über eine Klasse Riemannscher Mannigfaltigkeiten mit raumartigen pkf-ZusammenhÄngen

One considers m-dimensional Riemannian manifoldsM with tangent spaces T_p(M), p M that are a direct sum of a spacelike m-2 planeR _p and a 2-planeH _p. It is supposed that onM there exists a connection whose space-like components are parallel conformal flat (pkf). These components are generated by a vector field X. Assuming that X belongs to a pair X,Y of reciprocal quasi-cocircular vector fields and that the Pfaffian of this pair is the 1-form associated with the connection, the following results are derived: 1. X and Y are of equal constant length (This is true for all Riemannian manifolds). 2. The immersion of the integral manifold ofH _p intoM is cylindrical and the normal connection is flat. 3. The immersion of any space-like submanifold intoM is cylindrical with respect to the sections inH _p and umbilical with respect to all spacelike sections. 4. If m 4, the integral manifoldP _p is flat.

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Herrn Prof. Dr. WERNER BURAU zum 70.Geburtstag Klaus Buchner und Radu Rosca     

Influences of changes in multitopic tris(pyrazolyl)methane ligand topology on silver(I) supramolecular structures

The reactions between silver tetrafluoroborate and the ligands 1,2,4,5-C(6)H(2)[CH(2)OCH(2)C(pz)(3)](4) (L1, pz = pyrazolyl ring), o-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (L2), and m-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (L3) yield coordination polymers of the formula (C(6)H(6)(-)(n)[CH(2)OCH(2)C(pz)(3)](n)(AgBF4)(m))( infinity ) (n = 4, m = 2, 1; n = 2, ortho substitution, m = 1, 2; meta substitution, m = 2, 3). In the solid state, L2 molecules dimerize by a pair of C-H.pi interactions, forming an arrangement that resembles the tetratopic ligand L1. In the solid-state structure of 1, each silver atom is kappa(2)-bonded to two tris(pyrazolyl)methane units from different ligands with the overall structure a polymer made up from 32-atom macrocyclic rings formed by bonding tris(pyrazolyl)methane groups from nonadjacent positions on the central arene rings to the same two silver atoms. In 2, each silver is bonded to two tris(pyrazolyl)methane units in the same kappa(2)-kappa(2) fashion as with 1, forming a polymer chain. The chains are organized into dimeric units by strong face-to-face pi-pi stacking between the central arene rings making bitopic L2 act as half of tetratopic L1. The chains in both structures are organized by weak C-H.F hydrogen bonds and pi-pi stacking interactions into very similar 3D supramolecular architectures. The structure of 3 contains three types of silvers with the overall 3D supramolecular sinusoidal structure comprised of 32-atom macrocycles. Infrared studies confirm the importance of the noncovalent interactions. Calculations at the DFT (B3LYP/6-31G) level of theory have been carried out on L2 and also support C-H.pi interactions. Electrospray mass spectral data collected from acetone or acetonitrile show the presence of aggregated species such as [(L)Ag(2)(BF(4))](+) and [(L)Ag(2)](2+), despite the fact that (1)H NMR spectra of all compounds show that acetonitrile completely displaces the ligand whereas acetone does not.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Supramolecular structural variations with changes in anion and solvent in silver(I) complexes of a semirigid, bitopic tris(pyrazolyl)methane ligand

The bitopic ligand p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (pz = pyrazolyl ring) that contains two tris(pyrazolyl)methane units connected by a semirigid organic spacer reacts with silver(I) salts to yield [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgX)(2)]( infinity ), where X = CF(3)SO(3)(-) (1), SbF(6)(-) (2), PF(6)(-) (3), BF(4)(-) (4), and NO(3)(-) (5). Crystallization of the first three compounds from acetone yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgCF(3)SO(3))(2)]( infinity ) (1a), [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))(2)[(CH(3))(2)CO](2)]( infinity ) (2b), and [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)AgPF(6)]( infinity ) (3a), where the stoichiometry for the latter compound has changed from a metal:ligand ratio of 2:1 to 1:1. The structure of 1a is based on helical argentachains constructed by a kappa(2)-kappa(1) coordination to silver of the tris(pyrazolyl)methane units. These chains are organized into a tubular 3D structure by cylindrical [(CF(3)SO(3))(6)](6)(-) clusters that form weak C-H...O hydrogen bonds with the bitopic ligand. The same kappa(2)-kappa(1) coordination is present in the structure of 2a, but the structure is organized by six different tris(pyrazolyl)methane units from six ligands bonding with six silvers to form a 36-member argentamacrocycle core. The cores are organized in a tubular array by the organic spacers where each pair of macrocycles sandwich six acetone molecules and one SbF(6)(-) counterion. The structure of 3a is based on a kappa(2)-kappa(0) coordination mode of each tris(pyrazolyl)methane unit forming a helical coordination polymer, with two strands organized in a double stranded helical structure by a series of C-H...pi interactions between the central arene rings. Crystallization of 2-4 from acetonitrile yields complexes of the formula [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)[(AgX)(2)(CH(3)CN)(n)]]( infinity ) where n = 2 for X = SbF(6)(-) (2b), X = PF(6)(-) (3b) and n = 1 for X = BF(4)(-) (4b). All three structures contain argentachains formed by a kappa(2)-kappa(1) coordination mode of the tris(pyrazolyl)methane units linked by the organic spacer and arranged in a 2D sheet structure with the anions sandwiched between the sheets. Crystallization of 5 from acetonitrile yields crystals of the formula [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgNO(3))(2)(CH(3)CN)(4)]( infinity ), where the nitrate is bonded to the silver. The argentachains, again formed by kappa(2)-kappa(1) coordination, are arranged in W-shaped sheets that have an overall configuration very different from 2b-4b. Treating [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))(2)]( infinity ) with a saturated aqueous solution of KPF(6) or KO(3)SCF(3) slowly leads to complete exchange of the anion. Crystallization of a sample that contains an approximately equal mixture of SbF(6)(-)/PF(6)(-) from acetonitrile yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)[Ag(2)(PF(6))(0.78(1))(SbF(6))(1.22(1))(CH(3)CN)(2)][(CH(3)CN)(0.25) (C(4)H(10)O)(0.25)]]( infinity ), a compound with a sheet structure analogous to 2b-4b. Crystallization of the same mixture from acetone yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))[(CH(3))(2)CO](1.5)]( infinity ), where the metal-to-ligand ratio is 1:1 and the [C(pz)(3)] units are kappa(2)-kappa(0) bonded forming a coordination polymer. The supramolecular structures of all species are organized by a combination of C-H...pi, pi-pi, or weak C-H-F(O) hydrogen bonding interactions.     

Decomposing total IR spectra of aqueous systems into solute and solvent contributions: a computational approach using maximally localized Wannier orbitals

The theoretical principles underpinning the calculation of infrared spectra for condensed-phase systems in the context of ab initio molecular dynamics have been recently developed in literature. At present, most ab initio molecular dynamics calculations are restricted to relatively small systems and short simulation times. In this paper we devise a method that allows well-converged results for infrared spectra from ab initio molecular dynamics simulations using small systems and short trajectories characteristic of simulations typically performed in practice. We demonstrate the utility of our approach by computing the imaginary part of the dielectric constant epsilon"(omega) for H2O and D2O in solid and liquid phases and show that it compares well with experimental data. We further demonstrate that maximally localized Wannier orbitals can be used to separate the individual contributions of different molecular species to the linear spectrum of complex systems. The new spectral decomposition method is shown to be useful in present-day ab initio molecular dynamics calculations to compute the magnitude of the "continuous absorption" generated by excess protons in aqueous solutions with good accuracy even when other species present in the solutions absorb strongly in the same frequency window.     

Interdisciplinary study on pottery experimentally impregnated with wine

Experimentally developed ceramic pots, with two different sizes of grain, were half-filled with wine and subjected to thermal alteration at constant elevated temperature ((60 ± 2)°C) in darkness for 12 weeks. This work sought to characterise the samples thereby obtained from chemical and mineralogical perspectives using scanning electron microscopy and an energy-dispersive X-ray microanalysis system (SEM-EDX), Fourier transform infrared spectroscopy (FTIR) and capillary electrophoresis (CE) with UV detection as an alternative to chromatographic methods, due to its good resolution, automation, simplicity, high speed, low consumption of chemicals and short time required for sample preparation. The capillary electrophoresis method was used for the detection of five wine biomarkers: succinic acid, malic acid, tartaric acid, citric acid and lactic acid. In general, it was noted that the fine-grained ceramic assortment retained the organic material better than the coarser-grained ceramics. An interesting observation derived from this study was that not only could tartaric acid be considered as a biomarker for wine residues in archaeological pottery, but malic acid could also act similarly for white wine and lactic acid for red wine.     

Chain rules for linear openness in metric spaces and applications

In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given.     

Review of AdS/CFT Integrability,Chapter V.1: Scattering Amplitudes: A Brief Introduction

Letters in Mathematical Physics - We review current efficient techniques for the construction of multi-leg and multi-loop on-shell scattering amplitudes in supersymmetric gauge theories. Examples...     

A De Giorgi–Type Conjecture for Minimal Solutions to a Nonlinear Stokes Equation

We study the one-dimensional symmetry of solutions to the nonlinear Stokes equation which are periodic in the d − 1 last variables (living on the torus 𝕋^d−1) and globally minimize the corresponding energy in Ω = ℝ × 𝕋^d−1, i.e., Namely, we find a class of nonlinear potentials W ≥ 0 such that any global minimizer u of E connecting two zeros of W as x₁ → ± ∞ is one-dimensional; i.e., u depends only on the x₁ -variable. In particular, this class includes in dimension d = 2 the nonlinearities with w being a harmonic function or a solution to the wave equation, while in dimension d ≥ 3 , this class contains a perturbation of the Ginzburg-Landau potential as well as potentials W having d + 1 wells with prescribed transition cost between the wells. For that, we develop a theory of calibrations relying on the notion of entropy (coming from scalar conservation laws). We also study the problem of the existence of global minimizers of E for general potentials W providing in particular compactness results for uniformly finite energy maps u in Ω connecting two wells of W as x₁ → ± ∞ . © 2019 Wiley Periodicals, Inc.