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21.
Let V be a complex vector space with basis {x
1, x
2, . . . , x
n
} and G be a finite subgroup of GL(V). The tensor algebra T(V) over the complex is isomorphic to the polynomials in the non-commutative variables x
1, x
2, . . . , x
n
with complex coefficients. We want to give a combinatorial interpretation for the decomposition of T(V) into simple G-modules. In particular, we want to study the graded space of invariants in T(V) with respect to the action of G. We give a general method for decomposing the space T(V) into simple modules in terms of words in a Cayley graph of the group G. To apply the method to a particular group, we require a homomorphism from a subalgebra of the group algebra into the character
algebra. In the case of G as the symmetric group, we give an example of this homomorphism from the descent algebra. When G is the dihedral group, we have a realization of the character algebra as a subalgebra of the group algebra. In those two
cases, we have an interpretation for the graded dimensions and the number of free generators of the algebras of invariants
in terms of those words. 相似文献
22.
We develop a theory of symplectic cobordism and a Duistermaat-Heckman principle for Hamiltonian loop group actions. As an
application, we construct a symplectic cobordism between moduli spaces of flat connections on the three holed sphere and disjoint
unions of toric varieties. This cobordism yields formulas for the mixed Pontrjagin numbers of the moduli spaces, equivalent
to Witten's formulas in the case of symplectic volumes.
Received June 15, 1998 相似文献
23.
Sebastian Bcker David Bryant Andreas W. M. Dress Mike A. Steel 《Journal of Algorithms in Cognition, Informatics and Logic》2000,37(2):522
The amalgamation of leaf-labeled trees into a single (super)tree that “displays” each of the input trees is an important problem in classification. We discuss various approaches to this problem and show that a simple and well-known polynomial-time algorithm can be used to solve this problem whenever the input set of trees contains a minimum size subset that uniquely determines the supertree. Our results exploit a recently established combinatorial property concerning the structure of such collections of trees. 相似文献
24.
Serge Zaugg Mike van der Schaar Ludwig Houégnigan Michel André 《Applied Acoustics》2012,73(3):281-290
Acquisition of acoustic data from ocean observatories is expected to play a key role for the long-term monitoring of marine mammals and anthropogenic noise. It typically requires processing of a large volume of acoustic data and it must rely on automated identification of signals. We present an algorithmic framework for the detection of short tonal sounds (e.g. cetacean calls, anthropogenic pings) intended to act as a first stage in a system for the automated real-time detection, classification, and localisation of acoustic sources. The algorithm was validated under a diversity of scenarios expected at ocean observatories. Using simulated signals that emulate a variety of cetacean call-types, perfect identification of signal position was obtained for signal to noise ratios of ?15 to ?5 dB, depending on the signal-type. Separation of real-world data segments with short tonal sounds (mainly cetacean calls) from segments with other sounds or noise resulted in Area Under the ROC Curve values between 0.96 and 0.98. The algorithm can be used to automatically identify cetacean calls and anthropogenic short tonal sounds much faster than in real-time, thereby reducing the burden put on data transmission, storage, or processing by classification and localisation algorithms. 相似文献
25.
26.
Busby M Hartl F Matousek P Towrie M Vlcek A 《Chemistry (Weinheim an der Bergstrasse, Germany)》2008,14(23):6912-6923
Two multifunctional photoactive complexes [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) and [Re(MeDpe(+))(CO)(3)(bpy)](2+) (MeDpe(+)=N-methyl-4-[trans-2-(4-pyridyl)ethenyl]pyridinium, bpy=2,2'-bipyridine) were synthesized, characterized, and their redox and photonic properties were investigated by cyclic voltammetry; ultraviolet-visible-infrared (UV/Vis/IR) spectroelectrochemistry, stationary UV/Vis and resonance Raman spectroscopy; photolysis; picosecond time-resolved absorption spectroscopy in the visible and infrared regions; and time-resolved resonance Raman spectroscopy. The first reduction step of either complex occurs at about -1.1 V versus Fc/Fc(+) and is localized at MeDpe(+). Reduction alone does not induce a trans-->cis isomerization of MeDpe(+). [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) is photostable, while [Re(MeDpe(+))(CO)(3)(bpy)](2+) and free MeDpe(+) isomerize under near-UV irradiation. The lowest excited state of [Re(Cl)(CO)(3)(MeDpe(+))(2)](2+) has been identified as the Re(Cl)(CO)(3)-->MeDpe(+ 3)MLCT (MLCT=metal-to-ligand charge transfer), decaying directly to the ground state with lifetimes of approximately 42 (73 %) and approximately 430 ps (27 %). Optical excitation of [Re(MeDpe(+))(CO)(3)(bpy)](2+) leads to population of Re(CO)(3)-->MeDpe(+) and Re(CO)(3)-->bpy (3)MLCT states, from which a MeDpe(+) localized intraligand (3)pipi* excited state ((3)IL) is populated with lifetimes of approximately 0.6 and approximately 10 ps, respectively. The (3)IL state undergoes a approximately 21 ps internal rotation, which eventually produces the cis isomer on a much longer timescale. The different excited-state behavior of the two complexes and the absence of thermodynamically favorable interligand electron transfer in excited [Re(MeDpe(+))(CO)(3)(bpy)](2+) reflect the fine energetic balance between excited states of different orbital origin, which can be tuned by subtle structural variations. The complex [Re(MeDpe(+))(CO)(3)(bpy)](2+) emerges as a prototypical, multifunctional species with complementary redox and photonic behavior. 相似文献
27.
Clifford MN Lopez V Poquet L Williamson G Kuhnert N 《Rapid communications in mass spectrometry : RCM》2007,21(13):2014-2018
We report a systematic investigation of the effects and structural requirements for ion suppression in negative ion mode electrospray ionisation mass spectrometry of a series of carboxylic acids and present a structural model rationalising ion suppression effects. 相似文献
28.
Watari M Galbraith J Lang HP Sousa M Hegner M Gerber C Horton MA McKendry RA 《Journal of the American Chemical Society》2007,129(3):601-609
Free-standing cantilevers, which directly translate specific biochemical reactions into micromechanical motion, have recently attracted much attention as label-free biosensors and micro/nano robotic devices. To exploit this mechanochemical sensing technology, it is essential to develop a fundamental understanding of the origins of surface stress. Here we report a detailed study into the molecular basis of stress generation in aqueous environments focusing on the pH titration of model mercaptohexadecanoic acid self-assembled monolayers (SAMs), using in situ reference cantilevers coated with nonionizable hexadecanethiol SAMs. Semiautomated data analysis and a statistical model were developed to quantify cyclic deprotonation/protonation reactions on multiple arrays. In-plane force titrations were found to have the sensitivity to detect ionic hydrogen bond formation between protonated and nonprotonated carboxylic acid groups in the proximity of the surface pK1/2, which generated a mean tensile differential surface stress of +1.2 +/- 0.3 mN/m at pH 6.0, corresponding to 1 pN attractive force between two adjacent MHA molecules. Conversely, the magnitude of compressive differential surface stress was found to increase progressively with pH >/= 7.0, reaching a maximum of -14.5 +/- 0.5 mN/m at pH 9.0, attributed to enhanced electrostatic repulsion between deprotonated carboxylic acid groups. However, striking differences were observed in the micromechanical responses to different ionic strength and ion species present in the aqueous environment, highlighting the critical role of counter- and co-ions on surface stress. Our findings provide fundamental insights into the molecular mechanisms of in-plane mechanochemistry, which may be exploited for biosensing and nanoactuation applications. 相似文献
29.
Levy JN Latham CM Roisin L Kandziora N Di Fruscia P White AJ Woodward S Fuchter MJ 《Organic & biomolecular chemistry》2012,10(3):512-515
A synthetic route towards a number of novel IBiox N-heterocyclic carbene (NHC) ligands has been developed. The resulting ligands have restricted flexibility and high steric demand. Preliminary studies have shown these ligands to give high levels of asymmetric induction in the copper-free allylic alkylation of cinnamyl bromide. 相似文献
30.
Cole DJ Payne MC Csányi G Spearing SM Colombi Ciacchi L 《The Journal of chemical physics》2007,127(20):204704
We have developed a classical two- and three-body interaction potential to simulate the hydroxylated, natively oxidized Si surface in contact with water solutions, based on the combination and extension of the Stillinger-Weber potential and of a potential originally developed to simulate SiO(2) polymorphs. The potential parameters are chosen to reproduce the structure, charge distribution, tensile surface stress, and interactions with single water molecules of a natively oxidized Si surface model previously obtained by means of accurate density functional theory simulations. We have applied the potential to the case of hydrophilic silicon wafer bonding at room temperature, revealing maximum room temperature work of adhesion values for natively oxidized and amorphous silica surfaces of 97 and 90 mJm(2), respectively, at a water adsorption coverage of approximately 1 ML. The difference arises from the stronger interaction of the natively oxidized surface with liquid water, resulting in a higher heat of immersion (203 vs 166 mJm(2)), and may be explained in terms of the more pronounced water structuring close to the surface in alternating layers of larger and smaller densities with respect to the liquid bulk. The computed force-displacement bonding curves may be a useful input for cohesive zone models where both the topographic details of the surfaces and the dependence of the attractive force on the initial surface separation and wetting can be taken into account. 相似文献