The heat semigroup and Brownian motion on strip complexes

We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing “strips” along their natural boundaries according to a given graph structure. The most familiar example is the one-dimensional complex classically associated with a graph, in which case the strips are simply copies of the unit interval (our setup actually allows for variable edge length). A leading key example is treebolic space, a geometric object studied in a number of recent articles, which arises as a horocyclic product of a metric tree with the hyperbolic plane. In this case, the graph is a regular tree, the strips are [0,1]×R, and each strip is equipped with the hyperbolic geometry of a specific strip in upper half plane. We consider natural families of Dirichlet forms on a general strip complex and show that the associated heat kernels and harmonic functions have very strong smoothness properties. We study questions such as essential self-adjointness of the underlying differential operator acting on a suitable space of smooth functions satisfying a Kirchhoff type condition at points where the strip complex bifurcates. Compatibility with projections that arise from proper group actions is also considered.     

Subharmonic functions on graphs

We study the behaviour of subharmonic functions on a graph. We assume bounds on the growth of balls and functions in order to obtain Liouville type theorems.     

Partial least squares modeling of combined infrared, H NMR and C NMR spectra to predict long residue properties of crude oils

Research has been carried out to determine the potential of partial least squares (PLS) modeling of mid-infrared (IR) spectra of crude oils combined with the corresponding ¹H and ¹³C nuclear magnetic resonance (NMR) data, to predict the long residue (LR) properties of these substances. The study elaborates further on a recently developed and patented method to predict this type of information from only IR spectra. In the present study, PLS modeling was carried out for 7 different LR properties, i.e., yield long-on-crude (YLC), density (D_LR), viscosity (V_LR), sulfur content (S), pour point (PP), asphaltenes (Asph) and carbon residue (CR). Research was based on the spectra of 48 crude oil samples of which 28 were used to build the PLS models and the remaining 20 for validation. For each property, PLS modeling was carried out on single type IR, ¹³C NMR and ¹H NMR spectra and on 3 sets of merged spectra, i.e., IR + ¹H NMR, IR + ¹³C NMR and IR + ¹H NMR + ¹³C NMR. The merged spectra were created by considering the NMR data as a scaled extension of the IR spectral region. In addition, PLS modeling of coupled spectra was performed after a Principal Component Analysis (PCA) of the IR, ¹³C NMR and ¹H NMR calibration sets. For these models, the 10 most relevant PCA scores of each set were concatenated and scaled prior to PLS modeling. The validation results of the individual IR models, expressed as root-mean-square-error-of-prediction (RMSEP) values, turned out to be slightly better than those obtained for the models using single input ¹³C NMR or ¹H NMR data. For the models based on IR spectra combined with NMR data, a significant improvement of the RMSEP values was not observed neither for the models based on merged spectra nor for those based on the PCA scores. It implies, that the commonly accepted complementary character of NMR and IR is, at least for the crude oil and bitumen samples under study, not reflected in the results of PLS modeling. Regarding these results, the absence of sample preparation and the straightforward way of data acquisition, IR spectroscopy is preferred over NMR for the prediction of LR properties of crude oils at site.     

The chemistry and the stereochemistry of poly(N-alkyliminoalanes) : IX. Hexameric organoaluminum imides by reaction of (HAIN-iso-C3H7)6 with trialkylaluminums

(HAlN-iso-C₃H₇)₆ reacts with Al(CH₃)₃ or Al(C₂H₅)₃ to give compounds in which the hydridic hydrogens are partially or completely replaced by alkyl groups. The degree of alkylation depends on the reaction conditions and on the nature of the trialkylaluminum. Pure crystalline (CH₃AlN-iso-C₃H₇)₆, its crystallization product with [(CH₃AlN-iso-C₃H₇)₅(HAlN-iso-C₃H₇)] and a mixture of [(C₂H₅AlN-iso-C₃H₇)₄(HAlN-iso-C₃H₇)₂] isomers have been isolated. The reaction of Al(CH₃)₃ or Al(C₂H₅)₃ with iso-C₃H₇NH₂ gives tetramers (CH₃AlN-iso-C₃H₇)₄ and (C₂H₅AlN-iso-C₃H₇)₄.     

Random walks on generalized lattices

A generalized lattice is a graph on which the groupZ ^d acts almost transitively. The relations among various features of random walks on generalized lattices are studied. In particular we relate the mean displacement, the drift-freeness of the random walk and the existence of linear harmonic functions. Applications to recurrence criteria are given.     

Zur Bestimmung des Glycerins

Ohne Zusammenfassung