Springer basic sets and modular Springer correspondence for classical types

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic $p$, and with coefficients in a field of odd characteristic $?\ne p$): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols.     

Electrochemiluminescence Enhanced by the Synergetic Effect of Porphyrin and Multi-walled Carbon Nanotubes for Uric Acid Detection

The design and exploration of efficient, stable and environmentally compatible organic emitters for an electrochemiluminescence (ECL) sensor is a promising topic. Herein, a novel environmentally-friendly luminophore, ZnBCBTP@MWCNTs, were fabricated via self-assembly of porphyrin molecules (ZnBCBTP) onto multi-walled carbon nanotubes (MWCNTs). The resulting luminophore ZnBCBTP@MWCNTs displayed not only the highly ECL property and but also the good accelerated electron mobility. Then, a label-free ECL biosensor based ZnBCBTP@MWCNTs was constructed for the ultrasensitive detection of uric acid. Excitingly, this proposed ECL biosensor performed a good linear relationship in the range of 0–300 μM with a low detection limit of 1.4 μM, thus offering another reliable and feasible sensing platform for clinical bioanalysis with good selectivity, stability, and repeatability.     

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L²(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space H^σ (ℝ) (σ ⩾ 0) and reduces to L²(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).

     

Strategies in boosting photosensitization for biomedical applications

Science China Chemistry -     

平顶飞秒激光经圆锥透镜在熔融石英中成丝及超连续辐射

实验研究了平顶飞秒激光经圆锥透镜后在熔融石英中的成丝及超连续辐射.与高斯飞秒激光的成丝对比发现,平顶飞秒激光可以获得在圆锥透镜焦深区域内强度分布更为均匀的等离子体细丝,这一特征更有利于飞秒激光在固体介质中进行微纳加工等领域的应用.并且,在不损伤熔融石英的条件下,平顶飞秒激光成丝可以获得更高能量、更高转换效率的超连续辐射,这是因为若产生光强相近的细丝,平顶飞秒激光所需的初始激光能量更高,此激光能量下产生的细丝长度更长、均匀性更好.     

Facet-dependent antibacterial activity of Au nanocrystals

Engineered nanomaterials have attracted significantly attention as one of the most promising antimicrobial agents for against multidrug resistant infections. The toxicological responses of nanomaterials are closely related to their physicochemical properties, and establishment of a structure-activity relationship for nanomaterials at the nano-bio interface is of great significance for deep understanding antibacterial toxicity mechanisms of nanomaterials and designing safer antibacterial nanomaterials. In this study, the antibacterial behaviors of well-defined crystallographic facets of a series of Au nanocrystals, including {100}-facet cubes, {110}-facet rhombic dodecahedra, {111}-facet octahedra, {221}-facet trisoctahedra and {720}-facet concave cubes, was investigated, using the model bacteria Staphylococcus aureus. We find that Au nanocrystals display substantial facet-dependent antibacterial activities. The low-index facets of cubes, octahedra, and rhombic dodecahedra show considerable antibacterial activity, whereas the high-index facets of trisoctahedra and concave cubes remained inert under biological conditions. This result is in stark contrast to the previous paradigm that the high-index facets were considered to have higher bioactivity as compared with low-index facets. The antibacterial mechanism studies have shown that the facet-dependent antibacterial behaviors of Au nanocrystals are mainly caused by differential bacterial membrane damage as well as inhibition of cellular enzymatic activity and energy metabolism. The faceted Au nanocrystals are unique in that they do not induce generation of reactive oxygen species, as validated for most antibiotics and antimicrobial nanostructures. Our findings may provide a deeper understanding of facet-dependent toxicological responses and suggest the complexities of the nanomaterial-cell interactions, shedding some light on the development of high performance Au nanomaterials-based antibacterial therapeutics.     

Azobenzene‐Functionalized Cage Silsesquioxanes as Inorganic–Organic Hybrid,Photoresponsive, Nanoscale,Building Blocks

Mono‐ and octa‐azobenzene‐functionalized cage silsesquioxanes were easily synthesized by the reaction of 4‐bromoazobenzene with monovinyl‐substituted octasilsesquioxane and cubic octavinylsilsesquioxane through the Heck coupling reaction. Excited‐state energies obtained from time‐dependent density functional theory (TDDFT) and the CAM‐B3LYP functional correlate very well with experimental trans–cis photoisomerization results from UV/Vis spectroscopy. These azobenzene‐functionalized cages exhibit good thermal stability and are fluorescent with maximum emission at approximately 400 nm, making them potential materials for blue‐light emission.     

Uniform partition extensions,a generating functions perspective

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)j.In particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.     

Size reduction of “reformed casein micelles” by high-power ultrasound and high hydrostatic pressure

We investigated the effect of ultrasound (US) and high hydrostatic pressure (HHP) on the size of reformed casein micelles (RMCs) obtained by titrating calcium and phosphorous solution into sodium caseinate solutions. Both US and HHP reduced the size of the RMCs. A decrease in size from ~200 nm to ~170 nm when US (20 kHz, 0.46 W/mL) was applied for 30 min; and down to ~85 nm when HHP was applied 500 MPa for 15 min. Electron microscopic analysis showed that the RMCs before and after US are similar to milk native casein micelles, and that HHP extensively disintegrated the RMCs. Small angle X-ray scattering and SDS-PAGE showed that the internal structure of the RMCs as well as the casein molecules are not affected by the US and HHP treatments.     

Fused vs. spiro: Kinetic,not thermodynamic preference may direct the reaction of α-carbonyl oxonium ylides

Rh(II)-catalyzed decomposition of certain cyclic α-diazocarbonyl compounds in the presence of cyclic ethers has been shown to give bicyclic ring expansion products. These are thought to arise from a [1,4]-alkyl shift toward the carbonyl oxygen atom and are in contrast with the recently observed spirocyclic products of a Stevens-type [1,2]-alkyl shift within the postulated oxonium ylide intermediate. Quantum chemical calculations performed at the B3LYP/6-31G* level of theory showed that the former reaction pathway (toward fused bicycles) is kinetically preferred.