An experimental study of the phase inversion behavior of liquid-liquid dispersion has been conducted in a spray extraction column for systems of toluene / water, n-hexane/water, CCl4/water, toluene /water + glycerol (25 % wt), toluene + CCl4 (25 % wt) / water and toluene / acetic acid (5 % wt)/water. The effects of physical properties, mass transfer and column geometry...

We introduce and analyze numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the solution, together with the numerical simplicity of Galerkin methods. In a first step, we simply combi...

The minimal representation π of the indefinite orthogonal group O(m+ 1, 2) is realized on the Hilbert space of square integrable functions on R with respect to the measure |x|dx1 · · ·dxm. This article gives an explicit integral formula for the holomorphic extension of π to a holomorphic semigroup of O(m + 3,C) by means of the Bessel function. Taking its ‘boundary value’, we also find the integ...

Data-space inversion (DSI) is a data assimilation procedure that directly generates posterior flow predictions, for time series of interest, without calibrating model parameters. No forward simulation performed in the process. DSI instead uses prior generated by performing O(<m...

An invariant mean on a group G is a normalized, positive, translation invariant linear functional defined on the space of all bounded complex valued functions on G. Some groups possess an invariant mean (or are said to be amenable), while others do not. In particular, all abelian groups are amenable [2, §17.5]. An invariant mean on a group need not be inversion invariant. It is quite easy to sh...

Full waveform inversion (FWI) requires an accurate estimation of source signatures. Due to the coupling between signatures and subsurface model, small errors in former can translate into large latter. When direct methods are used solve forward problem, classical frequency-domain FWI efficiently processes multiple sources for signature wavefield estimations once a single Lower-Upper (LU) decompo...

The modern social space is increasingly determined by the trends of digitalization. Today we can talk about such consequences digitalization as appearance scattered identity and distancing – a new kind socialization in conditions spatial separation overcoming deprivation virtual transgression. These manifest themselves all spheres cultural, economic, political, etc. But at same time, processes ...