Norm equalities and inequalities for three circulant operator matrices

In this paper, three new circulant operator matrices, scaled circulant operator matrices, diag-circulant operator matrices and retrocirculant operator matrices, are given respectively. Several norm equalities and inequalities for these operator matrices are proved. We show the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norm. Pinching type inequality is also given for weakly unitarily invariant norms. These results are closely related to the nice structure of these special operator matrices. Furthermore, some special cases and specific examples are also considered.     

On realization of fusion rings from generalized Cartan matrices

The Casimir element of a fusion ring (R, B) gives rise to the so called Casimir matrix C of (R, B). This enables us to construct a generalized Cartan matrix D-C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D-C of finite (resp. affine) type. It turns out that there exists a fusion ring with D-C being of finite (resp. affine) type if and only if D-C has only the form A₂ (resp. A₁⁽¹⁾. We also realize all fusion rings with D-C being a particular generalized Cartan matrix of indefinite type.     

Miniaturized matrix solid-phase dispersion and solid-phase clear-up combined with capillary electrophoresis for efficient determination of trace bioactive components in complicated sample matrix: Take Wubi Shanyao Pill as an example

Accurate quantitative analysis of trace analytes in a complicated matrix is a challenge in modern analytical chemistry. An appropriate analytical method is considered to be one of the most common gaps during the whole process. In this study, a green and efficient strategy based on miniaturized matrix solid-phase dispersion and solid-phase extraction combined with capillary electrophoresis was first proposed for extracting, purifying and determining target analytes from complicated matrix, using Wubi Shanyao Pill as an example. In detail, 60 mg of samples were dispersed on MCM-48 to obtain high yields of analytes, then the extract was purified with a solid-phase extraction cartridge. Finally, four analytes in the purified sample solution were determined by capillary electrophoresis. The parameters affecting the extraction efficiency of matrix solid-phase dispersion, purification efficiency of solid-phase extraction and separation effect of capillary electrophoresis were investigated. Under the optimized conditions, all analytes demonstrated satisfactory linearity (R²>0.9983). What's more, the superior green potential of the developed method for the determination of complex samples was confirmed by the Analytical GREEnness Metric Approach. The established method was successfully applied in the accurate determination of target analytes in Wubi Shanyao Pill and thus provided reliable, sensitive, and efficient strategy support for its quality control.     

Matrix solid-phase dispersion combined with micro-fractionation bioactivity evaluation screening polymethoxylated flavones from Citrus peels

Polymethoxyflavones were a unique class of natural and safe flavonoids containing two or more methoxy groups, which were also the most abundant edible part in Citrus peel. The optimum condition in the process of selective extraction of polymethoxylated flavones from Citrus peel by matrix solid-phase dispersion (MSPD) was as follows: SBA-15 as adsorbent, ethyl acetate as eluent, the mass ratio of adsorbent to sample 1:1, and the mixture of sample and adsorbent was ground for 3 min. Twelve antioxidants were successfully screened by micro-fractionation bioactivity evaluation assay, in which four of them were flavonoid glycosides, seven of them were polymethoxylated flavones, and one was phenylpropanoid. 1-sinapoly-β-D-glucopyranoside (1) was reported for the first time in Citrus peel. And antioxidant capacity of 1-sinapoly-β-D-glucopyranoside, 5, 7, 8, 3′, 4′, 5′-hexamethoxyflavone (6), hexamethoxyflavone (11), and 5, 6, 7, 4′-tetramethoxyflavone (7) were reported for the first time. Nobiletin (compound 8), 3, 5, 6, 7, 8, 3′, 4′-heptamethoxyflavone (9) and tangeretin (10) were isolated and purified by countercurrent chromatography combined with preparative liquid chromatography. Antioxidant activity evaluation indicated that the three isolated polymethoxylated flavones owned similar antioxidant activity. This study indicated that MSPD combined with micro-fractionation bioactive evaluation was efficient in screening bioactive compounds for rapid extraction and effective pinpointing bioactive substances in natural products.     

Exploring artificial neural networks to model interatomic and intermolecular potential energy surfaces

We demonstrate how a back-propagation artificial neural network can be trained to represent a potential energy surface (PES) in a formless manner with limited data points and exploited to predict interaction energies for configurations not included in the training set. A similar exercise is undertaken for predicting the eigenvalues and eigenvectors of a model Hamiltonian matrix that delicately depends on parameters and exhibits crossing of eigen values.     

Circulating Levels of Dephosphorylated-Uncarboxylated Matrix Gla Protein in Patients with Acute Coronary Syndrome

Vascular calcification contributes to the pathogenesis of coronary artery disease while matrix Gla protein (MGP) was recently identified as a potent inhibitor of vascular calcification. MGP fractions, such as dephosphorylated-uncarboxylated MGP (dp-ucMGP), lack post-translational modifications and are less efficient in vascular calcification inhibition. We sought to compare dp-ucMGP levels between patients with acute coronary syndrome (ACS), stratified by ST-elevation myocardial infarction (STEMI) and non-ST-elevation myocardial infarction (NSTEMI) status. Physical examination and clinical data, along with plasma dp-ucMGP levels, were obtained from 90 consecutive ACS patients. We observed that levels of dp-ucMGP were significantly higher in patients with NSTEMI compared to STEMI patients (1063.4 ± 518.6 vs. 742.7 ± 166.6 pmol/L, p < 0.001). NSTEMI status and positive family history of cardiovascular diseases were only independent predictors of the highest tertile of dp-ucMGP levels. Among those with NSTEMI, patients at a high risk of in-hospital mortality (adjudicated by GRACE score) had significantly higher levels of dp-ucMGP compared to non-high-risk patients (1417.8 ± 956.8 vs. 984.6 ± 335.0 pmol/L, p = 0.030). Altogether, our findings suggest that higher dp-ucMGP levels likely reflect higher calcification burden in ACS patients and might aid in the identification of NSTEMI patients at increased risk of in-hospital mortality. Furthermore, observed dp-ucMGP levels might reflect differences in atherosclerotic plaque pathobiology between patients with STEMI and NSTEMI.     

β-Carotene Inhibits Expression of Matrix Metalloproteinase-10 and Invasion in Helicobacter pylori-Infected Gastric Epithelial Cells

Matrix metalloproteinases (MMPs), key molecules of cancer invasion and metastasis, degrade the extracellular matrix and cell–cell adhesion molecules. MMP-10 plays a crucial role in Helicobacter pylori-induced cell-invasion. The mitogen-activated protein kinase (MAPK) signaling pathway, which activates activator protein-1 (AP-1), is known to mediate MMP expression. Infection with H. pylori, a Gram-negative bacterium, is associated with gastric cancer development. A toxic factor induced by H. pylori infection is reactive oxygen species (ROS), which activate MAPK signaling in gastric epithelial cells. Peroxisome proliferator-activated receptor γ (PPAR-γ) mediates the expression of antioxidant enzymes including catalase. β-Carotene, a red-orange pigment, exerts antioxidant and anti-inflammatory properties. We aimed to investigate whether β-carotene inhibits H. pylori-induced MMP expression and cell invasion in gastric epithelial AGS (gastric adenocarcinoma) cells. We found that H. pylori induced MMP-10 expression and increased cell invasion via the activation of MAPKs and AP-1 in gastric epithelial cells. Specific inhibitors of MAPKs suppressed H. pylori-induced MMP-10 expression, suggesting that H. pylori induces MMP-10 expression through MAPKs. β-Carotene inhibited the H. pylori-induced activation of MAPKs and AP-1, expression of MMP-10, and cell invasion. Additionally, it promoted the expression of PPAR-γ and catalase, which reduced ROS levels in H. pylori-infected cells. In conclusion, β-carotene exerts an inhibitory effect on MAPK-mediated MMP-10 expression and cell invasion by increasing PPAR-γ-mediated catalase expression and reducing ROS levels in H. pylori-infected gastric epithelial cells.     

Impact of Matrix Metalloproteinase-9 during Periodontitis and Cardiovascular Diseases

Matrix metalloproteinase-9 (MMP-9) has been shown to play a key role in endothelial function and perhaps pivotal in the correlation between periodontal disease and cardiovascular disease (CVD). For the study, the impact of MMP-9 of periodontitis and CVD on serum and saliva concentrations was analyzed. For the study patients with periodontitis (n = 31), CVD (n = 31), periodontitis + CVD (n = 31), and healthy patients (n = 31) were enrolled. Clinical and demographic characteristics as well as serum and salivary MMP-9 were evaluated. MMP-9 concentrations in serum and saliva were statistically elevated in patients with CVD (p < 0.01) and in patients with periodontitis plus CVD (p < 0.001) compared to patients with periodontitis and healthy subjects. Multivariate regression analysis showed that c-reactive protein (hs-CRP) was the only significant predictor for MMP-9 serum (p < 0.001), whereas hs-CRP (p < 0.001) and total cholesterol (p = 0.029) were the statistically significant salivary MMP-9 predictors. This study evidenced that patients with CVD and periodontitis + CVD presented elevated MMP-9 concentrations in serum and saliva compared to patients with periodontitis and healthy subjects. Furthermore, hs-CRP was a negative predictor of serum and salivary MMP-9.     

Matrix Isolation Spectroscopic and Relativistic Quantum Chemical Study of Molecular Platinum Fluorides PtFn (n=1–6) Reveals Magnetic Bistability of PtF4

Molecular platinum fluorides PtF_n, n=1–6, are prepared by two different routes, photo-initiated fluorine elimination from PtF₆ embedded in solid noble-gas matrices, and the reaction of elemental fluorine with laser-ablated platinum atoms. IR spectra of the reaction products isolated in rare-gas matrices under cryogenic conditions provide, for the first time, experimental vibrational frequencies of molecular PtF₃, PtF₄ and PtF₅. Photolysis of PtF₆ enabled a highly efficient and almost quantitative formation of molecular PtF₄, whereas both PtF₅ and PtF₃ were formed simultaneously by subsequent UV irradiation of PtF₄. The vibrational spectra of these molecular platinum fluorides were assigned with the help of one- and two-component quasirelativistic DFT computation to account for scalar relativistic and spin–orbit coupling effects. Competing Jahn-Teller and spin–orbit coupling effects result in a magnetic bistability of PtF₄, for which a spin-triplet (³B_2g, D_2h) coexists with an electronic singlet state (¹A_1g, D_4h) in solid neon matrices.