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31.
Isaac Efrat 《Communications in Mathematical Physics》1988,119(3):443-451
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 相似文献
32.
Dr. Chaoran Li Shumin Zhang Dr. Bingchang Zhang Dr. Jingjing Liu Weihu Zhang Prof. Alexander A. Solovev Prof. Rujun Tang Dr. Feng Bao Jia Yu Prof. Qiao Zhang Prof. Yeshayahu Lifshitz Prof. Le He Prof. Xiaohong Zhang 《Angewandte Chemie (International ed. in English)》2018,57(14):3772-3776
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. 相似文献
33.
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. 相似文献
34.
Tsiala Saraidarov A. Gevorgian R. Reisfeld A. Sashchiuk M. Bashouti E. Lifshitz 《Journal of Sol-Gel Science and Technology》2007,44(2):87-95
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. 相似文献
35.
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
Cd1−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. 相似文献
36.
Alaverdian L Alaverdian S Bilenko O Bogdanov I Filippova E Gavrilov D Gorbovitski B Gouzman M Gudkov G Domratchev S Kosobokova O Lifshitz N Luryi S Ruskovoloshin V Stepoukhovitch A Tcherevishnick M Tyshko G Gorfinkel V 《Electrophoresis》2002,23(16):2804-2817
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. 相似文献
37.
38.
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. 相似文献
39.
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. 相似文献
40.
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: tign=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 βAr=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 相似文献