Computing the flow around a moving profile by numerically integrating the Navier–Stokes equations

A vorticity velocity formulation is proposed for the solution of the equations for viscous flow around a moving profile. A non-inertial reference frame is used and the velocities are computed from a Poincaré integral formula. The studies are directed towards the need to understand helicopter blade aerodynamics. Worked examples are given which validate the method and programme for laminar flows, at least for low Reynolds numbers. © 1998 John Wiley & Sons, Ltd.     

Spectral Properties of Foams and Emulsions

The optical and spectral properties of foams and emulsions provide information about their micro-/nanostructures, chemical and time stability and molecular data of their components. Foams and emulsions are collections of different kinds of bubbles or drops with particular properties. A summary of various surfactant and emulsifier types is performed here, as well as an overview of methods for producing foams and emulsions. Absorption, reflectance, and vibrational spectroscopy (Fourier Transform Infrared spectroscopy-FTIR, Raman spectroscopy) studies are detailed in connection with the spectral characterization techniques of colloidal systems. Diffusing Wave Spectroscopy (DWS) data for foams and emulsions are likewise introduced. The utility of spectroscopic approaches has grown as processing power and analysis capabilities have improved. In addition, lasers offer advantages due to the specific properties of the emitted beams which allow focusing on very small volumes and enable accurate, fast, and high spatial resolution sample characterization. Emulsions and foams provide exceptional sensitive bases for measuring low concentrations of molecules down to the level of traces using spectroscopy techniques, thus opening new horizons in microfluidics.     

Morse–Novikov cohomology of locally conformally Kähler manifolds

A locally conformally Kähler (LCK) manifold is a complex manifold admitting a Kähler covering, with the monodromy acting on this covering by holomorphic homotheties. We define three cohomology invariants, the Lee class, the Morse–Novikov class, and the Bott–Chern class, of an LCK-structure. These invariants play together the same role as the Kähler class in Kähler geometry. If these classes coincide for two LCK-structures, the difference between these structures can be expressed by a smooth potential, similar to the Kähler case. We show that the Morse–Novikov class and the Bott–Chern class of a Vaisman manifold vanish. Moreover, for any LCK-structure on a manifold, admitting a Vaisman structure, we prove that its Morse–Novikov class vanishes. We show that a compact LCK-manifold M$M$ with vanishing Bott–Chern class admits a holomorphic embedding into a Hopf manifold, if _dimCM?3${dim}_{\mathbb{C}}M?3$, a result which parallels the Kodaira embedding theorem.     

A Factor Analysis Perspective on Linear Regression in the ‘More Predictors than Samples’ Case

Linear regression (LR) is a core model in supervised machine learning performing a regression task. One can fit this model using either an analytic/closed-form formula or an iterative algorithm. Fitting it via the analytic formula becomes a problem when the number of predictors is greater than the number of samples because the closed-form solution contains a matrix inverse that is not defined when having more predictors than samples. The standard approach to solve this issue is using the Moore–Penrose inverse or the L2 regularization. We propose another solution starting from a machine learning model that, this time, is used in unsupervised learning performing a dimensionality reduction task or just a density estimation one—factor analysis (FA)—with one-dimensional latent space. The density estimation task represents our focus since, in this case, it can fit a Gaussian distribution even if the dimensionality of the data is greater than the number of samples; hence, we obtain this advantage when creating the supervised counterpart of factor analysis, which is linked to linear regression. We also create its semisupervised counterpart and then extend it to be usable with missing data. We prove an equivalence to linear regression and create experiments for each extension of the factor analysis model. The resulting algorithms are either a closed-form solution or an expectation–maximization (EM) algorithm. The latter is linked to information theory by optimizing a function containing a Kullback–Leibler (KL) divergence or the entropy of a random variable.     

mu-eta2:eta2-peroxodicopper(II) complex with a secondary diamine ligand: a functional model of tyrosinase

The activation of dioxygen (O(2)) by Cu(I) complexes is an important process in biological systems and industrial applications. In tyrosinase, a binuclear copper enzyme, a mu-eta(2):eta(2)-peroxodicopper(II) species is accepted generally to be the active oxidant. Reported here is the characterization and reactivity of a mu-eta(2):eta(2)-peroxodicopper(II) complex synthesized by reacting the Cu(I) complex of the secondary diamine ligand N,N'-di-tert-butyl-ethylenediamine (DBED), [(DBED)Cu(MeCN)](X) (1.X, X = CF(3)SO(3)(-), CH(3)SO(3)(-), SbF(6)(-), BF(4)(-)), with O(2) at 193 K to give [[Cu(DBED)](2)(O(2))](X)(2) (2.X(2)). The UV-vis and resonance Raman spectroscopic features of 2 vary with the counteranion employed yet are invariant with change of solvent. These results implicate an intimate interaction of the counteranions with the Cu(2)O(2) core. Such interactions are supported further by extended X-ray absorption fine structure (EXAFS) analyses of solutions that reveal weak copper-counteranion interactions. The accessibility of the Cu(2)O(2) core to exogenous ligands such as these counteranions is manifest further in the reactivity of 2 with externally added substrates. Most notable is the hydroxylation reactivity with phenolates to give catechol and quinone products. Thus the strategy of using simple bidentate ligands at low temperatures provides not only spectroscopic models of tyrosinase but also functional models.     

Reduction of Vaisman structures in complex and quaternionic geometry

We consider locally conformal Kähler geometry as an equivariant (homothetic) Kähler geometry: a locally conformal Kähler manifold is, up to equivalence, a pair $(K,\Gamma )$, where $K$ is a Kähler manifold and $\Gamma$ is a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kähler manifold $(K,\Gamma )$ as the rank of a natural quotient of $\Gamma$, and prove its invariance under reduction. This equivariant point of view leads to a proof that locally conformal Kähler reduction of compact Vaisman manifolds produces Vaisman manifolds and is equivalent to a Sasakian reduction. Moreover, we define locally conformal hyperKähler reduction as an equivariant version of hyperKähler reduction and in the compact case we show its equivalence with 3-Sasakian reduction. Finally, we show that locally conformal hyperKähler reduction induces hyperKähler with torsion (HKT) reduction of the associated HKT structure and the two reductions are compatible, even though not every HKT reduction comes from a locally conformal hyperKähler reduction.     

Polysilanes. A New Route Toward High Performance EL Devices

The discovery of a remarkable class of plastics that can conduct electricity has opened a new era of plastics science and technology that has just been recognized by the award of the 2000 Nobel prize for chemistry. They can be used to make a wide range of electronic devices such as transistors, light-emitting diodes, solar cells and even lasers, through much simpler manufacture than conventional inorganic materials, increasing flexibility, reducing cost, and opening up new markets. Polysilanes are subject of an intensive research work aiming to various optoelectronic applications. Through this work the chemical structure of polydiphenylsilane was modified to obtain both solubility in common solvents and to induce new properties by attaching of various organic segments.     

Nondegeneracy,from the prospect of wave-wave regular interactions of a gasdynamic type

A parallel is considered between Burnat's “algebraic” approach [restricted to a genuine nonlinearity] and Martin's “differential” approach regarding their contribution to describing some nondegenerate one-dimensional gasdynamic regular interaction solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)