Identifying Mixtures of Mixtures Using Bayesian Estimation

The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.     

Reaction of 1,2-diarylhydrazines with acetic anhydride catalyzed by 4-(dimethylamino)pyridine

Summary A new method for the synthesis of 1,2-diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-ones3 and 4-acetyl-1,2-diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-ones5 is presented. The reaction of 4,4-disubstituted 1,2-diarylhydrazines1 with acetic anhydride in the presence of an equimolar amount of 4-(dimethylamino)pyridine leads to mixtures of the corresponding acetyl derivatives2 and3. Under the same conditions, 2,2-disubstituted 1,2-diarylhydrazines yield mixtures of3 and5.

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4-(Dimethylamino)pyridin-katalysierte Reaktion von 1,2-Diarylhydrazinen mit Essigsäureanhydrid

Zusammenfassung Eine neue Methode zur Synthese von 1,2-Diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-onen3 und 4-Acetyl-1,2-diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-onen5 wird beschrieben. Die Reaktion von 4,4-disubstituierten 1,2-Diaryl-hydrazinen1 mit Essigsäureanhydrid führt in Gegenwart eines Äquivalentes 4-(Dimethylamino)pyridin zu Gemischen der entsprechenden Acetylderivate2 und3. Unter den gleichen Bedingungen werden aus 2,2-disubstituierten 1,2-Diarylhydrazinen Gemische aus3 und5 erhalten.

     

Reference spectra of important adsorbed organic and inorganic phosphate binding forms for soil P speciation using synchrotron‐based K‐edge XANES spectroscopy

Direct speciation of soil phosphorus (P) by linear combination fitting (LCF) of P K‐edge XANES spectra requires a standard set of spectra representing all major P species supposed to be present in the investigated soil. Here, available spectra of free‐ and cation‐bound inositol hexakisphosphate (IHP), representing organic P, and of Fe, Al and Ca phosphate minerals are supplemented with spectra of adsorbed P binding forms. First, various soil constituents assumed to be potentially relevant for P sorption were compared with respect to their retention efficiency for orthophosphate and IHP at P levels typical for soils. Then, P K‐edge XANES spectra for orthophosphate and IHP retained by the most relevant constituents were acquired. The spectra were compared with each other as well as with spectra of Ca, Al or Fe orthophosphate and IHP precipitates. Orthophosphate and IHP were retained particularly efficiently by ferrihydrite, boehmite, Al‐saturated montmorillonite and Al‐saturated soil organic matter (SOM), but far less efficiently by hematite, Ca‐saturated montmorillonite and Ca‐saturated SOM. P retention by dolomite was negligible. Calcite retained a large portion of the applied IHP, but no orthophosphate. The respective P K‐edge XANES spectra of orthophosphate and IHP adsorbed to ferrihydrite, boehmite, Al‐saturated montmorillonite and Al‐saturated SOM differ from each other. They also are different from the spectra of amorphous FePO₄, amorphous or crystalline AlPO₄, Ca phosphates and free IHP. Inclusion of reference spectra of orthophosphate as well as IHP adsorbed to P‐retaining soil minerals in addition to spectra of free or cation‐bound IHP, AlPO₄, FePO₄ and Ca phosphate minerals in linear combination fitting exercises results in improved fit quality and a more realistic soil P speciation. A standard set of P K‐edge XANES spectra of the most relevant adsorbed P binding forms in soils is presented.     

Phosphaniminato‐Komplexe des Zirconiums: Die Kristallstrukturen von [ZrCl3(NPPh3)(HNPPh3)2] und [ZrCl2(NPPh3)2(HNPPh3)2]

Phosphoraneiminato Complexes of Zirconium: Crystal Structures of [ZrCl₃(NPPh₃)(HNPPh₃)₂] and [ZrCl₂(NPPh₃)₂(HNPPh₃)₂] The phosphoraneiminato complexes [ZrCl₃(NPPh₃)(HNPPh₃)₂] ( 1 ) and [ZrCl₂(NPPh₃)₂(HNPPh₃)₂] ( 2 ) have been obtained by reaction of [ZrCl₄(THF)₂] with [CsNPPh₃]₄ in THF solution to give colourless moisture sensitive crystals which are characterized by X‐ray structure determinations. [ZrCl₃(NPPh₃)(HNPPh₃)₂] ( 1 ): Space group P 1, Z = 2, lattice dimensions at 193 K: a = 1209.4(2); b = 1480.8(2); c = 1814.2(2) pm; α = 71.203(13)°, β = 71.216(13)°, γ = 74.401(13)°; R = 0.0476. The zirconium atom of 1 is oktahedrally coordinated by the three chlorine atoms in meridional arrangement and by the three nitrogen atoms of the (NPPh₃^–) ligand and of the two phosphane imine molecules HNPPh₃. The ZrN bond distance of the (NPPh₃^–) group (193.5 pm) corresponds with a double bond. [ZrCl₂(NPPh₃)₂(HNPPh₃)₂] ( 2 ): Space group P 1, Z = 4, lattice dimensions at 193 K: a = 1447.6(2); b = 1925.7(2), c = 2457.0(2) pm; α = 67.317(12)°, β = 87.376(12)°, γ = 87.103(13)°; R = 0.0408. The zirconium atom in 2 is octahedrally coordinated by the two chlorine atoms in trans position, and by the nitrogen atoms of the two (NPPh₃^–) groups as well as by the two HNPPh₃ molecules. The ZrN distance of the (NPPh₃^–) ligands (198.9 and 202.0 pm) suggest some π‐interaction between the zirconium and the nitrogen atoms.     

Synthesen und Kristallstrukturen von Dialkylgalliumhydriden — dimere versus trimere Formeleinheiten

Syntheses and Crystal Structures of Dialkylgallium Hydrides — Dimeric versus Trimeric Formula Units Dialkylgallium hydrides (R = Me, Et, iPr, iBu, neopentyl) were obtained on two different synthetic routes. The dimethyl and diethyl compounds were formed by the reaction of LiH with the corresponding dialkylgallium chlorides via lithium dialkyldihydridogallate intermediates, which so far have not been isolated in a pure form. On the second route, trialkylgallium compounds were treated with [GaH₃·NMe₂Et] to yield the dialkylgallium hydrides by a substituent exchange reaction. The dimethyl, diethyl and diisopropyl compounds are trimeric in solution. That trimeric structure was verified for the diisopropyl derivative by a crystal structure determination. Di(neopentyl)gallium hydride has a dimeric structure in solution and in the solid state.