Generalized Games and Non-compact Quasi-variational Inequalities

AbstractIn this paper, by developing an approximation approach which is originally due to Tuleca in 1986, we prove the existence of equilibria for generalized games in which constraint mappings (correspondences) are lower (resp., upper) semicontinuous instead of having lower (resp., upper) open sections or open graphs in infinite dimensional topological spaces. Then, existence theorems of solutions for quasi-variational inequalities and non-compact generalized quasi-variational inequalities are also established. Finally, existence theorems of constrained games with non-compact strategy sets are derived. Our results unify and generalize many well known results given in the existing literature. In particular, we answer the question raised by Yannelis and Prabhakar in 1983 in the affirmative under more weaker conditions

4-Vinylguaiacol, an Active Metabolite of Ferulic Acid by Enteric Microbiota and Probiotics, Possesses Significant Activities against Drug-Resistant Human Colorectal Cancer Cells

Ferulic acid, a hydroxycinnamic acid, is abundant in vegetables, grains, and medicinal plants. Emerging evidence suggests that ferulic acid may exert beneficial effects against colorectal cancer. However, the anticancer activity of ferulic acid is relatively low, and its metabolism after oral administration is largely unknown. In this study, mimicking the enteric environment, human intestinal microflora and commercial probiotics were used to metabolize ferulic acid to its metabolites, and their anticancer activities were evaluated. Ferulic acid can be biotransformed to 4-vinylguaiacol (2-methoxy-4-vinylphenol), and the contents of ferulic acid and 4-vinylguaiacol in bio-transformed extracts were determined by high-performance liquid chromatography (HPLC). Using the chemotherapy-sensitive cell line HCT-116 and the chemo-resistant cell line HT-29, the cell proliferation was determined by the modified trichrome stain assay. The cell cycle and induction of apoptosis were assayed using flow cytometry. HPLC data showed that there was a marked transformation from ferulic acid to 4-vinylguaiacol, and the conversion rates of intestinal microflora and four probiotics were from 1.3 to 36.8%. Both ferulic acid and 4-vinylguaiacol possessed dose- and time-related anticancer activities on the two cell lines, while 4-vinylguaiacol showed more potent effects than ferulic acid. Interestingly, 4-vinylguaiacol exhibited significantly higher antiproliferative effects on the HT-29 cell line than that on HCT-116. The IC50 of the metabolite 4-vinylguaiacol on HT-29 cells was 350 μM, 3.7-fold higher than its parent compound. The potential of cancer cell growth inhibition of 4-vinylguaiacol was mediated by cell cycle arrest at the G1 phase and induction of apoptosis. Data from this study indicate that the oral administration of ferulic acid offers a promising approach to increase its anticancer activity through gut microbial conversion to 4-vinylguaiacol, and the biotransformation could also be achieved by selected commercial probiotics. 4-Vinylguaiacol is a potential anticancer metabolite from ferulic acid for chemotherapy-resistant colon cancer cells

Bis(μ-2-hydroxy­benozato)-κ3 O,O′:O′;κ3 O:O,O′-bis­[(2-hydroxy­benozato-κ2 O,O′)(1,10-phenanthroline-κ2 N,N′)cadmium(II)]

The dinuclear title compound, [Cd2(C7H5O3)4(C12H8N2)2], is located on a crystallographic rotation twofold axis. The two CdII ions are connected by two tridentate bridging 2-hydroxy­benzoate anions. Each CdII ion is seven-coordinated by five O atoms from three 2-hydroxy­benzoate ligands and two N atoms from 1,10-phenanthroline. The 2-hydroxy­benzoate mol­ecules adopt two kinds of coordination mode, bidentate chelating and tridentate bridging–chelating. Intra­molecular hydrogen bonds between hydr­oxy and carboxyl­ate groups from 2-hydroxy­benzoate groups and π–π stacking interactions between parallel 1,10-phenanthroline ligands [centroid–centroid distances = 3.707 (3) and 3.842 (3) Å] are observed. Furthermore, adjacent benzene rings from 2-hydroxy­benzoate ligands are involved in π–π inter­actions with inter­planar distances of 3.642 (3) Å, thereby forming a chain along the a axis direction

Cavity magnomechanics: from classical to quantum

Hybrid quantum systems based on magnons in magnetic materials have made significant progress in the past decade. They are built based on the couplings of magnons with microwave photons, optical photons, vibration phonons, and superconducting qubits. In particular, the interactions among magnons, microwave cavity photons, and vibration phonons form the system of cavity magnomechanics (CMM), which lies in the interdisciplinary field of cavity QED, magnonics, quantum optics, and quantum information. Here, we review the experimental and theoretical progress of this emerging field. We first introduce the underlying theories of the magnomechanical coupling, and then some representative classical phenomena that have been experimentally observed, including magnomechanically induced transparency, magnomechanical dynamical backactions, magnon-phonon cross-Kerr nonlinearity, etc. We also discuss a number of theoretical proposals, which show the potential of the CMM system for preparing different kinds of quantum states of magnons, phonons, and photons, and hybrid systems combining magnomechanics and optomechanics and relevant quantum protocols based on them. Finally, we summarize this review and provide an outlook for the future research directions in this field.Comment: Review article, 42 pages, 16 figure

Early Triassic microbialites from the Changxing Region of Zhejiang Province, South China

© 2019, The Author(s). Microbialites, often considered as a signal of extreme marine environment, are common in the Lower Triassic strata of South China where they flourished in the aftermath of the end-Permian mass extinction. Early Triassic microbialite facies are known to vary palaeogeographically, perhaps due to differing climates, ocean chemistry, and water depths. This paper provides the first record of a brief, but spectacular development of microbialites in the aftermath of the end-Permian mass extinction at Panjiazhuang section, Changxing Region of Zhejiang Province (eastern South China). Here, the Upper Permian Changxing Formation comprises typical shallow platform facies rich in calcareous algae and foraminifera, the development of which was terminated by the major end-Permian regression. A 3.4-m-thick microbialite began to form at the onset of the transgression in the earliest Triassic. The microbialite at Panjiazhuang section is composed of thrombolite that contains abundant calcified cyanobacteria, small gastropods, microconchid tubes and ostracods, representing a low-diversity shallow marine community in the aftermath of the end-Permian crisis. The microbialites are succeeded by thin-bedded micrites bearing thin-shelled bivalves, which record a rapid sea-level rise in the Early Triassic. Abundant populations of small pyrite framboids are observed in the upper part of the microbialites and the overlying thin-bedded micrites, suggesting that dysoxic water conditions developed at that time. The appearance of microbialites near the Permian–Triassic boundary (PTB) at Panjiazhuang section was the result of peculiar marine conditions following the end-Permian regression, whilst their disappearance was due to the increasing water depth and the development of dysoxia