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

Acta Mechanica Sinica -     

Excellent UV-absorbing cotton fabric with high durability and hydrophobicity based on surface-initiated ATRP of polymerizable organic UV-absorber

Cellulose - Ultraviolet (UV) protective cotton fabric is a convenient and reliable way to protect human body from sunlight. Herein, a polymerizable UV-absorber,...     

Understanding the solubility and crystallization of molybdenum in high-sodium borosilicate glasses: effect of lanthanum oxide

Journal of Radioanalytical and Nuclear Chemistry - The simplified 8-oxide system (SiO2-B2O3-Na2O-Al2O3-CaO-TiO2-MoO3-La2O3) has been prepared under two types of cooling methods, and analyzed with...     

A New Sufficient Degree Condition for a Graphic Sequence to Be Forcibly k-Edge-Connected

A graphic sequence π =(d₁, d₂,..., d_n) is said to be forcibly k-edge-connected if every realization of π is k-edge-connected. In this paper, we obtain a new sufficient degree condition for π to be forcibly k-edgeconnected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for π to be forcibly 2-edge-connected and a conjecture about a strongest monotone degree condition for π to be forcibly 3-edge-connected due to...     

ON THE EXISTENCE WITH EXPONENTIAL DECAY AND THE BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF SEMI-LINEAR CORNER-DEGENERATE PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.     

A note on statistical analysis of factor models of high dimension

Science China Mathematics - Linear factor models are familiar tools used in many fields. Several pioneering literatures established foundational theoretical results of the quasi-maximum likelihood...     

Fabricating Dual-Atom Iron Catalysts for Efficient Oxygen Evolution Reaction: A Heteroatom Modulator Approach

Understanding the thermal aggregation behavior of metal atoms is important for the synthesis of supported metal clusters. Here, derived from a metal–organic framework encapsulating a trinuclear Fe^III₂Fe^II complex (denoted as Fe₃) within the channels, a well-defined nitrogen-doped carbon layer is fabricated as an ideal support for stabilizing the generated iron nanoclusters. Atomic replacement of Fe^II by other metal(II) ions (e.g., Zn^II/Co^II) via synthesizing isostructural trinuclear-complex precursors (Fe₂Zn/Fe₂Co), namely the “heteroatom modulator approach”, is inhibiting the aggregation of Fe atoms toward nanoclusters with formation of a stable iron dimer in an optimal metal–nitrogen moiety, clearly identified by direct transmission electron microscopy and X-ray absorption fine structure analysis. The supported iron dimer, serving as cooperative metal–metal site, acts as efficient oxygen evolution catalyst. Our findings offer an atomic insight to guide the future design of ultrasmall metal clusters bearing outstanding catalytic capabilities.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Synthesis of Small‐Sized,Porous, and Low‐Toxic Magnetite Nanoparticles by Thin POSS Silica Coating

In this communication, we report the synthesis of small‐sized (<10 nm), water‐soluble, magnetic nanoparticles (MNPs) coated with polyhedral oligomeric silsesquioxanes (POSS), which contain either polyethylene glycol (PEG) or octa(tetramethylammonium) (OctaTMA) as functional groups. The POSS‐coated MNPs exhibit superparamagnetic behavior with saturation magnetic moments (51–53 emu g^?1) comparable to silica‐coated MNPs. They also provide good colloidal stability at different pH and salt concentrations, and low cytotoxicity to MCF‐7 human breast epithelial cells. The relaxivity data and magnetic resonance (MR) phantom images demonstrate the potential application of these MNPs in bioimaging.