Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales

AbstractLet T be a time scale such that 0,T∈T, β,γ⩾0 and 0<η<ρ(T). We consider the following p-Laplacian three-point boundary problem on time scales(φp(uΔ(t)))∇+λh(t)f(u(t))=0,t∈(0,T),u(0)−βuΔ(0)=γuΔ(η),uΔ(T)=0, where p>1, λ>0, h∈Cld((0,T),[0,∞)) and f∈C([0,∞),(0,∞)). Some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. In doing so the usual restriction that f0=limu→0+f(u)φp(u) and f∞=limu→∞f(u)φp(u) exist is removed. An example is also given to illustrate the main results

'Ruiduxiangyu': A new table grape with muscat flavor

Research Note

'Aishenmeigui': An extremely early maturing seedless grape with muscat flavor

Research Not

'Ruiduwuheyi Seedless': A new late-maturing seedless table grape

Research Note

Adiabatic continuity between Hofstadter and Chern insulator states

We show that the topologically nontrivial bands of Chern insulators are adiabatic cousins of the Landau bands of Hofstadter lattices. We demonstrate adiabatic connection also between several familiar fractional quantum Hall states on Hofstadter lattices and the fractional Chern insulator states in partially filled Chern bands, which implies that they are in fact different manifestations of the same phase. This adiabatic path provides a way of generating many more fractional Chern insulator states and helps clarify that nonuniformity in the distribution of the Berry curvature is responsible for weakening or altogether destroying fractional topological states

Metabolomics revealed the toxicity of cationic liposomes in HepG2 cells using UHPLC‐Q‐TOF/MS and multivariate data analysis

Cationic liposomes (CLs) are novel nonviral vectors widely used for delivering drugs or genes. However, applications of CLs are largely hampered by their cytotoxicity, partly because the potential mechanism underlying the cytotoxicity of CLs remains unclear. The aim of the present study was to explore the underlying mechanism of cytotoxicity induced by CLs on HepG2 cells. Differential metabolites were identified and quantified using ultra‐liquid chromatography quadrupole time‐of‐flight mass spectrometry (UHPLC‐Q‐TOF/MS). The toxicity of CLs on HepG2 cells was evaluated by multivariate data analysis and statistics. Additionally, CCK‐8 assay, heatmap, pathway and co‐expression network were carried out to explore the relations between the metabolites and the pathways. The results showed a dose‐dependent toxic effect of CLs on HepG2 cells, with an IC50 value of 119.9 μg/mL. Multivariate statistical analysis identified 42 potential metabolites between CLs exposure and control groups. Pathway analysis showed significant changes in pathways involving amino acid metabolism, energy metabolism, lipid metabolism and oxidative stress in the CLs exposure group vs the control group. Metabolites related to the above‐mentioned pathways included phenylalanine, methionine, creatine, oxalacetic acid, glutathione, oxidized glutathione, choline phosphate and several unsaturated fatty acids, indicating that cells were disturbed in amino acid metabolism, energy and lipid supply when CLs exposure‐induced injury occurred. It is concluded that CLs may induce cytotoxicity by enhancing reactive oxygen species in vitro, affect the normal process of energy metabolism, disturb several vital signaling pathways and finally induce cell death.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139913/1/bmc4036.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139913/2/bmc4036_am.pd

(4Z)-4-[(2-Chloro­anilino)(phen­yl)methyl­idene]-3-methyl-1-phenyl-1H-pyrazol-5(4H)-one

The title compound, C23H18ClN3O, exists in an enamine–keto form with the amino group involved in an intra­molecular N—H⋯O hydrogen bond. The five-membered ring is nearly planar, the largest deviation being 0.0004 (7) Å, and makes dihedral angles of 16.62 (6), 41.89 (5) and 71.27 (4)° with the phenyl rings. In the crystal, weak C—H⋯O hydrogen bonds link the mol­ecules into supra­molecular chains along the b axis