Korn inequality on irregular domains

In this paper, we study the weighted Korn inequality on some irregular domains, e.g., s-John domains and domains satisfying quasihyperbolic boundary conditions. Examples regarding sharpness of the Korn inequality on these domains are presented. Moreover, we show that Korn inequalities imply certain Poincaré inequality.     

A blow‐up criterion to the 2D full compressible magnetohydrodynamic equations

We establish a new regularity criterion for the 2D full compressible magnetohydrodynamic system in a bounded domain. Copyright © 2014 John Wiley & Sons, Ltd.     

Plasmonic Pollen Grain Nanostructures: A Three-Dimensional Surface-Enhanced Raman Scattering (SERS)-Active Substrate

A new route has been developed to design plasmonic pollen grain-like nanostructures (PGNSs) as surface-enhanced Raman scattering (SERS)-active substrate. The nanostructures consisting of silver (Ag) and gold (Au) nanoparticles along with zinc oxide (ZnO) nanoclusters as spacers were found highly SERS-active. The morphology of PGNSs and those obtained in the intermediate stage along with each elemental evolution has been investigated by a high-resolution field emission scanning electron microscopy. The optical band gaps and crystal structure have been identified by UV-vis absorption and X-ray powder diffraction (XRD) measurements, respectively. For PGNSs specimen, three distinct absorption bands related to constituent elements Ag, Au, and ZnO were observed, whereas XRD peaks confirmed the existence of Ag, Au, and ZnO within the composition of PGNSs. SERS-activity of PGNSs was confirmed using Rhodamine 6G (R6G) as Raman-active dyes. Air-cooled solid-state laser kits of 532 nm were used as excitation sources in SERS measurements. SERS enhancement factor was estimated for PGNSs specimen and was found as high as 3.5×10⁶. Finite difference time domain analysis was carried out to correlate the electromagnetic (EM) near-field distributions with the experiment results achieved under this investigation. EM near-field distributions at different planes were extracted for s-, p- and 45° of incident polarizations. EM near-field distributions for such nanostructures as well as current density distributions under different circumstances were demonstrated and plausible scenarios were elucidated given SERS enhancements. Such generic fabrication route as well as correlated investigation is not only indispensable to realize the potential of SERS applications but also unveil the underneath plasmonic characteristics of complex SERS-active nanostructures.     

Blocking Effect of Demethylzeylasteral on the Interaction between Human ACE2 Protein and SARS-CoV-2 RBD Protein Discovered Using SPR Technology

The novel coronavirus disease (2019-nCoV) has been affecting global health since the end of 2019, and there is no sign that the epidemic is abating. Targeting the interaction between the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike protein and the human angiotensin-converting enzyme 2 (ACE2) receptor is a promising therapeutic strategy. In this study, surface plasmon resonance (SPR) was used as the primary method to screen a library of 960 compounds. A compound 02B05 (demethylzeylasteral, CAS number: 107316-88-1) that had high affinities for S-RBD and ACE2 was discovered, and binding affinities (K_D, μM) of 02B05-ACE2 and 02B05-S-RBD were 1.736 and 1.039 μM, respectively. The results of a competition experiment showed that 02B05 could effectively block the binding of S-RBD to ACE2 protein. Furthermore, pseudovirus infection assay revealed that 02B05 could inhibit entry of SARS-CoV-2 pseudovirus into 293T cells to a certain extent at nontoxic concentration. The compoundobtained in this study serve as references for the design of drugs which have potential in the treatment of COVID-19 and can thus accelerate the process of developing effective drugs to treat SARS-CoV-2 infections.     

DOUBLESLICING: a non-iterative single profile multi-exponential curve resolution procedure. Application to time-domain NMR transverse relaxation data

A new non-iterative curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing, is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay curves simultaneously and thus fitting common pure exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO(4) solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6-159.4ms). Its performance was comparable to discrete exponential fitting with the advantage of being much faster - in terms of computation time, DoubleSlicing outperformed exponential fitting by a factor of four.     

双原子正方晶格光子晶体边界模式的光传输特性

利用平面波展开法,发现双原子正方晶格光子晶体中ΓM方向边界面存在着快慢两类边界模式,并且通过计算色散关系和电场分布研究了边界参量对这两类边界模式传输特性的影响.依据两种模式的色散关系,计算了群指数和群速度色散参量,结果表明边界参量的变化对第一类边界模式传输特性的影响较小,该模式的平均群指数始终维持在5.0左右;第二类边界模式与第一类模式明显不同,边界参量的变化能够有效地影响到这种模式的传输特性,该模式的最大平均群指数可达178左右.利用时域有限差分法记录了不同时刻电场强度在边界附近的分布及监测点处的电场幅度变化情况,结果表明,两类模式都能够被限制在边界附近并向前传播,时域有限差分法得到的群速度与平面波展开法的结果完全吻合.     

Discovery of Cell‐Permeable Inhibitors That Target the BRCT Domain of BRCA1 Protein by Using a Small‐Molecule Microarray

BRCTs are phosphoserine‐binding domains found in proteins involved in DNA repair, DNA damage response and cell cycle regulation. BRCA1 is a BRCT domain‐containing, tumor‐suppressing protein expressed in the cells of breast and other human tissues. Mutations in BRCA1 have been found in ca. 50 % of hereditary breast cancers. Cell‐permeable, small‐molecule BRCA1 inhibitors are promising anticancer agents, but are not available currently. Herein, with the assist of microarray‐based platforms, we have discovered the first cell‐permeable protein–protein interaction (PPI) inhibitors against BRCA1. By targeting the (BRCT)₂ domain, we showed compound 15 a and its prodrug 15 b inhibited BRCA1 activities in tumor cells, sensitized these cells to ionizing radiation‐induced apoptosis, and showed synergistic inhibitory effect when used in combination with Olaparib (a small‐molecule inhibitor of poly‐ADP‐ribose polymerase) and Etoposide (a small‐molecule inhibitor of topoisomerase II). Unlike previously reported peptide‐based PPI inhibitors of BRCA1, our compounds are small‐molecule‐like and could be directly administered to tumor cells, thus making them useful for future studies of BRCA1/PARP‐related pathways in DNA damage and repair response, and in cancer therapy.     

Stress-Induced Domain Wall Motion in a Ferroelastic Mn3+ Spin Crossover Complex

Domain wall motion is detected for the first time during the transition to a ferroelastic and spin state ordered phase of a spin crossover complex. Single-crystal X-ray diffraction and resonant ultrasound spectroscopy (RUS) revealed two distinct symmetry-breaking phase transitions in the mononuclear Mn³⁺ compound [Mn(3,5-diBr-sal₂(323))]BPh₄, 1. The first at 250 K, involves the space group change Cc→Pc and is thermodynamically continuous, while the second, Pc→P1 at 85 K, is discontinuous and related to spin crossover and spin state ordering. Stress-induced domain wall mobility was interpreted on the basis of a steep increase in acoustic loss immediately below the the Pc-P1 transition     

Cross-Module Enoylreduction in the Azalomycin F Polyketide Synthase

The colinearity of canonical modular polyketide synthases, which creates a direct link between multienzyme structure and the chemical structure of the biosynthetic end-product, has become a cornerstone of knowledge-based genome mining. Herein, we report genetic and enzymatic evidence for the remarkable role of an enoylreductase in the polyketide synthase for azalomycin F biosynthesis. This internal enoylreductase domain, previously identified as acting only in the second of two chain extension cycles on an initial iterative module, is shown to also catalyze enoylreduction in trans within the next module. The mechanism for this rare deviation from colinearity appears to involve direct cross-modular interaction of the reductase with the longer acyl chain, rather than back transfer of the substrate into the iterative module, suggesting an additional and surprising plasticity in natural PKS assembly-line catalysis.     

Enantioselective Synthesis of a Tricyclic,sp3-Rich Diazatetradecanedione: an Amino Acid-Based Natural Product-Like Scaffold

6-, 7-, and 8-membered rings are assembled from a linear precursor by successive cyclisation reactions to construct a tricyclic diazatricyclo[6.5.1.0^{4, 9}]-tetradecanedione scaffold. Advanced building blocks based on d -aspartic acid and l -pyroglutamic acid were combined by a sp³−sp² Negishi coupling. A carbamate-guided syn-diastereoselective epoxidation followed by an intramolecular epoxide opening allowed the construction of the piperidine ring. An efficient one-pot hydroxyl-group protection twofold deprotection reaction prepared the ground for the cyclisation to the bicycle. A final deprotection of the orthogonal protecting groups and lactamisation led to the novel, sp³-rich tricycle. The final compound is a substrate mimic of peptidyl-prolyl cis-trans isomerases featuring a locked trans-amide bond. Cheminformatic analysis of 179 virtual derivatives indicates favourable physicochemical properties and drug-like characteristics. As proof of concept we, show a low micromolar activity in a fluorescence polarisation assay towards the FK506-binding protein 12.