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71.
Jakob Jonsson 《Annals of Combinatorics》2010,14(4):487-505
Let 1 ≤ m ≤ n. We prove various results about the chessboard complex M
m,n
, which is the simplicial complex of matchings in the complete bipartite graph K
m,n
. First, we demonstrate that there is nonvanishing 3-torsion in
[(H)\tilde]d(\sf Mm,n; \mathbb Z){{\tilde{H}_d({\sf M}_{m,n}; {\mathbb Z})}} whenever
\fracm+n-43 £ d £ m-4{{\frac{m+n-4}{3}\leq d \leq m-4}} and whenever 6 ≤ m < n and d = m − 3. Combining this result with theorems due to Friedman and Hanlon and to Shareshian and Wachs, we characterize all triples
(m, n, d ) satisfying
[(H)\tilde]d (\sf Mm,n; \mathbb Z) 1 0{{\tilde{H}_d \left({\sf M}_{m,n}; {\mathbb Z}\right) \neq 0}}. Second, for each k ≥ 0, we show that there is a polynomial f
k
(a, b) of degree 3k such that the dimension of
[(H)\tilde]k+a+2b-2 (\sf Mk+a+3b-1,k+2a+3b-1; \mathbb Z3){{\tilde{H}_{k+a+2b-2}}\,\left({{\sf M}_{k+a+3b-1,k+2a+3b-1}}; \mathbb Z_{3}\right)}, viewed as a vector space over
\mathbbZ3{\mathbb{Z}_3}, is at most f
k
(a, b) for all a ≥ 0 and b ≥ k + 2. Third, we give a computer-free proof that
[(H)\tilde]2 (\sf M5,5; \mathbb Z) @ \mathbb Z3{{\tilde{H}_2 ({\sf M}_{5,5}; \mathbb {Z})\cong \mathbb Z_{3}}}. Several proofs are based on a new long exact sequence relating the homology of a certain subcomplex of M
m,n
to the homology of M
m-2,n-1 and M
m-2,n-3. 相似文献
72.
A. Ehn M. Levenius M. Jonsson M. Aldn J. Bood 《Journal of Raman spectroscopy : JRS》2013,44(4):622-629
A common problem when applying Raman scattering in applied research is spectral interference from laser‐induced fluorescence. Extensive work has been invested in developing spectral and polarization filters as well as modulation schemes to refine spontaneous Raman signals. This current work, however, focuses on utilizing the temporal domain using a picosecond laser system and ICCD cameras with relatively short decay of the camera gate to prevent the fluorescence tail from being captured in Raman experiments. Further, the approach of using an ICCD camera to perform temporal filtering is compared to earlier proposed detection schemes using streak cameras or Kerr gates. The temporal‐filtering scheme is evaluated in a spectroscopic investigation where a background subtraction algorithm is presented. The temporal‐filtering scheme was also evaluated for Raman imaging of a levitated water droplet surrounded by fluorescing toluene vapor. Furthermore, the temporal‐filter detection scheme was simulated in order to provide straight forward evaluation tools to estimate the potential of performing temporal filtering with a laser/camera system considering: laser‐pulse duration, time jitter, camera‐gate characteristics, gate delay times, fluorescence lifetimes, and relative signal strength between the Raman and fluorescence signal. The fluorescence signal was modeled with a closed two‐level system, and the simulated results were compared to results from an investigation of the rising slope of toluene fluorescence. These evaluation tools and experimental investigations may serve as guidelines for planning and performing Raman measurements in situations where traditional filter‐rejection schemes are insufficient. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
73.
We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's σ-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then τ(N) ≥ min{τ(M), Λ n }, where Λ n is a positive constant depending only on n = dim M. Various topological conclusions can be drawn, in particular that τ is a spin-bordism invariant below Λ n . Also, below Λ n the values of τ cannot accumulate from above when varied over all manifolds of dimension n. 相似文献
74.
The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However,
even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium.
By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly
improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special
case. 相似文献
75.
Jonsson LM Santandrea F Gorelik LY Shekhter RI Jonson M 《Physical review letters》2008,100(18):186802
We investigate theoretically multimode electromechanical "shuttle" instabilities in dc voltage-biased nanoelectromechanical single-electron tunneling devices. We show that initially irregular (quasiperiodic) oscillations that occur as a result of the simultaneous self-excitation of several mechanical modes with incommensurable frequencies self-organize into periodic oscillations with a frequency corresponding to the eigenfrequency of one of the unstable modes. This effect demonstrates that a local probe can selectively excite global vibrations of extended objects. 相似文献
76.
Sensitive temperature-induced line shifts of the near-band-edge emission from ZnO:Ga and ZnO:Zn are investigated for two-dimensional (2D) thermometry with nanosecond time resolution. Spectral and temporal concerns for 2D measurements and the feasibility for utilizing the line shifts for temperature measurements using a spectral ratio are investigated. Owing to the high temperature sensitivity, a precision of 1% at 800 K is reported for spectral ratio measurements. The technique is demonstrated by 2D measurements of the liquid temperature of burning methanol droplets. 相似文献
77.
We reveal the non-metric geometry underlying ω→0 Brans–Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints. 相似文献
78.
79.
The interaction between cells and biomaterials has been mimicked using nylon microparticles as pseudo-cells and PLMA and PIBMA as biomaterial model acrylate polymers. The shift of fundamental resonance frequencies was negative for both polymers, indicating mass-coupling to the sensor surface. The shifts of the 3rd, 5th and 7th overtone frequencies were initially positive for both polymers, indicating a particle slip or wobbling on the surface. The QCM technique could discriminate between the two different polymers, showing increased interaction between microparticle and PLMA. The dissipation shift was positive for all overtones on both polymers, but again with faster and more prominent response for PLMA. 相似文献
80.
Jakob Jonsson 《Journal of Combinatorial Theory, Series A》2008,115(8):1504-1526
Building on work by Bouc and by Shareshian and Wachs, we provide a toolbox of long exact sequences for the reduced simplicial homology of the matching complex Mn, which is the simplicial complex of matchings in the complete graph Kn. Combining these sequences in different ways, we prove several results about the 3-torsion part of the homology of Mn. First, we demonstrate that there is nonvanishing 3-torsion in whenever , where . By results due to Bouc and to Shareshian and Wachs, is a nontrivial elementary 3-group for almost all n and the bottom nonvanishing homology group of Mn for all n≠2. Second, we prove that is a nontrivial 3-group whenever . Third, for each k?0, we show that there is a polynomial fk(r) of degree 3k such that the dimension of , viewed as a vector space over Z3, is at most fk(r) for all r?k+2. 相似文献