Positive definite functions on the Heisenberg group

Work supported in part by the NSF     

Determination of sulfinpyrazone and two of its metabolites in human plasma and urine by gas chromatography and selective detection

A selective and sensitive gas chromatographic method for simultaneous determination of sulfinpyrazone and two of its metabolites (the para-hydroxylated metabolite and the sulfone metabolite) in biological fluids using alkali flame ionization detection (AFID), electron capture detection (ECD) and mass fragmentographic detection is described. The compounds are extracted from the samples, methylated and separated on 2% OV-17 or 3% OV-225 columns. Phenylbutazone is used as internal standard. Standard curves are linear. The coefficient of variation at 10 microgram/ml of sulfinpyrazone in plasma was shown to be 1.8% (AFID), and the detection limits were 0.1 microgram/ml (AFID) and 10 ng/ml (ECD). Mass spectra of the methylated compounds are shown and serum concentration curves after oral administration of 100 mg sulfinpyrazone to two persons are determined together with the excreted amounts of drug and metabolites.     

Refinement of borate structures from 11B MAS NMR spectroscopy and density functional theory calculations of 11B electric field gradients

The refinement of borate structures using DFT calculations combined with experimental (11)B quadrupole coupling parameters from solid-state NMR spectroscopy is presented. The (11)B electric field gradient (EFG) tensors, calculated using the WIEN2k software for trigonal and tetrahedral boron sites in a series of model compounds, exhibit a convincing linear correlation with the quadrupole coupling tensor elements, determined from (11)B MAS NMR spectra of the central or satellite transitions. The model compounds include Li(2)B(4)O(7), Mg(2)B(2)O(5), Mg(3)B(2)O(6), NH(4)B(C(6)H(5))(4), and colemanite (CaB(3)O(4)(OH)(3).H(2)O). The (11)B quadrupole moment, Q = 0.0409 +/- 0.0002 barn, derived from the linear correlation, is in excellent agreement with the accepted value for Q((11)B). This demonstrates that DFT (WIEN2k) calculations can provide precise (11)B quadrupole coupling parameters on an absolute scale. On the other hand, DFT calculations based on the reported crystal structures for datolite (CaBSiO(4)(OH)) and danburite (CaB(2)Si(2)O(8)) cannot reproduce the experimental (11)B quadrupole coupling parameters to the same high precision. However, optimization of these structures by minimization of the forces between the atoms (obtained by DFT) results in a significant improvement between the calculated and experimental (11)B quadrupole coupling parameters, which indicates that reliable refinements of the borate structures are obtained by this method. Finally, the DFT calculations also provide important structural information about the sign and orientation of the EFG tensor elements in the crystal frame, a kind of information that cannot be achieved from (11)B NMR experiments on powdered samples.     

The complete 51V MAS NMR spectrum of surface vanadia nanoparticles on anatase (TiO2): vanadia surface structure of a DeNOx catalyst

The first observations of the complete manifold of spinning sidebands (ssbs) including both the central and satellite transitions in (51)V MAS NMR spectra of surface vanadia nanoparticles on titania in DeNO(x) catalysts are presented. (51)V quadrupole coupling and chemical shift anisotropy parameters for the dominating vanadia structure are determined from (51)V MAS NMR spectra recorded at 9.4 and 14.1 T. Based on correlations previously established between (51)V NMR parameters and crystal structure data for inorganic vanadates, the NMR data are consistent with vanadium in a distorted octahedral oxygen coordination environment for the so-called strongly bonded vanadia species on the surface. The investigation includes two vanadia-titania model catalysts and six industrial-type DeNO(x) catalysts.     

Synthesis of 1-hydroxy-substituted pyrazolo[3,4-c]- and pyrazolo[4, 3-c]quinolines and -isoquinolines from 4- and 5-aryl-substituted 1-benzyloxypyrazoles

1-Hydroxypyrazolo[3,4-c]quinoline (22), 1-hydroxypyrazolo[4, 3-c]quinoline (21), 1-hydroxypyrazolo[3,4-c]isoquinoline (20), and 1-hydroxypyrazolo[4,3-c]isoquinoline (19) were prepared from 1-benzyloxypyrazole (6), establishing the pyridine B-ring in the terminal step. The pyridine ring of pyrazoloquinolines 14 and 18 was formed via cyclization of a formyl group at C-4 or C-5 and an amino group of a 2-aminophenyl substituent at C-5 or C-4 in 1-benzyloxypyrazole. The pyridine ring of pyrazoloisoquinolines 5 and 9 was created via cyclization of a formyl group in a 2-formylphenyl substituent at C-4 or C-5 with an iminophosphorane group installed at C-5 or C-4 of 1-benzyloxypyrazole by lithiation followed by reaction with tosyl azide and then with tributylphoshine utilizing the Staudinger/aza-Wittig protocol. The 2-aminophenyl and the 2-formylphenyl substituent were introduced at C-5 or C-4 by regioselective metalation followed by transmetalation to the pyrazolylzinc halide and subsequent palladium-catalyzed cross-coupling with 2-iodoaniline or 2-bromobenzaldehyde. The order of reactions and use of protecting groups in the individual sequences have been optimized. The 1-benzyloxy-substituted pyrazoloquinolines and isoquinolines thus obtained were debenzylated by strong acid to the corresponding 1-hydroxy-substituted pyrazoloquinolines and isoquinolines 19-22.     

High-Resolution Infrared Synchrotron Investigation of (HCN)2 and a Semi-Experimental Determination of the Dissociation Energy D0

The high-resolution infrared absorption spectrum of the donor bending fundamental band ν of the homodimer (HCN)₂ has been collected by long-path static gas-phase Fourier transform spectroscopy at 207 K employing the highly brilliant 2.75 GeV electron storage ring source at Synchrotron SOLEIL. The rovibrational structure of the ν transition has the typical appearance of a perpendicular type band associated with a Σ–Π transition for a linear polyatomic molecule. The total number of 100 assigned transitions are fitted employing a standard semi-rigid linear molecule Hamiltonian, providing the band origin ν₀ of 779.05182(50) cm⁻¹ together with spectroscopic parameters for the degenerate excited state. This band origin, blue-shifted by 67.15 cm⁻¹ relative to the HCN monomer, provides the final significant contribution to the change of intra-molecular vibrational zero-point energy upon HCN dimerization. The combination with the vibrational zero-point energy contribution determined recently for the class of large-amplitude inter-molecular fundamental transitions then enables a complete determination of the total change of vibrational zero-point energy of 3.35±0.30 kJ mol⁻¹. The new spectroscopic findings together with previously reported benchmark CCSDT(Q)/CBS electronic energies [Hoobler et al. ChemPhysChem. 19 , 3257–3265 (2018)] provide the best semi-experimental estimate of 16.48±0.30 kJ mol⁻¹ for the dissociation energy D₀ of this prototypical homodimer.     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).     

Stress-Induced Domain Wall Motion in a Ferroelastic Mn3+ Spin Crossover Complex

Domain wall motion is detected for the first time during the transition to a ferroelastic and spin state ordered phase of a spin crossover complex. Single-crystal X-ray diffraction and resonant ultrasound spectroscopy (RUS) revealed two distinct symmetry-breaking phase transitions in the mononuclear Mn³⁺ compound [Mn(3,5-diBr-sal₂(323))]BPh₄, 1. The first at 250 K, involves the space group change Cc→Pc and is thermodynamically continuous, while the second, Pc→P1 at 85 K, is discontinuous and related to spin crossover and spin state ordering. Stress-induced domain wall mobility was interpreted on the basis of a steep increase in acoustic loss immediately below the the Pc-P1 transition