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

Acta Mechanica Sinica -     

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...     

A smooth homotopy method for incomplete markets

Mathematical Programming - In the general equilibrium with incomplete asset markets (GEI) model, the excess demand functions are typically not continuous at the prices for which the assets have...     

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...     

On s-hamiltonian line graphs of claw-free graphs

For an integer $s\ge 0$, a graph $G$ is $s$-hamiltonian if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian, and $G$ is $s$-hamiltonian connected if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian connected. Thomassen in 1984 conjectured that every 4-connected line graph is hamiltonian (see Thomassen, 1986), and Ku?zel and Xiong in 2004 conjectured that every 4-connected line graph is hamiltonian connected (see Ryjá?ek and Vrána, 2011). In Broersma and Veldman (1987), Broersma and Veldman raised the characterization problem of $s$-hamiltonian line graphs. In Lai and Shao (2013), it is conjectured that for $s\ge 2$, a line graph $L\left(G\right)$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected. In this paper we prove the following.(i) For an integer $s\ge 2$, the line graph $L\left(G\right)$ of a claw-free graph $G$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected.(ii) The line graph $L\left(G\right)$ of a claw-free graph $G$ is 1-hamiltonian connected if and only if $L\left(G\right)$ is 4-connected.     

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.     

A post curing strategy toward the feasible covalent adaptable networks in polyacrylate latex films

The implementation of covalent adaptable networks (CANs) in general resin system is becoming attractive. In this work, we propose a simple post-curing strategy based on the core-shell structured acrylate latex for the achievement on both the improved general performance and the CANs characteristics in latex films. The building to the CANs was relied on the introduction of 4,4′-diaminophenyl disulfide as the curing agent, which cured the acetoacetoxy decorated shell polymer through the ketoamine reaction. The metathesis reaction of aromatic disulfides in the crosslinking segments enabled the thermally induced dynamic behavior of the network as revealed in the stress relaxation tests by comparison with other diamine crosslinking agents without the incorporation of disulfide. The synergism of the dynamic crosslinking of the shell polymer and static crosslinking in the core polymer contributed to the improved mechanical strength (15 MPa, strain% = 250%) and the suppressed water adsorption (~1% in 24 h of soaking) of the latex film, which exhibited above 90% of recovery in both strength and strain from a cut-off film damage within 1 h at 80°C. Moreover, the cured latex film could be recycled, and 75% of the mechanical performance was regained after three fragmentation-hot-pressing cycles. These, in addition with the feasible and environmental friendly characteristics, suggest a sustainable paradigm toward the smart thermosetting latex polymers.