Enynones in organic synthesis. I. Spiroannulation by tandem oxy-cope rearrangement-electrocyclic ring closure

Bis-acetylenic alcohols of proper design undergo a facile oxy-Cope rearrangement to afford mixtures of E- and Z-enynones. These latter compounds afford methylenecyclopentenones upon enolization and electrocyclic ring closure.     

Anthropogenic changes of nitrogen loads in a small river: external nutrient sources vs. internal turnover processes

Anthropogenic nutrient inputs increase the N-load in many aquatic systems, leading to eutrophication and potential changes of biological N-retention capacity. In this study, nitrate inputs in a small river were investigated along a gradient of anthropogenic influence. We aimed to determine changes in nitrate load and isotope signatures in the water column and to identify the anthropogenic influence on biological nitrogen assimilation and nitrification or denitrification in sediments. In seasonal sampling campaigns, we analysed dissolved inorganic nitrogen concentrations, and stable isotopes of nitrate. To differentiate rates of nitrate production and consumption in the pristine vs. agricultural river section, intact sediment cores were incubated with ¹⁵N-labelled nitrate. δ¹⁵N values of nitrate in the pristine river section were low, reflecting natural sources, but, as expected, increased with nitrate concentration in all seasons along the gradient. In general, nitrate retention and consumption were higher in the anthropogenically impacted than in the pristine river section, and nitrate consumption exceeded production. In addition to our measurements, modelled results also show that even in a small river, the anthropogenically enhanced consumption capacity is overwhelmed by surplus N-inputs, and nitrate consumption cannot increase in turn with external loads.     

Vibrational properties of hexagonal boron nitride: inelastic X-ray scattering and ab initio calculations

The phonon dispersion relations of bulk hexagonal boron nitride have been determined from inelastic x-ray scattering measurements and analyzed by ab initio calculations. Experimental data and calculations show an outstanding agreement and reconcile the controversies raised by recent experimental data obtained by electron-energy loss spectroscopy and second-order Raman scattering.     

Real loci of based loop groups

Let (G, K) be a Riemannian symmetric pair of maximal rank, where G is a compact simply connected Lie group and K is the fixed point set of an involutive automorphism σ. This induces an involutive automorphism τ of the based loop space Ω(G). There exists a maximal torus T ⊂ G such that the canonical action of T × S ¹ on Ω(G) is compatible with τ (in the sense of Duistermaat). This allows us to formulate and prove a version of Duistermaat’s convexity theorem. Namely, the images of Ω(G) and Ω(G) ^τ (fixed point set of τ) under the T × S ¹ moment map on Ω(G) are equal. The space Ω(G) ^τ is homotopy equivalent to the loop space Ω(G/K) of the Riemannian symmetric space G/K. We prove a stronger form of a result of Bott and Samelson which relates the cohomology rings with coefficients in \mathbbZ₂ {\mathbb{Z}_2} of Ω(G) and Ω(G/K). Namely, the two cohomology rings are isomorphic, by a degree-halving isomorphism (Bott and Samelson [BS] had proved that the Betti numbers are equal). A version of this theorem involving equivariant cohomology is also proved. The proof uses the notion of conjugation space in the sense of Hausmann, Holm, and Puppe [HHP].     

Alcohols as Fluoroalkyl Synthons: Ni-catalyzed Dehydrogenative Approach to Access Polyfluoroalkyl Bis-indoles

An acceptorless dehydrogenative strategy for the synthesis of polyfluoroalkylated bis-indoles is described by employing an earth-abundant nickel-based catalytic system under air. The notable feature of the present transformation is the use of bench stable and easily affordable polyfluorinated alcohols without any pre-functionalization for the introduction of precious polyfluoroalkyl groups. The developed straightforward protocol accomplished biologically relevant fluoroalkyl bis-indoles in a sustainable fashion. Extensive DFT study predicts the unique role of indole molecules which stabilizes the transition states during the dehydrogenation process of polyfluorinated alcohols, presumably through non-covalent π⋅⋅⋅π and H-bonding interactions.     

Inverse estimation of indoor airflow patterns using singular value decomposition

The fast pace in the development of indoor sensors and communication technologies is allowing a great amount of sensor data to be utilized in various areas of indoor air applications, such as estimating indoor airflow patterns. The development of such an inverse model and the design of a sensor system to collect appropriate data are discussed in this study. Algebraic approaches, including singular value decomposition (SVD), are evaluated as methods to inversely estimate airflow patterns given limited sensor measurements. In lieu of actual sensor data, computational fluid dynamics data are used to evaluate the accuracy of the airflow patterns estimated by the inverse models developed in this study. It was found that the airflow patterns estimated by the linear inverse SVD model were as accurate as those estimated by the nonlinear inverse-multizone model. For the zones tested, sensor measurements along on the walls and near the inlet and outlet provided the greatest improvement in the accuracy of the estimated airflow patterns when compared with the results using measurements from other locations.     

Valid inequalities for MIPs and group polyhedra from approximate liftings

In this paper, we present an approximate lifting scheme to derive valid inequalities for general mixed integer programs and for the group problem. This scheme uses superadditive functions as the building block of integer and continuous lifting procedures. It yields a simple derivation of new and known families of cuts that correspond to extreme inequalities for group problems. This new approximate lifting approach is constructive and potentially efficient in computation. J.-P. P. Richard was supported by NSF grant DMI-348611.     

Sooting tendencies of nonvolatile aromatic hydrocarbons

We have measured sooting tendencies of 72 nonvolatile aromatic hydrocarbons, only five of which have been previously reported in the literature. The tested compounds include long-chain alkylbenzenes up to tridecylbenzene, methyl-substituted benzenes, naphthalenes, biaryls, and polycyclic aromatic hydrocarbons (PAH) with up to four rings. Sooting tendency was defined as the maximum soot concentration f_v,max in a methane/air coflow nonpremixed flame with 5-80 ppm of the aromatic added to the fuel. The f_v,max were converted into Yield Sooting Indices (YSI’s) by the equation YSI = C^∗f_v,max + D, where C and D are constants chosen so that YSI-2-heptanone = 17 and YSI-phenanthrene = 191. The aromatics were dissolved in 2-heptanone and added to the fuel mixture with a syringe pump. Soot concentrations were measured with laser-induced incandescence (LII). The burner and fuel lines were heated; time-resolved soot measurements verified that all of the test compounds were quantitatively transmitted to the flame without losses to the walls. The uncertainties in the results range from ±3 to ±10%.     

Congruences of multipartition functions modulo powers of primes

Let p _r (n) denote the number of r-component multipartitions of n, and let S _γ,λ be the space spanned by η(24z) ^γ ?(24z), where η(z) is the Dedekind’s eta function and ?(z) is a holomorphic modular form in \(M_{\lambda}(\mathrm{SL}_{2}(\mathbb{Z}))\) . In this paper, we show that the generating function of \(p_{r}(\frac{m^{k} n +r}{24})\) with respect to n is congruent to a function in the space S _γ,λ modulo m ^k . As special cases, this relation leads to many well known congruences including the Ramanujan congruences of p(n) modulo 5,7,11 and Gandhi’s congruences of p ₂(n) modulo 5 and p ₈(n) modulo 11. Furthermore, using the invariance property of S _γ,λ under the Hecke operator \(T_{\ell^{2}}\) , we obtain two classes of congruences pertaining to the m ^k -adic property of p _r (n).