A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model

This paper studies the asymptotic behavior of coexistence steady-states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion coefficients tends to infinity, Lou and Ni [18] derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady-states. Recently, a formal observation by Kan-on [10] implied the existence of a limiting system including the nonstationary problem as both cross-diffusion coefficients tend to infinity at the same rate. This paper gives a rigorous proof of his observation as far as the stationary problem. As a key ingredient of the proof, we establish a uniform $L^{\infty }$ estimate for all steady-states. Thanks to this a priori estimate, we show that the asymptotic profile of coexistence steady-states can be characterized by a solution of the limiting system.     

Design,synthesis and evaluation of novel dehydroabietic acid-dithiocarbamate hybrids as potential multi-targeted compounds for tumor cytotoxicity

In the present study, novel representatives of the important group of biologically-active, dehydroabietic acid-bearing dithiocarbamate moiety, were synthesized and characterized by ¹H NMR, ¹³C NMR, HR-MS. The in vitro antiproliferative activity evaluation (MTT) indicated that these compounds exhibited potent inhibitory activities in various cancer cell lines (HepG-2, MCF-7, HeLa, T-24, MGC-803). Particularly, compound III-b possessed extraordinary cytotoxicity with low micromolar IC₅₀ values ranging from 4.07 to 38.84 µM against tested cancer cell lines, while displayed weak cytotoxicity on two normal cell lines (LO-2 and HEK 293 T). Subsequently, the potential mechanisms of representative compound III-b were elementarily investigated by Transwell experiment, which showed III-b can inhibit cancer cells migration. Annexin-V/PI dual staining showed that the compound can induce HepG-2 cells apoptosis in a dose-dependent manner. Meanwhile this apoptosis may be related to the upregulated protein expression of cleaved-caspase 3, cleaved-caspase 9, Bax and downregulated of Bcl-2 indicated by Western Blot. Later study further confirmed that ROS levels in HepG-2 cells increased significantly with the rise of concentrations. In addition, through the network pharmacology data analyzing, the core targets and signaling pathways of compound III-b for treatment of liver neoplasms were forecasted. Molecular docking model showed that compound III-b had high affinity with hub targets (CASP3, EGFR, HSP90AA1, MAPK1, ERBB2, MDM2), suggesting that compound III-b might target the hub protein to modulate signaling activity. Taken together, these data indicated that dehydroabietic acid structural modification following the “Molecular hybridization” principle is a feasible way to discover the potential multi-targeted antitumor compounds.     

Mass spectrometry combined with affinity probes for the identification of CP4 EPSPS in genetically modified soybeans

Sample preparation methods used for genetically modified organisms (GMOs) analysis are often time consuming, require extensive manual manipulation, and result in limited amounts of purified protein, which may complicate the detection of low‐abundance GM protein. A robust sample pretreatment method prior to mass spectrometry (MS) detection of the transgenic protein (5‐enolpyruvylshikimate‐3‐phosphate synthase [CP4 EPSPS]) present in Roundup Ready soya is investigated. Liquid chromatography‐multiple reaction monitoring tandem MS (nano LC‐MS/MS‐MRM) was used for the detection and quantification of CP4 EPSPS. Gold nanoparticles (AuNPs) and concanavalin A (Con A)‐immobilized Sepharose 4B were used as selective probes for the separation of the major storage proteins in soybeans. AuNPs that enable the capture of cysteine‐containing proteins were used to reduce the complexity of the crude extract of GM soya. Con A‐sepharose was used for the affinity capture of β‐conglycinin and other glycoproteins of soya prior to enzymatic digestion. The methods enabled the detection of unique peptides of CP4 EPSPS at a level as low as 0.5% of GM soya in MRM mode. Stable‐isotope dimethyl labeling was further applied to the quantification of GM soya. Both probes exhibited high selectivity and efficiency for the affinity capture of storage proteins, leading to the quantitative detection at 0.5% GM soya, which is a level below the current European Union's threshold for food labeling. The square correlation coefficients were greater than 0.99. The approach for sample preparation is very simple without the need for time‐consuming protein prefractionation or separation procedures and thus presents a significant improvement over existing methods for the analysis of the GM soya protein.     

Second moment of error term of mean value for binary Egyptian fractions

We study the mean square of the error term of the mean value for binary Egyptian fractions.We get an asymptotic formula under the Riemann Hypothesis.