Versatility of the dipolar filter selection: from 1H nuclear spin diffusion experiment to the measurement of nuclear Overhauser effect in homopolymer melts

Dipolar filters select ¹H magnetization according to local dipolar dephasing, which corresponds to site mobility in systems with heterogeneous molecular mobility. Combined with a conventional exchange experiment, it is usually applied to polymeric samples exhibiting structures on the nanometer length scale associated with a strong dynamic contrast. There, the resulting ¹H nuclear spin diffusion experiment yields the size of the structure. When the same experiment is applied to homopolymer melts exhibiting a weak dynamic contrast and dynamic heterogeneities on significant shorter length scales, the recorded magnetization decay is in agreement with decays expected from a heterogeneous nanostructure. However, dipolar filters actually can also select mobile parts of the repeat unit, e.g. the end of the alkyl side chains and the subsequent magnetization transfer then can occur via cross relaxation due to non coherent zero-quantum transitions (nuclear Overhauser effect, NOE). The difficulties of distinguishing these two cases are examined and it is demonstrated that NOE experiments exploiting magnetization selection via the dipolar filter allow quantifying the local dynamics of the side chains. This opens new possibilities for measurements of local dynamics in non isotopically labeled homopolymer melts.     

Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

The ν1 and ν4 fundamental bands of H3SiCl investigated with high resolution

The gas phase infrared spectrum of monoisotopic H₃Si³⁷Cl has been reinvestigated in the ν₁/ν₄ region near 2200 cm⁻¹, using a Fourier transform spectrometer, with a nominal resolution of 0.0027 cm⁻¹. The rovibrational analysis confirms, besides the weak Coriolis x, y resonance between the (v₁ = 1) and (v₄ = 1) levels, the existence of two strong local perturbations in the ν₄ band. These are caused by rotational (Δk = Δl = ±1) type resonances with and , respectively. Another local perturbation of the 12 ? KΔK ? 14 subbands of the ν₄ band, probably due to a (Δk = Δl = ±1) interaction with , was detected and analyzed. All these local perturbations have been studied individually using a simple model of two interacting sublevels. Without the transitions involved in the local perturbations, more than 2000 lines of the ν₁/ν₄ band system were used to obtain a complete set of vibration-rotation parameters set for the v₁ = 1 and v₄ = 1 states. By means of a band contour simulation, both the transition moment ratio ∣M₄:M₁∣ = 1.25 and a positive sign of the Coriolis intensity perturbation were determined.The present results, together with the accurate existing data for ν₂, ν₃, ν₅, and ν₆ bands, allowed us to derive the experimental values, A_e = 2.8722945(37) cm⁻¹ and B_e = 0.2182248(22) cm⁻¹, which are compared with those of ab initio calculations.     

Quasilinear evolutionary equations and continuous interpolation spaces

In this paper we analyze the abstract parabolic evolutionary equations

     

On theorems of Gelfond and Selberg concerning integral-valued entire functions

For each sN define the constant θ_s with the following properties: if an entire function g(z) of type t(g)<θ_s satisfies then g is a polynomial; conversely, for any δ>0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g)<θ_s+δ. The result θ₁=log2 is known due to Hardy and Pólya. We provide the upper bound θ_sπs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941).     

Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity

We study smoothing properties for time-dependent Schrödinger equations , , with potentials which satisfy V(x)=O(|x|^m) at infinity, m?2. We show that the solution u(t,x) is 1/m times differentiable with respect to x at almost all , and explain that this is the result of the fact that the sojourn time of classical particles with energy λ in arbitrary compact set is less than CTλ^−1/m during [0,T] when λ is very large. We also show Strichartz's inequality with derivative loss for such potentials and give its application to nonlinear Schrödinger equations.     

小波双线性插值搜索算法及其在光学遥感图像中的应用

详细分析了在小波双线性插值中高频外推阈值门限与峰值信噪比的变化关系,提出了基于峰值信噪比最大的小波双线性插值搜索算法。提出的算法能够自动搜索到峰值信噪比最大的高频外推最佳阈值门限,实现了在不破坏光学遥感图像原始信息的情况下,提高了图像的空间分辨率,有利于对图像的细节信息进行观察分析。实验结果表明:该算法能够得到比双线性插值和全小波插值更高的峰值信噪比、熵值和更好的图像细节效果,是一种适合提高光学遥感图像分辨率的有效算法。     

Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition _K/h_K c₀ > 0 is not satisfied, whereh_K is the diameter of the element K and _K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L²-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.     

Interpolation between and

We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .

     

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.