Higher order log-concavity in Euler’s difference table

For 0≤k≤n, let be the entries in Euler’s difference table and let . Dumont and Randrianarivony showed equals the number of permutations on [n] whose fixed points are contained in {1,2,…,k}. Rakotondrajao found a combinatorial interpretation of the number in terms of k-fixed-points-permutations of [n]. We show that for any n≥1, the sequence is essentially 2-log-concave and reverse ultra log-concave.     

一类函数增量的局部渐近性质

文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。     

Interpolating Thin-Shell and Sharp Large-Deviation Estimates for Lsotropic Log-Concave Measures

Given an isotropic random vector X with log-concave density in Euclidean space \mathbbRⁿ{\mathbb{R}^n} , we study the concentration properties of |X| on all scales, both above and below its expectation. We show in particular that

A Partial First-Order Affine-Scaling Method

We present a partial first-order affine-scaling method for solving smooth optimization with linear inequality constraints. At each iteration, the algorithm considers a subset of the constraints to reduce the complexity. We prove the global convergence of the algorithm for general smooth objective functions, and show it converges at sublinear rate when the objective function is quadratic. Numerical experiments indicate that our algorithm is efficient.     

A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations

The $p$-step backward difference formula (BDF) for solving systems of ODEs can be formulated as all-at-once linear systems that are solved by parallel-in-time preconditioned Krylov subspace solvers (see McDonald et al. [36] and Lin and Ng [32]). However, when the BDF$p$ (2 ≤ $p$ ≤ 6) method is used to solve time-dependent PDEs, the generalization of these studies is not straightforward as $p$-step BDF is not selfstarting for $p$ ≥ 2. In this note, we focus on the 2-step BDF which is often superior to the trapezoidal rule for solving the Riesz fractional diffusion equations, and show that it results into an all-at-once discretized system that is a low-rank perturbation of a block triangular Toeplitz system. We first give an estimation of the condition number of the all-at-once systems and then, capitalizing on previous work, we propose two block circulant (BC) preconditioners. Both the invertibility of these two BC preconditioners and the eigenvalue distributions of preconditioned matrices are discussed in details. An efficient implementation of these BC preconditioners is also presented, including the fast computation of dense structured Jacobi matrices. Finally, numerical experiments involving both the one- and two-dimensional Riesz fractional diffusion equations are reported to support our theoretical findings.     

A molecular dynamics simulation of nanoscale convective heat transfer with the effect of axial heat conduction

Effective heat dissipation from nano-fluidic devices is sometimes necessary to ensure their performance and lifespan. In the molecular dynamics simulation of nanoscale convective heat transfer, thermostats cannot be directly applied to the fluid because of the non-uniform temperature distribution. Periodic boundary is typically utilised, but unrealistic axial heat conduction exists when there is a temperature difference between the outlet and images of inlet atoms. In this paper, the effect of axial conduction caused by periodic boundary is investigated through the Péclet number (Pe). Taking viscous dissipation into consideration, the magnitude of outlet thermal diffusion is observed to decrease with increasing Pe. The local average temperature of fluid changes in an exponential form except in the region close to the outlet. Results show that the contribution of outlet axial conduction to the local average temperature is less than 2.0% when Pe > 10. The main reason is that the magnitude of fluid velocity and viscous heat dissipation in nanochannels is much larger than that in macro-channels at the same Péclet number.     

A bubble detection technique based on light intensity and Mie scattering theory for spinning solution

A novel bubble detection technique based on light intensity and Mie scattering theory for spinning solution is presented theoretically and experimentally. With the light intensity in every direction, the particle or bubble size distribution can be calculated with the Mie scattering theory. The light intensity distribution in every direction, corresponding to the light intensity received by every assumed annulus of the detector has been calculated theoretically. According to the light intensity distribution, the size distribution of bubbles can be deduced. A series of standardized polystyrene micro-sphere (with 7 μm diameter) solution has been used not only as sample for experiments and calibration, but also as the bubbles in the glycerin. Theoretical and experimental results show that the technique can be used for bubble detection, in order to improve the traditional bubble detection scheme, and to lower production costs.     

Performance characteristics of single photon pulse ranging system using Monte Carlo simulation

Single photon pulse ranging system with extremely high sensitivity has been widely used in distance measurement and 3D imaging. To analyze the factors that affect the measurement precision and accuracy will help to improve system performance. According to system structure and principle, we mainly discussed the following factors: laser intensity, pulse width, detection efficiency and time jitter. A simulation model based on Monte Carlo stochastic method was constructed in this paper, and we get the specific influence of factors on measurement precision and accuracy by simulation. Finally, we set up laboratory experiment system and took effective experiments on ranging precision and accuracy.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.