL) as compared to Complex 1 (IC₅₀ = 44.40 μg/mL) .     

Structural characterization of disperse black 9 based Cu (II) complex and investigation of its some properties

We obtained the azo‐imine ligand (2,2′‐[4‐(5‐methoxy salicylidene‐4‐iminophenylazo)phenylimino]diethanol) (HL) and its Cu (II) complex (CuL) from the ethanol solution. The complex Cu(L)₂ was obtained as single crystals from the CH₃OH solution and structurally characterized. The electronic and photoluminescence properties of the ligand and its Cu (II) complex were investigated both in DMF solution and solid state. The oxidation and reduction behaviours of the compounds were studied in the solution and found that the redox processes are irreversible. Thermal studies show that the ligand has higher thermal stability than the CuL complex. Single crystals of the complex were obtained from slow evaporation of a DMF solution of the complex. Crystals of the complex showed a diffraction pattern; however, the structure of the complex was able to be solved.     

Synthesis,characterization, and electrochemistry of monophosphine‐containing diiron propane‐1,2‐dithiolate complexes related to the active site of [FeFe]‐hydrogenases

Five monophosphine‐substituted diiron propane‐1,2‐dithiolate complexes as the active site models of [FeFe]‐hydrogenases have been synthesized and characterized. Reactions of complex [Fe₂(CO)₆{μ‐SCH₂CH(CH₃)S}] ( 1 ) with a monophosphine ligand tris(4‐methylphenyl)phosphine, diphenyl‐2‐pyridylphosphine, tris(4‐chlorophenyl)phosphine, triphenylphosphine, or tris(4‐fluorophenyl)phosphine in the presence of the oxidative agent Me₃NO·2H₂O gave the monophosphine‐substituted diiron complexes [Fe₂(CO)₅(L){μ‐SCH₂CH(CH₃)S}] [L = P(4‐C₆H₄CH₃)₃, 2 ; Ph₂P(2‐C₅H₄N), 3 ; P(4‐C₆H₄Cl)₃, 4 ; PPh₃, 5 ; P(4‐C₆H₄F)₃, 6 ] in 81%–94% yields. Complexes 2 – 6 have been characterized by elemental analysis, spectroscopy, and X‐ray crystallography. In addition, electrochemical studies revealed that these complexes can catalyze the reduction of protons to H₂ in the presence of HOAc.     

Acoustic scattering in a rarefied gas: Solving the R13 equations in spherical polar coordinates

In some circumstances, sound waves in a rarefied gas can be studied using a linearised form of the regularised 13-moment equations of Struchtrup and Torrilhon. We build solutions of those equations in spherical polar coordinates using vector spherical harmonics. We first solve a reduced system of equations (with 11 unknowns) after introduction of a force vector (divergence of the stress). We then show that the stresses themselves can be recovered by solving five additional equations. The results obtained are expected to be useful for problems such as acoustic scattering of a plane wave by a sphere in a rarefied gas.     

Sulfono‐γ‐AApeptides as a New Class of Nonnatural Helical Foldamer

Foldamers offer an attractive opportunity for the design of novel molecules that mimic the structures and functions of proteins and enzymes including biocatalysis and biomolecular recognition. Herein we report a new class of nonnatural helical sulfono‐γ‐AApeptide foldamers of varying lengths. The crystal structure of the sulfono‐γ‐AApeptide monomer S6 illustrates the intrinsic folding propensity of sulfono‐γ‐AApeptides, which likely originates from the bulkiness of tertiary sulfonamide moiety. The two‐dimensional solution NMR spectroscopy data for the longest sequence S1 demonstrates a 10/16 right‐handed helical structure. Optical analysis using circular dichroism further supports well‐ defined helical conformation of sulfono‐γ‐AApeptides in solution containing as few as five building blocks. Future development of sulfono‐γ‐AApeptides may lead to new foldamers with discrete functions, enabling expanded application in chemical biology and biomedical sciences.     

Structure determination of KScS2, RbScS2 and KLnS2 (Ln = Nd,Sm, Tb,Dy, Ho,Er, Tm and Yb) and crystal–chemical discussion

The title structures of KScS₂ (potassium scandium sulfide), RbScS₂ (rubidium scandium sulfide) and KLnS₂ [Ln = Nd (potassium neodymium sufide), Sm (potassium samarium sulfide), Tb (potassium terbium sulfide), Dy (potassium dysprosium sulfide), Ho (potassium holmium sulfide), Er (potassium erbium sulfide), Tm (potassium thulium sulfide) and Yb (potassium ytterbium sulfide)] are either newly determined (KScS₂, RbScS₂ and KTbS₂) or redetermined. All of them belong to the α‐NaFeO₂ structure type in agreement with the ratio of the ionic radii r³⁺/r⁺. KScS₂, the member of this structural family with the smallest trivalent cation, is an extreme representative of these structures with rare earth trivalent cations. The title structures are compared with isostructural alkali rare earth sulfides in plots showing the dependence of several relevant parameters on the trivalent cation crystal radius; the parameters thus compared are c, a and c/a, the thicknesses of the S—S layers which contain the respective constituent cations, the sulfur fractional coordinates z(S²⁻) and the bond‐valence sums.     

NMR studies on 4‐thio‐5‐furan‐modified and 4‐thio‐5‐thiophene‐modified nucleosides

Systematic NMR characterization of 4‐thio‐5‐furan‐pyrimidine nucleosides or 4‐thio‐5‐thiophene‐pyrimidine nucleosides (ribonucleosides and 2′‐deoxynucleosides) was performed. All proton and carbon signals of 4‐thio‐5‐thiophene‐ribouridine and related analogues were unambiguously assigned. The orientations of the base (4‐thiouridine or its deoxy analogue) relative to the ring (furan or thiophene) are explored by a NMR approach and further supported by X‐ray crystallographic studies. The procedures presented here would be applicable to other modified nucleosides and nucleotides. Copyright © 2016 John Wiley & Sons, Ltd.