Approximately counting cliques

We present a very simple, randomized approximation algorithm for determining the number of cliques in a random graph. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 395–411 (1997)     

Towards a bifurcation theory for nonautonomous difference equations

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. This article contains an approach to overcome this deficit in the context of nonautonomous difference equations. Based on special notions of attractivity and repulsivity, nonautonomous bifurcation phenomena are studied. We obtain generalizations of the well-known one-dimensional transcritical and pitchfork bifurcation.     

New examples of curves with a one-dimensional family of pencils of minimal degree

We give a geometric construction of sub-linear systems on a K3 surface consisting of smooth curves C with infinitely many ${g^1_{{\rm gon}(C)}}$ ??s.     

A multiresolution remeshed Vortex-In-Cell algorithm using patches

We present a novel multiresolution Vortex-In-Cell algorithm using patches of varying resolution. The Poisson equation relating the fluid vorticity and velocity is solved using Fast Fourier Transforms subject to free space boundary conditions. Solid boundaries are implemented using the semi-implicit formulation of Brinkman penalization and we show that the penalization can be carried out as a simple interpolation. We validate the implementation against the analytic solution to the Perlman test case and by free-space simulations of the onset flow around fixed and rotating circular cylinders and bluff body flows around bridge sections.     

On hidden symmetries of extremal Kerr–NUT–AdS–dS black holes

It is well known that the Kerr–NUT–AdS–dS black hole admits two linearly independent Killing vectors and possesses a hidden symmetry generated by a rank-2 Killing tensor. The near-horizon geometry of an extremal Kerr–NUT–AdS–dS black hole admits four linearly independent Killing vectors, and we show how the hidden symmetry of the black hole itself is carried over by means of a modified Killing–Yano potential which is given explicitly. We demonstrate that the corresponding Killing tensor of the near-horizon geometry is reducible as it can be expressed in terms of the Casimir operators formed by the four Killing vectors.     

Carroll rearrangement to construct the norneolignan skeleton

A three-step synthesis of the norneolignan skeleton involving the Carroll rearrangement as the key step has been developed and used for synthesis of the norneolignan skeleton, 1,3-diphenylpenta-1,4-diene and hinokiresinol.     

Monitoring catalysts at work in their final form: spectroscopic investigations on a monolithic catalyst

A monolithic vanadia-titania based catalyst has been subjected to studies with in situ FTIR spectroscopy coupled with mass spectrometry, during the SCR (Selective Catalytic Reduction) reaction. A device based on a transmission reactor cell for monolithic samples was constructed, dedicated to the study of surface species during reaction. After analysing the steady state SCR activity under industrially relevant conditions, NH(3) chemisorption phenomena as a function of temperature and the subsequent SCR reaction of NO + O(2) with chemisorbed ammonia and ammonium ion species were also investigated. The observations reported here serve as a demonstration of the great potential for the application of operando spectroscopy on monolithic systems. This cross disciplinary approach aims to identify reaction pathways, active sites, intermediate- and spectator-species for catalytic reactions under truly industrial conditions in a shaped monolithic catalyst based on monitoring chemical profiles along its channels. In particular, by demonstrating the feasibility of the approach using the technically challenging operando transmission FTIR spectroscopy methodology, we foresee easy future adaption of this approach with other surface or bulk sensitive techniques, e.g. Raman and UV-vis spectroscopy.     

Capillary condensation hysteresis in overlapping spherical pores: a monte carlo simulation study

The mechanisms of hysteretic phase transformations in fluids confined to porous bodies depend on the size and shape of pores, as well as their connectivity. We present a Monte Carlo simulation study of capillary condensation and evaporation cycles in the course of Lennard-Jones fluid adsorption in the system of overlapping spherical pores. This model system mimics pore shape and connectivity in some mesoporous materials obtained by templating cubic surfactant mesophases or colloidal crystals. We show different mechanisms of capillary hysteresis depending on the size of the window between the pores. For the system with a small window, the hysteresis cycle is similar to that in a single spherical pore: capillary condensation takes place upon achieving the limit of stability of adsorption film and evaporation is triggered by cavitation. When the window is large enough, the capillary condensation shifts to a pressure higher than that of the isolated pore, and the possibility for the equilibrium mechanism of desorption is revealed. These finding may have important implications for practical problems of assessment of the pore size distributions in mesoporous materials with cagelike pore networks.     

Vanadium complex of 2-(2'-Pyridyl)-4,5-dicyanoimidazole showing spermicidal and cytotoxic properties

Two complexes having the formulas VO(DCIPy)2(H2O).1.5H2O and VO(DCIPy)2(H2O).2MeOH have been synthesized and characterized (DCIPy = 2-(2'-pyridyl)-4,5-dicyanoimidazolato). The methanol solvated species has been studied by X-ray diffraction, and single crystals form in the space group P2(1)/n. The hydrated species was studied by electron paramagnetic resonance spectroscopy in both the solid state and in a frozen solution, and the values of A( parallel) examined using the additivity relationship. The hydrated species was shown to exhibit both spermicidal and cytoxic properties.     

Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations

Recently, the existence of Morse decompositions for nonautonomous dynamical systems was shown for three different time domains: the past, the future and—in the linear case—the entire time. In this article, notions of exponential dichotomy are discussed with respect to the three time domains. It is shown that an exponential dichotomy gives rise to an attractor-repeller pair in the projective space, which is a building block of a Morse decomposition. Moreover, based on the notions of exponential dichotomy, dichotomy spectra are introduced, and it is proved that the corresponding spectral manifolds lead to Morse decompositions in the projective space.