Zeolitic imidazolate framework-67 (ZIF-67) rhombic dodecahedrons as full-spectrum light harvesting photocatalyst for environmental remediation

The inferior utilization efficiency of light is the main obstacle to the practical application of traditional photocatalysts such as TiO₂ and ZnO. In this regard, the development of novel photocatalysts with the capability of harvesting full spectrum light (from ultraviolet (UV) to near-infrared (NIR)) energy is a promising solution for solar energy conversion and environmental remediation. Here, we report the discovery of a single material that can harvest UV, visible (VIS), and NIR radiations to decompose heavy metal contaminants in aqueous solution. Zeolitic imidazolate framework-67 (ZIF-67) rhombic dodecahedrons were synthesized through a facile solution approach and employed in the reduction of Cr(VI) under UV−VIS−NIR pulsed laser irradiation, which was generated from the fundamental, second and third harmonics of Nd:YAG laser, respectively. The nanostructures showed efficient Cr(VI) reduction under UV, VIS and NIR laser irradiation and the measured reduction efficiency (%) was 71.22%, 69.52%, and 40.79%, respectively after 120 min. A possible explanation for the photocatalytic activity in Cr(VI) reduction was proposed. This is the first study of its kind where pulsed laser and ZIF-67 rhombic dodecahedrons capable of harvesting full spectrum light energy have been employed for the removal of Cr(VI) from water. The extraordinary capacity of harvesting full-spectrum light and long-term stability make ZIF-67 a potential photocatalyst for environmental remediation.     

Hydrogen production and photocatalytic activity of g-C3N4/Co-MOF (ZIF-67) nanocomposite under visible light irradiation

Herein, cobalt (Co)-based metal–organic zeolitic imidazole frameworks (ZIF-67) coupled with g-C₃N₄ nanosheets synthesized via a simple microwave irradiation method. SEM, TEM and HR-TEM results showed that ZIF-67 were uniformly dispersed on g-C₃N₄ surfaces and had a rhombic dodecahedron shape. The photocatalytic properties of g-C₃N₄/ZIF-67 nanocomposite were evaluated by photocatalytic dye degradation of crystal violet (CV), 4-chlorophenol (4-CP) and photocatalytic hydrogen (H₂) production. In presence of visible light illumination, the photocatalytic dye results showed that 95% CV degradation and 53% 4-CP degradation within 80 min. The H₂ production of the g-C₃N₄/ZIF-67 composite was 2084 μmol g⁻¹, which is 3.84 folds greater than that of bare g-C₃N₄ (541 μmol g⁻¹).     

Design,Synthesis, and Anticancer Screening for Repurposed Pyrazolo[3,4-d]pyrimidine Derivatives on Four Mammalian Cancer Cell Lines

The present study reports the synthesis of new purine bioisosteres comprising a pyrazolo[3,4-d]pyrimidine scaffold linked to mono-, di-, and trimethoxy benzylidene moieties through hydrazine linkages. First, in silico docking experiments of the synthesized compounds against Bax, Bcl-2, Caspase-3, Ki67, p21, and p53 were performed in a trial to rationalize the observed cytotoxic activity for the tested compounds. The anticancer activity of these compounds was evaluated in vitro against Caco-2, A549, HT1080, and Hela cell lines. Results revealed that two (5 and 7) of the three synthesized compounds (5, 6, and 7) showed high cytotoxic activity against all tested cell lines with IC₅₀ values in the micro molar concentration. Our in vitro results show that there is no significant apoptotic effect for the treatment with the experimental compounds on the viability of cells against A549 cells. Ki67 expression was found to decrease significantly following the treatment of cells with the most promising candidate: drug 7. The overall results indicate that these pyrazolopyrimidine derivatives possess anticancer activity at varying doses. The suggested mechanism of action involves the inhibition of the proliferation of cancer cells.     

Singular p-Laplacian equations with superlinear perturbation

We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter $\lambda >0$ varies. In addition, we show that for every admissible parameter $\lambda >0$ the problem has a smallest positive solution ${\stackrel{￣}{u}}_{\lambda }$ and we establish the monotonicity and continuity properties of the map $\lambda \to {\stackrel{￣}{u}}_{\lambda }$.     

Metal-organic framework derived NiCoP hollow polyhedrons electrocatalyst for pH-universal hydrogen evolution reaction

Hollow nanostructures have attracted increasing research interest in hydrogen evolution reaction owing to their unique structural features.Herein,Ni-Co mixed metal phosphide hollow and porous polyhedrons was successfully composited(expressed as NiCoP).Benefiting from the synergistic effects of ZIF-67 by doping Ni elements and the well-defined hollow and porous structure,the as-synthesized NiCoP hollow and porous polyhedrons exhibit better electrochemical properties and mechanical stability for hydrogen evolution reaction over a pH-universal range,with a small Tafel slopes of 72,101,176 mV/dec,and a low overpotential of 82,102,261 mV at a current density of 10 mA/cm² in 0.5 mol/L H₂SO₄,1 mol/L KOH and1 mol/L phosphate buffer solution(PBS).This general strategy can also be applied to fabricate other hollow cobalt-based phosphides and MOFs-derived materials for HER.     

Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

Cohomological relation between Jacobi forms and skew‐holomorphic Jacobi forms

Eichler and Zagier developed a theory of Jacobi forms to understand and extend Maass' work on the Saito‐Kurokawa conjecture. Later Skoruppa introduced skew‐holomorphic Jacobi forms, which play an important role in understanding liftings of modular forms and Jacobi forms. In this paper, we explain a relation between Jacobi forms and skew‐holomorphic Jacobi forms in terms of a group cohomology. More precisely, we introduce an isomorphism from the direct sum of the space of Jacobi cusp forms on and the space of skew‐holomorphic Jacobi cusp forms on with the same half‐integral weight to the Eichler cohomology group of with a coefficient module coming from polynomials.     

In situ Growth of a Cobalt‐based Metal‐organic Framework on Multi‐walled Carbon Nanotubes for Simultaneously Detection of Hydroquinone and Catechol.

In the present study, we report a facile method for preparing a porous MWCNTs/ZIF‐67 nanocomposite with the help of a morphology‐maintained ZIF‐67 in situ growth on multi‐walled carbon nanotubes. Interesting, the MWCNTs/ZIF‐67 nanocomposite demonstrated excellent electrochemical activity for hydroquinone (HQ) and catechol (CC) attribute to the effective interconnections ZIF‐67 crystals and MWCNTs. The analytical curves for HQ and CC obtained by differential pulse voltammetry (DPV) were linear in the range from 0.5 to 100 μM. Benefitting from the excellent conductivity of MWCNTs as well as the high surface area and porosity of ZIF‐67, the advanced nanocomposite displayed good reproducibility, high selectivity and excellent stability, and was successfully employed to assay the content of dihydroxybenzene isomers in the lake water samples.     

A priori estimate for non-uniform elliptic equations

A priori estimate for non-uniform elliptic equations with periodic boundary conditions is concerned. The domain considered consists of two sub-regions, a connected high permeability region and a disconnected matrix block region with low permeability. Let ? denote the size ratio of one matrix block to the whole domain. It is shown that in the connected high permeability sub-region, the Hölder and the Lipschitz estimates of the non-uniform elliptic solutions are bounded uniformly in ?. But Hölder gradient estimate and Lp estimate of the second order derivatives of the solutions in general are not bounded uniformly in ?.     

Entropy of Hadamard spaces

We consider a geodesically complete and proper Hadamard metric measure space X endowed with a Borel measure. Assuming that there exists a certain non-amenable group of isometry of X which acts freely, properly discontinuously and cocompactly on X and preserves the measure we show that the topological entropy of the geodesic flow on the orbit space is positive.