On the Cayley-Bacharach Property

The Cayley-Bacharach Property (CBP), which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebras over arbitrary base fields. We present characterizations and explicit algorithms for checking the CBP directly, via the canonical module, and in combination with the property of being a locally Gorenstein ring. Moreover, we characterize strict Gorenstein rings by the CBP and the symmetry of their affine Hilbert function, as well as by the strict CBP and the last difference of their affine Hilbert function.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

Further results on an abstract model for branching and its application to mixed integer programming

Mathematical Programming - A key ingredient in branch and bound (B&B) solvers for mixed-integer programming (MIP) is the selection of branching variables since poor or arbitrary selection...     

Conditional marginal expected shortfall

Extremes - In the context of bivariate random variables $\left (Y^{(1)},Y^{(2)}\right )$ , the marginal expected shortfall, defined as $\mathbb {E}\left (Y^{(1)}|Y^{(2)} \ge Q_{2}(1-p)\right )$ for...     

Thermoelectric power generation

Although the polarisation of the light was discovered at the beginning of the nineteenth century, the Vikings could have used the polarised light around the tenth century in their navigation to America, using a ‘sunstone’ evoked in the Icelandic Sagas. Indeed, the birefringence of the Iceland spar (calcite), a common crystal in Scandinavia, permits a simple observation of the axis of polarisation of the skylight at the zenith. From this, it is possible to guess the azimuth of a hidden Sun below the horizon, for instance. The high sensitivity of the differential method provided by the ordinary and extraordinary beams of calcite at its so-called isotropy point is about two orders higher than that of the best dichroic polariser and permits to reach an accuracy of ±1° for the Sun azimuth (at sunrise and sunset). Unfortunately, due to the relative fragility of calcite, only the so-called Alderney crystal was discovered on board a 16th ancient ship. Curiously, beyond its use as a sunstone by the Vikings, during these last millennia calcite has led to the discovery of the polarisation of the light itself by Malus and is currently being used to detect the atmospheres of exoplanets. Moreover, the differential method for the light polarisation detection is widely used in the animal world.     

Pressure evolution of two polymorphs of Tb 2(MoO 4)3

We have studied the high pressure behavior of the α and β^′-phases of Tb ₂(MoO ₄)₃ using a combination of powder X-ray diffraction and ab initio calculations. The α-Tb ₂(MoO ₄)₃ phase did not undergo any structural phase transition in the pressure range from 0 up to the maximum experimental pressure of 21 GPa. We observed line broadening of the diffraction patterns at pressures above 7 GPa, which may be due to non-hydrostatic conditions. The complete amorphization of the sample was not reached in the pressure range studied, as expected from previous Raman studies. The behavior under pressure of the β^′-Tb ₂(MoO ₄)₃ phase is similar to that of other rare-earths trimolybdates with the same structure at room temperature. A phase transition was observed at 2 GPa. The new phase, which can be identified as the δ-phase, has never been completely characterized by diffraction studies. A tentative indexation has been performed and good refined cell parameters were obtained. We detect indications of amorphization of the δ-Tb ₂(MoO ₄)₃ phase at 5 GPa.     

Optical pressure sensors for high-pressure–high-temperature studies in a diamond anvil cell

We review the various optical pressure sensors that are suitable for high-pressure and high-temperature studies in a diamond anvil cell. Two different kinds of sensors are considered: those based on the pressure shift of a fluorescence line (ruby, SrB₄O₇:Sm²⁺) and those based on the pressure shift of a Raman line (c-BN, diamond). The calibration of those sensors are presented in detail, and discussion is made on their useful pressure and temperature ranges.     

带宽对平顶高斯宽带激光传输特性的影响

研究了横向分布为平顶高斯模式的宽带激光在自由空间的传输特性,分析了频带宽度对其强度分布的影响。首先推导了平顶高斯模式宽带激光的每一频率分量在自由空间的传输公式,然后将频率域的传输公式通过傅里叶变换得到时间域的传输公式。基于推导的公式通过数值算例给出了不同频带宽度激光光束的强度分布结果,详细分析了空间模式的变化和时空耦合现象。研究结果表明：随着传输距离增大,平顶高斯空间模式趋于高斯分布。同时随着带宽增大,平顶高斯模式宽带激光表现出更强的时空耦合现象,并导致其空间横向分布发生明显变化。变化的主要特征为波前的强度分布随带宽增大而变窄,波后的强度分布则随带宽增大而远离轴中心向外扩展。     

Recent Progress in Type I Aggregation-Induced Emission Photosensitizers for Photodynamic Therapy

In modern medicine, precision diagnosis and treatment using optical materials, such as fluorescence/photoacoustic imaging-guided photodynamic therapy (PDT), are becoming increasingly popular. Photosensitizers (PSs) are the most important component of PDT. Different from conventional PSs with planar molecular structures, which are susceptible to quenching effects caused by aggregation, the distinct advantages of AIE fluorogens open up new avenues for the development of image-guided PDT with improved treatment accuracy and efficacy in practical applications. It is critical that as much of the energy absorbed by optical materials is dissipated into the pathways required to maximize biomedical applications as possible. Intersystem crossing (ISC) represents a key step during the energy conversion process that determines many fundamental optical properties, such as increasing the efficiency of reactive oxygen species (ROS) production from PSs, thus enhancing PDT efficacy. Although some review articles have summarized the accomplishments of various optical materials in imaging and therapeutics, few of them have focused on how to improve the phototherapeutic applications, especially PDT, by adjusting the ISC process of organic optics materials. In this review, we emphasize the latest advances in the reasonable design of AIE-active PSs with type I photochemical mechanism for anticancer or antibacterial applications based on ISC modulation, as well as discuss the future prospects and challenges of them. In order to maximize the anticancer or antibacterial effects of type I AIE PSs, it is the aim of this review to offer advice for their design with the best energy conversion.     

光纤四波混频多波长时钟信号整形

将两路时钟信号作为泵浦光,与连续探测光一同耦合进高非线性光纤中,四波混频产生的两路闲频光作为整形后的时钟信号,并通过控制两路时钟信号之间的相对时间延迟来减小光纤四波混频干扰。研究了整形前时钟信号占空比的变化与整形后时钟质量的关系以及最佳占空比下输入时钟信号和输出时钟信号的相对幅度抖动的关系,发现在占空比由小到大变化的过程中,整形后时钟信号的质量总体上先变好后变坏;在最佳占空比0.14下,两路时钟信号的相对幅度抖动由原来的13.934 9%和13.958 6%下降到2.03%和2.12%,表明了该方案的可行性。