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.     

FeOOH@Metal–Organic Framework Core–Satellite Nanocomposites for the Serum Metabolic Fingerprinting of Gynecological Cancers

High-throughput metabolic analysis is of significance in diagnostics, while tedious sample pretreatment has largely hindered its clinic application. Herein, we designed FeOOH@ZIF-8 composites with enhanced ionization efficiency and size-exclusion effect for laser desorption/ionization mass spectrometry (LDI-MS)-based metabolic diagnosis of gynecological cancers. The FeOOH@ZIF-8-assisted LDI-MS achieved rapid, sensitive, and selective metabolic fingerprints of the native serum without any enrichment or purification. Further analysis of extracted serum metabolic fingerprints successfully discriminated patients with gynecological cancers (GCs) from healthy controls and also differentiated three major subtypes of GCs. Given the low cost, high-throughput, and easy operation, our approach brings a new dimension to disease analysis and classification.     

Multiwave interaction solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill. Moreover, a new algorithm is proposed with the aid of the simplified Hirota method, the conjugated parameters assignment and long wave limit strategies, from which multiwave interaction solutions among solitons, breathers and lump waves are generated.     

Stabilizing DNAzymes through Encapsulation in a Metal–Organic Framework

DNAzymes are a promising class of bioinspired catalyst; however, their structural instability limits their potential. Herein, a method to stabilize DNAzymes by encapsulating them in a metal–organic framework (MOF) host is reported. This biomimetic mineralization process makes DNAzymes active under a wider range of conditions. The concept is demonstrated by encapsulating hemin-G-quadruplex (Hemin-G4) into zeolitic imidazolate framework-90 (ZIF-90), which indeed increases the DNAzyme's structural stability. The stabilized DNAzymes show activities in the presence of Exonuclease I, organic solvents, or high temperature. Owing to its elevated stability and heterogeneous nature, it is possible to perform catalysis under continuous-flow conditions, and the DNAzyme can be reactivated in situ by introducing K⁺. Moreover, it is found that the encapsulated DNAzyme maintains its high enantiomer selectivity, demonstrated by the sulfoxidation of thioanisole to (S)-methyl phenyl sulfoxide. This concept of stabilizing DNAzymes expands their potential application in chemical industry.     

Gorenstein projective bimodules via monomorphism categories and filtration categories

We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras A and B, we use the special monomorphism category $\mathsf{Mon}(B,A\text{-}\mathsf{Gproj})$ to describe some Gorenstein projective bimodules over the tensor product of A and B. If one of the two algebras is Gorenstein, we give a sufficient and necessary condition for $\mathsf{Mon}(B,A\text{-}\mathsf{Gproj})$ being the category of all Gorenstein projective bimodules. In addition, if both A and B are Gorenstein, we can describe the category of all Gorenstein projective bimodules via filtration categories. Similarly, in this case, we get the same result for infinitely generated Gorenstein projective bimodules.     

Family of curves with large unitary summand in the Hodge bundle

Mathematische Zeitschrift - In this note, we construct non-isotrivial families of curves of genus $$g\ge 2$$ , where the rank of the unitary summand contained in the Hodge bundle can be as large as...     

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

We prove the existence of solutions to the nonlinear Schrödinger equation ${\epsilon }^2{(i\mathrm{?}+\mathit{A})}^{2}u+V(y)u?|u{|}^{p?1}u=0$ in ${\mathbb{R}}^2$ with a magnetic potential $\mathit{A}=(A_1,A_2)$. Here V represents the electric potential, the index p is greater than 1. Along some sequence $\{{\epsilon }_n\}$ tending to zero we exhibit complex-value solutions that concentrate along some closed curves.     

Ultrafast Excited State Dynamics of Biliverdin Dimethyl Ester Coordinate with Zinc Ions

As one of the biological endogenous pigments, biliverdin (BV) and its dimethyl ester (BVE) have extremely weak fluorescence in solution with quantum yield less than 0.01%. However, the situation reverses with the addition of zinc ions. The strength for fluorescence of BVE-Zn\begin{document}$ ^{2+} $\end{document} complex is greatly enhanced and fluorescence quantum yield can increase to \begin{document}$ \sim $\end{document}5%. Herein, we studied ultrafast excited state dynamics of BVE-Zn\begin{document}$ ^{2+} $\end{document} complex in ethanol, \begin{document}$ n $\end{document}-propanol, and DMSO solutions in order to reveal the mechanism of fluorescence quantum yield enhancement. The results show that BVE can form a stable coordination complex with zinc with 1:1 stoichiometry in solution. BVE is structurally and energetically more stable in the complex. Using picosecond time-resolve fluorescence and femtosecond transient absorption spectroscopy, we show that smaller non-radiative rate constant of BVE-Zn\begin{document}$ ^{2+} $\end{document} complex in DMSO is the key to increasing its fluorescence quantum yield and the excited state decay mechanism is also revealed. These results provide valuable information about the fluorescence property change after BVE binding to metal ions and may provide a guidance for the study of phytochromes or other fluorescence proteins in which BV/BVE acts as chromophores.