Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection

In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.     

Twist-bend nematics,liquid crystal dimers,structure–property relations

ABSTRACT

One of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (N_TB) and determine its properties. During our earlier hunt for the N_TB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the N_TB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the ²H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase.     

Symmetric nonnegative realizability via partitioned majorization

A sufficient condition for symmetric nonnegative realizability of a spectrum is given in terms of (weak) majorization of a partition of the negative eigenvalues by a selection of the positive eigenvalues. If there are more than two positive eigenvalues, an additional condition, besides majorization, is needed on the partition. This generalizes observations of Suleǐmanova and Loewy about the cases of one and two positive eigenvalues, respectively. It may be used to provide insight into realizability of 5-element spectra and beyond.     

A fast algorithm for the spectral radii of weakly reducible nonnegative tensors

In this paper, we propose a fast algorithm for computing the spectral radii of symmetric nonnegative tensors. In particular, by this proposed algorithm, we are able to obtain the spectral radii of weakly reducible symmetric nonnegative tensors without requiring the partition of the tensors. As we know, it is very costly to determine the partition for large‐sized weakly reducible tensors. Numerical results are reported to show that the proposed algorithm is efficient and also able to compute the spectral radii of large‐sized tensors. As an application, we present an algorithm for testing the positive definiteness of Z‐tensors. By this algorithm, it is guaranteed to determine the positive definiteness for any Z‐tensor.     

The zero curvature equation for rigid CR-manifolds

In this paper, we present the general analytic solution to the zero curvature equation for rigid three-dimensional CR-manifolds. The solutions are uniquely determined by one function and four real parameters.     

First stability eigenvalue characterization of CMC Hopf tori into Riemannian Killing submersions

We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also characterize constant mean curvature Hopf tori as the only ones attaining the bound in certain cases.     

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.     

基于支座反力影响线曲率差分的等截面连续梁损伤识别方法

为了实现仅采用损伤状态信息对等截面连续梁进行损伤识别,通过推导三跨不等跨连续梁在移动荷载作用下的支座反力影响线,发现支座反力影响线求曲率并作差分后的曲线在损伤位置会发生突变,基于该现象提出了一种损伤定位方法,进一步建立了损伤程度计算方法,可对损伤程度进行较精确的定量。通过一三跨连续梁和一四跨连续梁工程实例的仿真分析,证明了支座反力影响线曲率差分指标损伤定位和相应的损伤程度定量方法对等截面连续梁损伤识别具有可行性。     

复空间形式中常数量曲率的完备全实伪脐子流形

设CNnc是具有常全纯截面曲率c(≤O)的复n维的复空间形式,Mn是CNnc中常数量曲率的完备全实伪脐子流形,R,‖h‖2分别表示Mn的标准数量曲率和第二基本形式模长的平方.假设R≥c/4.利用丘成桐的广义极大值原理和自伴随算子研究了关于‖h‖2的pinching问题,得到了两个Mn成为全测地或全脐的刚性定理.