Gap theorems for Lagrangian submanifolds in complex space forms

Geometriae Dedicata - Inspired by a recent work of Grove and Petersen (Alexandrov spaces with maximal radius, 2018), where the authors studied positively curved Alexandrov spaces with largest...     

On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

Isolation of 212Pb from natural thorium for targeted alpha-therapy

Targeted alpha-therapy (TAT) is increasingly attractive due to its extraordinary antitumor efficacy. However, the supply of α-emitters for TAT is insufficient and under control by a limited number of countries. ²¹²Pb is a promising α-emitter with an optimal half-life (10.6 h) and favored decay chain. Of interest, ²¹²Pb can be extracted directly from natural thorium, which may be abundant in the mining waste of rare-earth, uranium, etc. Indeed, radioactive thorium waste has been a longstanding environmental challenge that needs immediate action. Developing an on-demand and facile process to isolate ²¹²Pb from natural thorium would be ideal to meet the above challenges, yet is difficult. In theory, the ratio of ²¹²Pb to ^natTh is below 10^?13 in commercially available thorium salts. As a pilot study, 2.2 MBq of ²¹²Pb was successfully extracted from a 5 L solution of thorium nitrate by using a Pb-selective resin. The radiochemical purity of ²¹²Pb is over 99.9% according to gamma-ray analysis. The purified ²¹²Pb was applied to radiolabel a couple of peptides used in clinics (i.e. PSMA, TATE and FAPI-04), and the radiochemical yields are >85%. Of note, ²¹²Pb can be repeatedly separated from the thorium solution every 2 days. In summary, a practical and scalable method was developed to isolate ²¹²Pb for potentially clinical use, which may be of great importance as it does not require either cyclotron or nuclear reactor.     

Correction to: Practical framework for data-driven RANS modeling with data augmentation

Acta Mechanica Sinica -     

Emerging Trends in Fluorescence Bioimaging of Divalent Metal Cations Using Small-Molecule Indicators

Visualization of cation dynamics inside a living system represent a major breakthrough at the crossroad of chemistry and cellular physiology. Since the inception of BAPTA-based cellular calcium indicators in the 1980s, generations of chemical and genetically encoded ion indicators spanning the visible spectrum have been developed. In this article, we bring up three emerging concepts in this field: 1. red-shifting cation indicators towards far-red and near-infrared (NIR) channels; 2. directing the indicators to various subcellular localizations; 3. lowering the phototoxicity of indicators for long term recording. These initiatives collectively echo the advocate of 4D cellular physiology, where biological processes within living systems can be panoramically unveiled under 3D, long-term, and multi-channel imaging with unprecedented spatial and temporal resolution. This outlook poses exciting challenges and opportunities for chemists to upgrade the toolkit of fluorescent indicators as key enablers for a new era of imageomics.     

Relative volume comparison of Ricci flow

In this paper we derive a relative volume comparison of Ricci flow under a certain local curvature condition. It is a refinement of Perelman's no local collapsing theorem in Perelman(2002).     

Study on the static properties of spiral springs under static loading

Applied Mathematics and Mechanics - Spiral springs have a wide range of applications in various fields. As a result of the complexity of friction, few theoretical analyses of spring belts under...     

Applications of photocatalytic titanium dioxide-based nanomaterials in sustainable agriculture

Photocatalytic materials are attracting attention as emerging resources for agricultural applications. This timely review assesses the current developments in the use of biocompatible titanium dioxide (TiO₂)-based photocatalytic nanomaterials (TiO₂-PN) as models to unravel agricultural growth, harvest, and post-harvest problems. Such developments can lead to technological innovations aimed at addressing the pressing global environmental challenges faced by farming. TiO₂-PN have been used as antimicrobial, growth-regulating, and fertilizer-like agents. The promising agricultural research applications of TiO₂-PN are highlighted along with a discussion of the main challenges that will need to be overcome to fully understand the roles of TiO₂-PN in the sustainable and productive exploitation of land and water for agricultural applications under natural conditions. In particular, rhizosphere internalization, translocation, and plant bioaccumulation pathways of photocatalytic materials from environmental exposition are outlined to illustrate the effect of TiO₂ on the agricultural cycle. Nanotoxicology and regulations are also discussed to illustrate the importance of biocompatibility and green synthesis of nanomaterials for safe use in real applications. This overview is focused on motivating and intensifying our understanding of on-site agricultural studies. Complementary biological approaches and structural damage observed by biological transmission electron, scanning electron, and optical microscopies should accelerate the practical contribution of TiO₂-PN to sustainable agriculture in conjunction with plant factories and plasma nitrogen fixation technology. Loadings below 10 μg/L of TiO₂-PN with a size of 40 nm benefit seed germination and root elongation as well as partially suppressing metal root translocation. However, only approximately 5% of current studies were carried out in real agricultural settings.     

Athermal and Soft Multi-Nanopatterning of Azopolymers: Phototunable Mechanical Properties

Imprinting nanopatterns on flexible substrates has diverse applications in advanced fabrication. However, the traditional thermal nanoimprint lithography (T-NIL) often causes shrinkage upon cooling. Here, a simple yet versatile method is introduced to fabricate multiple nanopatterns on a flexible substrate coated with an azopolymer by combining athermal nanoimprint lithography (AT-NIL) and photolithography. The azopolymer has various mechanical properties upon photoirradiation: 1) phototunable glass-transition temperatures (T_g) and concomitantly photoinduced switch from glassy plastic to viscoplastic polymer; 2) prominent modulation of viscoplasticity under light illumination at different wavelengths. Regionally selective multiple nanopatterns are conveniently fabricated, presenting angle-dependent structural color images on poly(ethylene terephthalate) (PET) substrates. The flexible, athermal and multiple nanopatterning method has the potential for on-demand fabrication of complex nanopatterns.