Determinants of Laplacians on surfaces of finite volume

Determinants of the Laplace and other elliptic operators on compact manifolds have been an object of study for many years (see [MP, RS, Vor]). Up until now, however, the theory of determinants has not been extended to non-compact situations, since these typically involve a mixture of discrete and continuous spectra. Recent advances in this theory, which are partially motivated by developments in mathematical physics, have led to a connection, in the compact Riemann surface case, between determinants of Laplacians on spinors and the Selberg zeta function of the underlying surface (see [DP, Kie, Sar, Vor]).Our purpose in this paper is to introduce a notion of determinants on non-compact (finite volume) Riemann surfaces. These will be associated to the Laplacian shifted by a parameters(1–s), and will be defined in terms of a Dirichlet series (w, s) which is a sum that represents the discrete as well as the continuous spectrum. It will be seen to be regular atw=0, and our main theorem (see Sect. 1) will express exp as the Selberg zeta function of the surface times the appropriate -factor.A Sloan Fellow and partially supported by NSF grant DMS-8701865     

Local‐Curvature‐Controlled Non‐Epitaxial Growth of Hierarchical Nanostructures

Site‐selective growth on non‐spherical seeds provides an indispensable route to hierarchical complex nanostructures that are interesting for diverse applications. However, this has only been achieved through epitaxial growth, which is restricted to crystalline materials with similar crystal structures and physicochemical properties. A non‐epitaxial growth strategy is reported for hierarchical nanostructures, where site‐selective growth is controlled by the curvature of non‐spherical seeds. This strategy is effective for site‐selective growth of silica nanorods from non‐spherical seeds of different shapes and materials, such as α‐Fe₂O₃, NaYF₄, and ZnO. This growth strategy is not limited by the stringent requirements of epitaxy and is thus a versatile general method suitable for the preparation of hierarchical nanostructures with controlled morphologies and compositions to open up a verity of applications in self‐assembly, nanorobotics, catalysis, electronics, and biotechnology.     

Kinetic energy release distributions (KERDs) for the dissociation of metastable enol ions

Bimodal kinetic energy release distributions (KERDs) were obtained for the metastable ion reactions: CH₃C(OH) = ^*CH₂?⁺ → CH₃ + ^*CH₃CO⁺ and CH₃CH₂C(OH)=CH₂?⁺ → C₂H₅ + CH₃CO⁺. The bimodality is attributed to incomplete intramolecular energy redistribution in the short-lived intermediate keto ions, CH₃COCH₃?⁺ and CH₃CH₂COCH₃?⁺, respectivley, formed en route to the dissociation products.     

Synthesis,structural and electrical characterization of PbS NCs in titania sol–gel films

Nanocrystals of lead sulfide were grown in TiO₂ (titania) thin films prepared by a sol-gel process. The synthetic procedure as well as the structural, optical, and electrical properties of the films are demonstrated. The structures and morphology of PbS nanocrystals were analyzed using HRTEM, SAED, AFM, HRSEM, XRD and EDAX elemental analysis technique. When the concentration of PbS in the titania matrix is 20 mol%, PbS NCs with a diameter of 2.0 nm are created. At a higher PbS concentration (> 40 mole%) in the titania matrix, PbS NCs and PbS clusters are created not only within the TiO₂ film but also on the external surface of the TiO₂ film. By increasing the PbS concentration up to 50 mol%, PbS nanocrystals of 6–8 nm in diameter are formed within the titania film and PbS clusters with a base size of about 100 nm² and a height up to about 20 nm were self assembled on the external surface of TiO₂ film. Quantum size effect and band gap energies were obtained from shifts of the absorption edge. For electrical measurements, PbS–TiO₂ films were deposited on an ITO/glass substrate, and then covered with gold contact. The electrical properties of ITO/PbS NCs–TiO₂/Au and ITO/PbS NCs–TiO₂/PbS cluster/Au structures were studied. I–V characteristics of the one layer structure are nearly linear and symmetric, while those of the two-layer structure exhibit rectifying behavior.     

Spectroscopic investigations on II–VI-semiconductor nanocrystals and their assemblies

This review points out that (magneto-)optical measurements may help to shine light on the recombination processes taking place in semiconductor nanocrystals. The surface capping with thiols creates a CdS shell around CdTe cores and forms a Cd site that is not fourfold-coordinated at the surface. It is pointed out how specific cappings such as thio-amines and thio-acids assist in coupling NCs and how we may distinguish between NC–NC interactions via electrostatic and covalent linking with the aid of the optical measurements. Furthermore, with static and time-resolved ODMR studies on IR-active core-shell HgTe/Hg _x Cd_1−x Te(S) particles it is demonstrated how the nature of the recombination emission being associated with a Cd–Hg mixed site is elucidated and by this yielding structural information on the NC core-shell interface. With these examples we show that and how nanomaterials of probable technological interest are studied beneficially with advanced spectroscopic techniques.     

A family of novel DNA sequencing instruments based on single-photon detection

We have developed a family of high-performance capillary DNA sequencing instruments based on a novel multicolor fluorescent detection technology. This technology is based on two technical innovations: the multilaser excitation of fluorescence of labeled DNA fragments and the "color-blind" single-photon detection of modulated fluorescence. Our machines employ modern digital and broadband techniques that are essential for achieving superior instrument performance. We discuss the design and testing results for several versions of the automated single lane DNA sequencers, as well as our approach to scaling up to multilane instruments.     

Bounds for resultants of univariate and bivariate polynomials

The paper considers bounds on the size of the resultant for univariate and bivariate polynomials. For univariate polynomials we also extend the traditional representation of the resultant by the zeros of the argument polynomials to formal resultants, defined as the determinants of the Sylvester matrix for a pair of polynomials whose actual degree may be lower than their formal degree due to vanishing leading coefficients. For bivariate polynomials, the resultant is a univariate polynomial resulting by the elimination of one of the variables, and our main result is a bound on the largest coefficient of this univariate polynomial. We bring a simple example that shows that our bound is attainable and that a previous sharper bound is not correct.     

The protonated betaine/ammonia complex: how stable is the gas-phase zwitterion structure?

The ammonium ion stabilizes a betaine zwitterion in the gas phase forming a salt-bridge structure, [(CH₃)₃N⁺CH₂COO^–NH₄⁺] that is 3.7 kcal/mol less stable than the ion/molecule complex between protonated betaine and neutral ammonia, (CH₃)₃N⁺CH₂COOH/NH₃. DFT calculations have reversed the previously determined relative stability based on PM3 calculations and are in agreement with black-body infrared radiative dissociation experiments. A double-well potential energy surface is formed with a rather low central barrier separating the two complexes. This is conducive to efficient hydrogen/deuterium exchange in agreement with experiment. It prevents the existence of the salt-bridge complex as a distinct species under thermal conditions.     

Thermal ignition of acetonitrile. Experimental results and kinetic modeling

Ignition delay times of acetonitrile (CH₃CN) in mixtures containing acetonitrile and oxygen diluted in argon were studied behind reflected shock waves. The temperature range covered was 1420–1750 K at overall concentrations behind the reflected shock wave ranging from 2 to 4×10⁻⁵ mol/cm³. Over this temperature and concentration range the ignition delay times varied by approximately one order of magnitude, ranging from ca. 100 μs to slightly above 1 ms. From a total of some 70 tests the following correlation for the ignition delay times was derived: t_ign=9.77×10⁻¹² exp(41.7×10³/RT)×{[CH₃CN]^0.12[O₂]^−0.76[Ar]^0.34} s, where concentrations are expressed in units of mol/cm³ and R is expressed in units of cal/(K mol). The ignition delay times were modeled by a reaction scheme containing 36 species and 111 elementary reactions. Good agreement between measured and calculated ignition delay times was obtained. A least-squares analysis of 60 computed ignition delay times from six different groups of initial conditions gave the following temperature and concentration dependence: E=46.2×10³ cal/mol, β=0.43, β=−1.18, and β_Ar=0.18. The ignition process is initiated by H-atom ejection from acetonitrile. The addition of oxygen atoms to the system from the dissociation of molecular oxygen and from the reaction CH₃CN+O₂ → HO₂·+CH₂CN·is negligible. In view of the relatively high concentration of methyl radicals obtained in the reaction CH₃CN+H → CH₃+HCN, the branching step CH₃+O₂ → CH₃O+O plays a more important role than the parallel step H+O₂→ OH+O. A discussion of the mechanism in view of the sensitivity analysis is presented. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 839–849, 1997