Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

Role of the Bridge in Photoinduced Electron Transfer in Porphyrin–Fullerene Dyads

The role of π‐conjugated molecular bridges in through‐space and through‐bond electron transfer is studied by comparing two porphyrin–fullerene donor–acceptor (D–A) dyads. One dyad, ZnP–Ph–C₆₀ (ZnP=zinc porphyrin), incorporates a phenyl bridge between D and A and behaves very similarly to analogous dyads studied previously. The second dyad, ZnP–EDOTV–C₆₀, introduces an additional 3,4‐ethylenedioxythienylvinylene (EDOTV) unit into the conjugated bridge, which increases the distance between D and A, but, at the same time, provides increased electronic communication between them. Two essential outcomes that result from the introduction of the EDOTV unit in the bridge are as follows: 1) faster charge recombination, which indicates enhanced electronic coupling between the charge‐separated and ground electronic states; and 2) the disappearance of the intramolecular exciplex, which mediates photoinduced charge separation in the ZnP–Ph–C₆₀ dyad. The latter can be interpreted as a gradual decrease in electronic coupling between locally excited singlet states of D and A when introducing the EDOTV unit into the D–A bridge.     

Synthesis and Diverse Transformations of a Dinitrogen Dititanium Hydride Complex Bearing Rigid Acridane-Based PNP-Pincer Ligands

Studies on N₂ activation and transformation by transition metal hydride complexes are of particular interest and importance. The synthesis and diverse transformations of a dinitrogen dititanium hydride complex bearing the rigid acridane-based ^acriPNP-pincer ligands {[(^acriPNP)Ti]₂(μ₂-η¹:η²-N₂)(μ₂-H)₂} are presented. This complex enabled N₂ cleavage and hydrogenation even without additional H₂ or other reducing agents. Furthermore, diverse transformations of the N₂ unit with a variety of organometallic compounds such as ZnMe₂, MgMe₂, AlMe₃, B(C₆F₅)₃, PinBH, and PhSiH₃ have been well established at the rigid ^acriPNP-ligated dititanium framework, such as reversible bonding-mode change between the end-on and side-on/end-on fashions, diborylative N=N bond cleavage, the formal insertion of two dimethylaluminum species into the N=N bond, and the formal insertion of two silylene units into the N=N bond. This work has revealed many unprecedented aspects of dinitrogen reaction chemistry.     

波形钢板-UHPC组合桥面板结构截面优化

对实腹式波形顶板-UHPC(超高性能混凝土)组合桥面板进行了改进, 采用空腹式结构建立波形钢板-UHPC组合桥面板有限元模型, 研究UHPC层厚度、波形钢板厚度、波形长度、下缘板宽度和波形高度等截面参数变化对组合桥面板受力特性的影响, 并确定其合理取值范围. 在此基础上, 通过理想点法对参数组合进行优化, 得到合理的参数匹配. 研究结果表明 相较于实腹式组合桥面板, 优化后的组合桥面板自重减小35%, 钢板弯折处应力减小16%; 相较于正交异性钢桥面板, 桥面板用钢量减小7%, 顶板与U肋连接位置应力减小47%.     

沙丘背风侧不同铁路结构形式对风沙环境的适应性分析

当铁路穿越大风沙漠地区时,风沙灾害会对铁路工程及其正常运营产生严重威胁,而设计一种合理的铁路结构形式能够减小风沙沉积对铁路工程的危害. 在本文中,以敦煌至格尔木铁路沙山沟段落为研究对象,采用多相流的方法对越过沙丘的风沙运动过程进行数值模拟,分别讨论了风沙运动对位于沙丘背风坡的铁路路基工程和桥梁工程的影响. 主要的模拟结果显示:路基工程明显降低了风速并且将沙丘后的回流区分成了两部分,而桥梁工程的导流效应则压缩了沙丘背风坡的回流区;轨道间的道碴增大了铁路表面的粗糙度,在轨道间有少量沙粒沉积,而路基工程两侧则有大量积沙;铁路表面的积沙量与摩阻风速呈现出非线性关系,随着摩阻风速的增大,路基工程沙粒沉积的增加速度大于风蚀能力的增加速度,而桥梁工程则正好相反. 在防止风沙危害铁路方面,设置桥梁工程明显优于路基工程. 本研究为风沙运动对铁路工程的影响提供了理论支持,也为今后的铁路工程设计提供了新的思路与研究工具.      

RIGID EQUILIBRIUM AS EXEMPLIFIED BY BIRDS STANDING ON A BRANCH1)

为了提高理论力学课堂的趣味性,本文以树枝上小鸟作为刚体平衡的例子,应用力的平行四边形法则、力的可传性、三力平衡汇交定理等基本原理分析了树枝上小鸟的双腿受力,以及啄木鸟尾巴在保持身体平衡中的作用,并讨论了小鸟不同姿态对其受力的影响,期望达到提高学习兴趣、寓教于乐、改善教学效果的目的。     

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ‐BIBDs are (mod ) and . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ‐RBIBD, namely (mod ) and , are sufficient. A few new pairwise balanced designs are also given.     

The Effect of Calcium-Silicate Cements on Reparative Dentinogenesis Following Direct Pulp Capping on Animal Models

Dental pulp vitality is a desideratum for preserving the health and functionality of the tooth. In certain clinical situations that lead to pulp exposure, bioactive agents are used in direct pulp-capping procedures to stimulate the dentin-pulp complex and activate reparative dentinogenesis. Hydraulic calcium-silicate cements, derived from Portland cement, can induce the formation of a new dentin bridge at the interface between the biomaterial and the dental pulp. Odontoblasts are molecularly activated, and, if necessary, undifferentiated stem cells in the dental pulp can differentiate into odontoblasts. An extensive review of literature was conducted on MedLine/PubMed database to evaluate the histological outcomes of direct pulp capping with hydraulic calcium-silicate cements performed on animal models. Overall, irrespective of their physico-chemical properties and the molecular mechanisms involved in pulp healing, the effects of cements on tertiary dentin formation and pulp vitality preservation were positive. Histological examinations showed different degrees of dental pulp inflammatory response and complete/incomplete dentin bridge formation during the pulp healing process at different follow-up periods. Calcium silicate materials have the ability to induce reparative dentinogenesis when applied over exposed pulps, with different behaviors, as related to the animal model used, pulpal inflammatory responses, and quality of dentin bridges.     

Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement

The dynamic response of submerged and confined disk-like structures is of interest in engineering applications, such as in hydraulic turbine runners. This response is difficult to be estimated with accuracy due to the strong influence of the boundary conditions. Small radial gaps as well as short axial distances to rigid surfaces greatly modify the dynamic response because of the added mass and damping effects.In this paper, the influence of the axial nearby rigid distance on the dynamic response of a submerged disk is evaluated when the radial gap is very small. Moreover, the effects of the fluid depth and fluid viscosity on the natural frequencies and damping ratio of the submerged disk are studied. The study has been performed experimentally and numerically using structural–acoustic simulations.For the experimental investigation a test rig has been developed. It consists of a disk attached to a shaft and confined with a small radial gap inside a cylindrical container full of water. The disk can be moved up and down along the shaft to vary the axial distance to the nearby rigid surface. Piezoelectric patches are used to excite the disk and the response is measured with submersible accelerometers. Several excitation patterns can be used due to the disposition of these piezoelectric patches. For each configuration tested, the dynamic response of the structure is studied analyzing the natural frequencies and damping ratio of the disk attached to the shaft. The numerical results have been compared with the experimental results.