Concavity property of minimal L2L^{2} integrals with Lebesgue measurable gain II

In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain on weakly pseudoconvex K\"ahler manifolds. As applications, we give a necessary condition for the concavity degenerating to linearity, and a characterization for the holding of the equality in optimal jets $L^2$ extension problem on open Riemann surfaces.Comment: 48 pages, comments are welcomed. arXiv admin note: substantial text overlap with arXiv:2209.0363

Gold Catalysis Enabled Cascade Reactions from C-C Triple Bonds

Homogeneous gold catalysis has been a very hot topic in recent decades. With its unparalleled π-acidity, cationic gold complex exhibits a strong affinity to alkynes and promotes nucleophilic attack across C-C triple bonds. Such nucleophilic attacks lead to various reactive intermediates that trigger a wide range of cascade reactions, building molecular complexity readily in one step. My doctoral study is focused on the development and application of gold-catalyzed cascade reaction with alkyne substrates. In this dissertation, two methodology studies and two applications of gold-catalyzed cascades will be discussed. Namely: 1) one-pot synthesis of fused pyrroles from ketones and N-alkylhydroxylations via a gold catalysis-triggered cascade; 2) synthesis of polycyclic 2H-pyran-3(6H)-ones via a vinyl cation C(sp3)-H insertion triggered by oxidative gold catalysis; 3) streamlined synthesis of highly potent mitomycin C analogs with gold/platinum-catalyzed cycloisomerization cascade; and 4) gold-catalysis-activated stereoselective glycosylation reaction to construct 1,2-cis glycosyl linkage in glycoconjugates and oligosaccharides

Boundary points, minimal L2L^2 integrals and concavity property III---linearity on Riemann surfaces

In this article, we consider a modified version of minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As an application, we give a characterization for the concavity degenerating to linearity on open Riemann surfaces.Comment: 48 pages, all comments are welcome. arXiv admin note: substantial text overlap with arXiv:2203.0772

Optimal L2L^2 extension for holomorphic vector bundles with singular hermitian metrics

In the present paper, we study the properties of singular Nakano positivity of singular hermitian metrics on holomorphic vector bundles, and establish an optimal $L^2$ extension theorem for holomorphic vector bundles with singular hermitian metrics on weakly pseudoconvex K\"{a}hler manifolds. As applications, we give a necessary condition for the holding of the equality in optimal $L^2$ extension theorem, and present singular hermitian holomorphic vector bundle versions of some $L^2$ extension theorems with optimal estimate.Comment: 76pages, comments are welcomed. Some typos are correcte

Tame maximal weights, relative types and valuations

In this article, we obtain a class of tame maximal weights (Zhou weights), whose relative types (Zhou numbers) satisfy the tropical multiplicativity and tropical additivity, and characterize the multiplier ideal sheaves of plurisubharmonic functions. Especially, the relative types to them are valuations (Zhou valuations) on the ring of germs of holomorphic functions, and characterize the division relations of the ring. We consider a global version of these weights on domains in $\mathbb{C}^n$, and obtain some properties of them, including the continuity and some approximation results.Comment: 51 pages, all comments are welcome

On the multipoled global Zhou weights and semi-continuity for Zhou numbers

In the present paper, we give the definition and properties of the multipoled global Zhou weights. Some approximation and convergence results of multipoled global Zhou weights are given. We also establish a semi-continuity result for the Zhou numbers.Comment: 27 pages. All comments are welcome

New Developments in Aromatic Halogenation, Borylation, and Cyanation

Several green procedures have been developed for synthesizing functionalized aromatics: i) AuCl3-catalyzed halogenation of aromatic compounds, including aryl boronates; ii) Fe2O3-catalyzed direct aromatic C–H bond borylation; iii) Pd-catalyzed direct cyanation of indoles; iv) direct conversion of arylamines to pinacol boronates

SN 2022vqz: A Peculiar SN 2002es-like Type Ia Supernova with Prominent Early Excess Emission

We present extensive photometric and spectroscopic observations of a peculiar type Ia supernova (SN Ia) 2022vqz. It shares many similarities with the SN 2002es-like SNe Ia, such as low luminosity (i.e., $M_{B,\rm max}=-18.11\pm0.16$ mag) and moderate post-peak decline rate (i.e., $\Delta m_{15,B}=1.33\pm0.11$ mag). The nickel mass synthesized in the explosion is estimated as $0.20\pm0.04~{\rm M}_\odot$ from the bolometric light curve, which is obviously lower than normal SNe Ia. SN 2022vqz is also characterized by a slow expanding ejecta, with Si II velocities persisting around 7000 km s$^{-1}$ since 16 days before the peak, which is unique among all known SNe Ia. While all these properties imply a less energetic thermonuclear explosion that should leave considerable amount of unburnt materials, however, absent signature of unburnt carbon in the spectra of SN 2022vqz is puzzling. A prominent early peak is clearly detected in the $c$- and $o$-band light curves of ATLAS and in the $gr$-band data of ZTF within days after the explosion. Possible mechanisms for the early peak are discussed, including sub-Chandrasekhar mass double detonation model and interaction of SN ejecta with circumstellar material (CSM). We found both models face some difficulties in replicating all aspects of the observed data. As an alternative, we propose a hybrid CONe white dwarf as progenitor of SN 2022vqz which can simultaneously reconcile the tension between low ejecta velocity and absence of carbon. We further discuss the diversity of 02es-like objects and possible origins of different scenarios.Comment: 24 pages, 12 figures, submitted to MNRA

Novel, Real-Time Cell Analysis for Measuring Viral Cytopathogenesis and the Efficacy of Neutralizing Antibodies to the 2009 Influenza A (H1N1) Virus

A novel electronic cell sensor array technology, the real-time cell analysis (RTCA) system, was developed to monitor cell events. Unlike the conventional methods labeling the target cells with fluorescence, luminescence, or light absorption, the RTCA system allows for label-free detection of cell processes directly without the incorporation of labels. Here, we used this new format to measure the cytopathic effect (CPE) of the 2009 influenza A (H1N1) virus and the efficacy of neutralizing antibodies in human sera to this virus. The real-time dynamic monitoring of CPE was performed on MDCK cell cultures infected with the H1N1 virus, ranging from 5.50×102 to 5.50×107 copies/mL. The resulting CPE kinetic curves were automatically recorded and were both time and viral load dependent. The CPE kinetics were also distinguishable between different H1N1 stains, as the onset of CPE induced by the A/Shanghai/37T/2009 H1N1 virus was earlier than that of the A/Shanghai/143T/2009 H1N1 virus. Furthermore, inhibition of H1N1 virus-induced CPE in the presence of human specific anti-sera was detected and quantified using the RTCA system. Antibody titers determined using this new neutralization test correlated well with those obtained independently via the standard hemagglutination inhibition test. Taken together, this new CPE assay format provided label-free and high-throughput measurement of viral growth and the effect of neutralizing antibodies, illustrating its potential in influenza vaccine studies