Crystal and molecular structure of 1-hydroxy-2,3-dicarbomethoxy-1,3-cycloheptadiene

The crystal structure of 1-hydroxy-2,3-dicarbomethoxy-1,3-cycloheptadiene has been determined from three-dimensional counter data, and refined by full-matrix least-squares techniques. The crystals belong to the triclinic space groupP¯1, witha = 10.721(7),b = 8.628(6),c = 6.214(6) Å, = 91.65(5), = 83.14(5), = 81.66(5) °, andD _c = 1.33 g cm^–3 forZ = 2. The finalR factor for 1385 observed reflections is 0.058. The compound exists in the enolic configuration.     

Products of reflections in the general linear group over a division ring

Let F be a division ring and A?GL_n(F). We determine the smallest integer k such that A admits a factorization A=R₁R₂?R_k?1B, where R₁,…,R_k?1 are reflections and B is such that rank(B?I_n)=1. We find that, apart from two very special exceptional cases, k=rank(A?I_n). In the exceptional cases k is one larger than this rank. The first exceptional case is the matrices A of the form I_m⊕αI_n?m where n?m?2, α≠?1, and α belongs to the center of F. The second exceptional case is the matrices A satisfying (A?I_n)²=0, rank(A?I_n)?2 in the case when char F≠2 only. This result is used to determine, in the case when F is commutative, the length of a matrix A?GL_n(F) with detA=±1 with respect to the set of all reflections in GL_n(F).     

There is no roughening singularity at finite temperature

It is shown, for any non-zero temperature and finite coupling, that there are large transverse fluctuations in the electric flux tubes connecting quark-antiquark pairs. For large $\text{q}\text{q}$ separation L, the average distance of the flux tube from its equilibrium position diverges like $\text{√}\text{L}$. Hence the flux tube is rough. The consequent absence of a roughening singularity may imply that rotational invariance and the continuum limit are approached more gradually than at zero temperature.     

Structure of vertex-transitive graphs

Every vertex-transitive graph has a characteristic structure. The specific details of structure of a vertex-transitive graph are closely related to the configuration of the parts of any minimum separating set of that graph. It is shown for a vertex-transitive graph G that (i) the number n of isomorphic atomic parts admitted by any minimum separating set S is unique for that G; (ii) G is then isomorphic to a disjoint union of m(≥2) copies of such a set of n atomic parts together with some additional edges joining them; (iii) any minimum separating set S of G consists of the vertex set of the union of some k(≥1) copies of the set of n atomic parts; (iv) at most one nonatomic part will be admitted in conjunction with one or more atomic parts by any minimum separating set of G.This configuration of structure extends to nonatomic parts. A vertex-transitive graph G may contain a not necessarily unique minimum separating set S which admits t(≥3) nonatomic parts. Then it is shown that (i) some (t ? 1)-set of these nonatomic parts are pairwise isomorphic; (ii) if the remaining nonatomic part is nonisomorphic to the others then it contains more vertices than the other parts; (iii) G is isomorphic to a disjoint union of d(≥2) copies of the set of q(≥t ? 1) isomorphic nonatomic parts together with some additional edges joining them; (iv) a minimum separating set S consists of the vertex set of the union of some y(≥1) copies of the set of q isomorphic nonatomic parts. For the case of t = 2 non-atomic parts admitted by a minimum separating set S, counterexamples of (iii) and (iv) are given.     

Polynomial deformations and cohomology of Calabi-Yau manifolds

We study the method of polynomial deformations that is used in the physics literature to determine the Hodge numbers of Calabi-Yau manifolds as well as the related Yukawa couplings. We show that the argument generally presented in the literature in support of these computations is seriously misleading, give a correct proof which applies to all the cases we found in the literature, and present examples which show that the method is not universally valid. We present a general analysis which applies to all Calabi-Yau manifolds embedded as complete intersections in products of complex projective spaces, yields sufficient conditions for the validity of the polynomial deformation method, and provides an alternative computation of all the Hodge numbers in many cases in which the polynomial method fails.     

Selective CO2 Adsorption in a Supramolecular Organic Framework

Considering the rapidly rising CO₂ level, there is a constant need for versatile materials which can selectively adsorb CO₂ at low cost. The quest for efficient sorptive materials is still on since the practical applications of conventional porous materials possess certain limitations. In that context, we designed, synthesized, and characterized two novel supramolecular organic frameworks based on C‐pentylpyrogallol[4]arene (PgC₅) with spacer molecules, such as 4,4′‐bipyridine (bpy). Highly optimized and symmetric intermolecular hydrogen‐bonding interactions between the main building blocks and comparatively weak van der Waals interactions between solvent molecules and PgC₅ leads to the formation of robust extended frameworks, which withstand solvent evacuation from the crystal lattice. The evacuated framework shows excellent affinity for carbon dioxide over nitrogen and adsorbs ca. 3 wt % of CO₂ at ambient temperature and pressure.     

Exponential Decay of Dispersion-Managed Solitons for General Dispersion Profiles

We show that any weak solution of the dispersion management equation describing dispersion-managed solitons together with its Fourier transform decay exponentially. This strong regularity result extends a recent result of Erdo?an, Hundertmark, and Lee in two directions, to arbitrary non-negative average dispersion and, more importantly, to rather general dispersion profiles, which cover most, if not all, physically relevant cases.     

Rational tuning of the thiolate donor in model complexes of superoxide reductase: direct evidence for a trans influence in Fe(III)-OOR complexes

Iron peroxide species have been identified as important intermediates in a number of nonheme iron as well as heme-containing enzymes, yet there are only a few examples of such species either synthetic or biological that have been well characterized. We describe the synthesis and structural characterization of a new series of five-coordinate (N4S(thiolate))Fe(II) complexes that react with tert-butyl hydroperoxide ((t)BuOOH) or cumenyl hydroperoxide (CmOOH) to give metastable alkylperoxo-iron(III) species (N4S(thiolate)Fe(III)-OOR) at low temperature. These complexes were designed specifically to mimic the nonheme iron active site of superoxide reductase, which contains a five-coordinate iron(II) center bound by one Cys and four His residues in the active form of the protein. The structures of the Fe(II) complexes are analyzed by X-ray crystallography, and their electrochemical properties are assessed by cyclic voltammetry. For the Fe(III)-OOR species, low-temperature UV-vis spectra reveal intense peaks between 500-550 nm that are typical of peroxide to iron(III) ligand-to-metal charge-transfer (LMCT) transitions, and EPR spectroscopy shows that these alkylperoxo species are all low-spin iron(III) complexes. Identification of the vibrational modes of the Fe(III)-OOR unit comes from resonance Raman (RR) spectroscopy, which shows nu(Fe-O) modes between 600-635 cm(-1) and nu(O-O) bands near 800 cm(-1). These Fe-O stretching frequencies are significantly lower than those found in other low-spin Fe(III)-OOR complexes. Trends in the data conclusively show that this weakening of the Fe-O bond arises from a trans influence of the thiolate donor, and density functional theory (DFT) calculations support these findings. These results suggest a role for the cysteine ligand in SOR, and are discussed in light of the recent assessments of the function of the cysteine ligand in this enzyme.