Small ball probabilities for Gaussian random fields and tensor products of compact operators

We find the logarithmic -small ball asymptotics for a large class of zero mean Gaussian fields with covariances having the structure of ``tensor product'. The main condition imposed on marginal covariances is the regular behavior of their eigenvalues at infinity that is valid for a multitude of Gaussian random functions including the fractional Brownian sheet, Ornstein - Uhlenbeck sheet, etc. So we get the far-reaching generalizations of well-known results by Csáki (1982) and by Li (1992). Another class of Gaussian fields considered is the class of additive fields studied under the supremum-norm by Chen and Li (2003). Our theorems are based on new results on spectral asymptotics for the tensor products of compact self-adjoint operators in Hilbert space which are of independent interest.

     

Single-molecule observations of surfactant diffusion at the solution-solid interface

Individual fatty acid molecules adsorbed at the interface between hexadecane and fused silica have been tracked using total internal reflection fluorescence microscopy. Two cooperative diffusive mechanisms are observed: continuous small-scale Brownian motion and occasional large "jumps." The continuous diffusion exhibits evidence of confinement. The effective interfacial diffusion coefficients for each mechanism increase systematically with temperature; an Arrhenius analysis gives an activation barrier of approximately 50 kJ/mol for "jumping" and an upper limit of approximately 10 kJ/mol for confined diffusion.     

Surface protonation at the rutile (110) interface: explicit incorporation of solvation structure within the refined MUSIC model framework

The detailed solvation structure at the (110) surface of rutile (alpha-TiO2) in contact with bulk liquid water has been obtained primarily from experimentally verified classical molecular dynamics (CMD) simulations of the ab initio-optimized surface in contact with SPC/E water. The results are used to explicitly quantify H-bonding interactions, which are then used within the refined MUSIC model framework to predict surface oxygen protonation constants. Quantum mechanical molecular dynamics (QMD) simulations in the presence of freely dissociable water molecules produced H-bond distributions around deprotonated surface oxygens very similar to those obtained by CMD with nondissociable SPC/E water, thereby confirming that the less computationally intensive CMD simulations provide accurate H-bond information. Utilizing this H-bond information within the refined MUSIC model, along with manually adjusted Ti-O surface bond lengths that are nonetheless within 0.05 A of those obtained from static density functional theory (DFT) calculations and measured in X-ray reflectivity experiments (as well as bulk crystal values), give surface protonation constants that result in a calculated zero net proton charge pH value (pHznpc) at 25 degrees C that agrees quantitatively with the experimentally determined value (5.4+/-0.2) for a specific rutile powder dominated by the (110) crystal face. Moreover, the predicted pHznpc values agree to within 0.1 pH unit with those measured at all temperatures between 10 and 250 degrees C. A slightly smaller manual adjustment of the DFT-derived Ti-O surface bond lengths was sufficient to bring the predicted pHznpcvalue of the rutile (110) surface at 25 degrees C into quantitative agreement with the experimental value (4.8+/-0.3) obtained from a polished and annealed rutile (110) single crystal surface in contact with dilute sodium nitrate solutions using second harmonic generation (SHG) intensity measurements as a function of ionic strength. Additionally, the H-bond interactions between protolyzable surface oxygen groups and water were found to be stronger than those between bulk water molecules at all temperatures investigated in our CMD simulations (25, 150 and 250 degrees C). Comparison with the protonation scheme previously determined for the (110) surface of isostructural cassiterite (alpha-SnO2) reveals that the greater extent of H-bonding on the latter surface, and in particular between water and the terminal hydroxyl group (Sn-OH) results in the predicted protonation constant for that group being lower than for the bridged oxygen (Sn-O-Sn), while the reverse is true for the rutile (110) surface. These results demonstrate the importance of H-bond structure in dictating surface protonation behavior, and that explicit use of this solvation structure within the refined MUSIC model framework results in predicted surface protonation constants that are also consistent with a variety of other experimental and computational data.     

Sensitive determination of anions in saliva using capillary electrophoresis after transient isotachophoretic preconcentration

A transient isotachophoresis-capillary electrophoresis (tITP-CE) system for the determination of minor inorganic anions in saliva is described. The complete separation and quantification of bromide, iodide, nitrate, nitrite, and thiocyanate has been achieved with only centrifugation and dilution of the saliva sample. In-line tITP preconcentration conditions, created by introduction of the plugs of 5 mM dithionic acid (leading electrolyte) and 10 mM formic acid (terminating electrolyte) before and after the sample zone, respectively, allowed the limits of direct UV absorption detection (at 200 nm) to be up to 50-fold improved as compared with CE without tITP. As a result, nitrate and thiocyanate were still detectable at 4.6 and 3.8 μg l⁻¹, respectively, in 1000 times diluted saliva. The daily variations of anionic concentrations in saliva samples taken from a smoking health volunteer were discussed based on the results of tITP-CE analysis. It was confirmed that the thiocyanate concentration in saliva noticeably increased after smoking. This is apparently the first report on simultaneous quantification of more than four anionic salivary constituents using CE.     

2,6,7-trithiabicyclo[2.2.2]octanes as promising photolabile tags for combinatorial encoding

The adducts of trithiabicyclo[2.2.2]octane (TTBO) and carbonyl compounds undergo efficient photoinduced fragmentation with quantum yields comparable to that of dithiane adducts. The effect of the third sulfur on the stability of the respective radical cations and radicals is examined computationally and experimentally in a laser flash photolysis study. A straightforward synthetic approach to a variety of 4-substituted trithiabicyclo[2.2.2]octanes from 3-bromo-2,2-bis(bromomethyl)propanol is developed, making a diverse set of mass-differentiated photolabile tags readily available for combinatorial encoding.     

Functionalized heteroarylpyridazines and pyridazin-3(2H)-one derivatives via palladium-catalyzed cross-coupling methodology

A general method for the synthesis of functionalized pyridazinylboronic acids/esters is described involving a directed ortho metalation (DoM)--boronation protocol (Schemes 1 and 2). A comprehensive study of the reactivity of the C-B bond in palladium-catalyzed cross-couplings with aryl/heteroaryl halides is presented. Aryl-/heteroarylpyridazines are thereby obtained in synthetically viable yields (typically 40-75%) although in some cases competing protodeboronation has been observed. A series of pyridazin-3(2H)-one derivatives, including 4,6-diaryl/heteroaryl derivatives, have been obtained from the corresponding 3-methoxypyridazines in straightforward procedures (Schemes 3 and 4). Several X-ray crystal structures of aryl-/heteroarylpyridazines and derived pyridazin-3(2H)-one derivatives are reported. These multi-ring systems are of considerable interest in contemporary N-heterocyclic chemistry.     

Competitive aryl-iodide vs aryl-aryl reductive elimination reactions in Pt(IV) complexes: experimental and theoretical studies

The platinum(IV) complex trans-(dmpe)Pt(IV)(Ar)2I2 (2, dmpe = 1,2-dimethylphosphinoethane, Ar = 4-FC6H4) rapidly reacts, upon moderate heating in solution under ambient light, via two distinct pathways: isomerization to the corresponding cis-isomer (3) and Ar-I reductive elimination to give (dmpe)Pt(II)(Ar)I (4). Complex 3 undergoes, upon prolonged heating at high temperatures, an exclusive Ar-Ar reductive elimination reaction to give (dmpe)Pt(II)I2. Experimental and DFT studies showed that the 2-to-3 isomerization proceeds via three pathways: photochemical or thermal phosphine chelate opening and a mechanism involving cleavage of the Pt-I bond. The isomerization reaction is significantly slowed down but not stopped in the absence of light or in the presence of an excess of tetra-n-butylammonium iodide. On the other hand, the Ar-I reductive elimination from 2 proceeds via the Pt(delta+)-I(delta-) ion pairlike transition state. Use of the rigid dmpe analogue 1,2-dimethylphosphinobenzene (dmpbz) as the ligand shuts down the chelate ring-opening isomerization pathway and enables faster Ar-I reductive elimination thus making the latter reaction the major reaction route for the dmpbz supported trans-diiodo Pt(IV) complex 8.     

Spectroscopic and theoretical study of a mononuclear manganese(III) complex exhibiting a tetragonally compressed geometry

Inelastic neutron scattering and high-field electron paramagnetic resonance data are presented for [Mn(bpia)(OAc)(OCH(3))](PF(6)), where bpia is bis(picolyl)(N-methylimidazole-2-yl)amine. Modeling of the data to the conventional fourth-order spin-Hamiltonian yielded the following parameters: D = 3.526(3) cm(-1), E = 0.588(6) cm(-1), B(0)(4) = -0.00084(7) cm(-1), B(2)( 4)= -0.002(2) cm(-1), (4)(4) = -0.0082(5) cm(-1), g(x) = 1.98(1), g(y) = 1.952(6), and g(z) = 1.978(5). The complex is of particular interest given the biochemical activity and the unusual stereochemistry distinguished by a rare example of a tetragonally compressed octahedron and a pronounced angular distortion imposed by the tetradentate tripodal bpia ligand. Ligand field, density functional theory, and complete active space self-consistent field ab initio calculations are presented that aim to relate the spectroscopic data to the molecular geometry.     

Comparison of the internal energy deposition of venturi-assisted electrospray ionization and a venturi-assisted array of micromachined ultrasonic electrosprays (AMUSE)

The internal energy deposition of a Venturi-assisted array of micromachined ultrasonic electrosprays (AMUSE), with and without the application of a DC charging potential, is compared with equivalent experiments for Venturi-assisted electrospray ionization (ESI) using the "survival yield" method on a series of para-substituted benzylpyridinium salts. Under conditions previously shown to provide maximum ion yields for standard compounds, the observed mean internal energies were nearly identical (1.93-2.01 eV). Operation of AMUSE without nitrogen flow to sustain the air amplifier focusing effect generated energetically colder ions with mean internal energies that were up to 39% lower than those for ESI. A balance between improved ion transfer, adequate desolvation, and favorable ion energetics was achieved by selection of optimum operational ranges for the parameters that most strongly influence the ion population: the air amplifier gas flow rate and API capillary temperature. Examination of the energy landscapes obtained for combinations of these parameters showed that a low internal energy region (相似文献