An optimal perturbation bound

Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.     

Ferroelectric liquid crystals from banana-shaped achiral molecules with vinyl end groups

Banana-shaped achiral compounds, the 1,3-phenylene bis[4-(alkenyloxyphenyliminomethyl)benzoate]s, were synthesized with varying length of the alkenyl group; their ferroelectric properties are described. The smectic mesophases, including a switchable chiral smectic C (SmC*) phase, were characterized by differential scanning calorimetry, polarizing optical microscopy and the triangular wave method. The presence of vinyl groups at the ends of the linear side-wings in the banana-shaped achiral molecules, containing a Schiff's base mesogen, induced a decrease in melting temperature and formation of the switchable SmC* phase in the melt. The compound having the octenyloxy group exhibited a spontaneous polarization of 120 nC cm^?2 on reversal of an applied electric field.     

3D MRI of non-Gaussian (3)He gas diffusion in the rat lung

In (3)He magnetic resonance images of pulmonary air spaces, the confining architecture of the parenchymal tissue results in a non-Gaussian distribution of signal phase that non-exponentially attenuates image intensity as diffusion weighting is increased. Here, two approaches previously used for the analysis of non-Gaussian effects in the lung are compared and related using diffusion-weighted (3)He MR images of mechanically ventilated rats. One approach is model-based and was presented by Yablonskiy et al., while the other approach utilizes the second order decay contribution that is predicted from the cumulant expansion theorem. Total lung coverage is achieved using a hybrid 3D pulse sequence that combines conventional phase encoding with sparse radial sampling for efficient gas usage. This enables the acquisition of nine 3D images using a total of only approximately 1 L of hyperpolarized (3)He gas. Diffusion weighting ranges from 0 s/cm(2) to 40 s/cm(2). Results show that the non-Gaussian effects of (3)He gas diffusion in healthy rat lungs are directly attributed to the anisotropic geometry of lung microstructure as predicted by the Yablonskiy model, and that quantitative analysis over the entire lung can be reliably repeated in time-course studies of the same animal.     

Adaptive discretization for signal detection in statistical inverse problems

We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous studies revealed that using the discretization level as regularizing procedure is possible, but its application is limited unless discretization is restricted to the singular value decomposition, see C. Marteau and P. Mathé, General regularization schemes for signal detection in inverse problems, 2013. General linear regularization may circumvent this, and we propose a regularization of the discretized equations. The discretization level may be chosen adaptively, which may save computational budget. This results in tests which are known to yield the optimal separation rate up to some constant in many cases.     

光栅投影相位法系统模型及标定方法

本文针对传统投影光栅相位法的光学三角法模型进行了改进,采用直入射光路并配合使用一种简便易行的标定方法,只需使用相移公式求取相位差,而不会引入与系统几何位置关系有关的量,简化了求取高度矩阵的要求。实验结果表明,新系统模型精度良好,测量误差为0.107 mm。采用该模型和标定方法可以克服传统方法系统模型的局限性,最大限度减少误差源并提高抗干扰性。     

Reception pattern influence on magnetoacoustic tomography with magnetic induction

Based on the acoustic radiation theory of a dipole source,the influence of the transducer reception pattern is studied for magnetoacoustic tomography with magnetic induction(MAT-MI).Numerical studies are conducted to simulate acoustic pressures,waveforms,and reconstructed images with unidirectional,omnidirectional,and strong directional transducers.With the analyses of equivalent and projection sources,the influences of the model dimension and the layer effect are qualitatively analyzed to evaluate the performance of MAT-MI.Three-dimensional simulation studies show that the strong directional transducer with a large radius can reduce the influences of equivalent sources,projection sources,and the layer effect effectively,resulting in enhanced pressure and improved image contrast,which is beneficial for boundary pressure extraction in conductivity reconstruction.The reconstructed conductivity contrast images present the conductivity boundaries as stripes with different contrasts and polarities,representing the values and directions of the conductivity changes of the scanned layer.The favorable results provide solid evidence for transducer selection and suggest potential practical applications of MAT-MI in biomedical imaging.     

Higher‐Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E₈ gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT .     

Quantum Dots for Display Applications

This article offers a materials-chemistry perspective for colloidal quantum dots (QDs) in the field of display, including QD-enhanced liquid-crystal-display (QD-LCD) and QD-based light-emitting-diodes (QLEDs) display. The rapid successes of QDs for display in the past five years are not accidental but have a deep root in both maturity of their synthetic chemistry and their unique chemical, optical, and optoelectronic properties. This article intends to discuss the natural match of QD emitters for display and chemical means to eventually bring about their full potential.