Solutions and conservation laws of a (3+1)-dimensional Zakharov–Kuznetsov equation

In this paper, we study a nonlinear evolution partial differential equation, namely the (3+1)-dimensional Zakharov–Kuznetsov equation. Kudryashov method together with Jacobi elliptic function method is used to obtain the exact solutions of the (3+1)-dimensional Zakharov–Kuznetsov equation. Furthermore, the conservation laws of the (3+1)-dimensional Zakharov–Kuznetsov equation are obtained by using the multiplier method.     

Screening of Carbonic Anhydrase,Acetylcholinesterase, Butyrylcholinesterase,and α-Glycosidase Enzyme Inhibition Effects and Antioxidant Activity of Coumestrol

Coumestrol (3,9-dihydroxy-6-benzofuran [3,2-c] chromenone) as a phytoestrogen and polyphenolic compound is a member of the Coumestans family and is quite common in plants. In this study, antiglaucoma, antidiabetic, anticholinergic, and antioxidant effects of Coumestrol were evaluated and compared with standards. To determine the antioxidant activity of coumestrol, several methods—namely N,N-dimethyl-p-phenylenediamine dihydrochloride radical (DMPD^•+)-scavenging activity, 2,2′-azinobis-(3-ethylbenzothiazoline-6-sulphonate) radical (ABTS^•+)-scavenging activity, 1,1-diphenyl-2-picrylhydrazyl radical (DPPH^•)-scavenging activity, potassium ferric cyanide reduction ability, and cupric ion (Cu²⁺)-reducing activity—were performed. Butylated hydroxyanisole (BHA), Trolox, α-Tocopherol, and butylated hydroxytoluene (BHT) were used as the reference antioxidants for comparison. Coumestrol scavenged the DPPH radical with an IC₅₀ value of 25.95 μg/mL (r²: 0.9005) while BHA, BHT, Trolox, and α-Tocopherol demonstrated IC₅₀ values of 10.10, 25.95, 7.059, and 11.31 μg/mL, respectively. When these results evaluated, Coumestrol had similar DPPH^•-scavenging effect to BHT and lower better than Trolox, BHA and α-tocopherol. In addition, the inhibition effects of Coumestrol were tested against the metabolic enzymes acetylcholinesterase (AChE), butyrylcholinesterase (BChE), carbonic anhydrase II (CA II), and α-glycosidase, which are associated with some global diseases such as Alzheimer’s disease (AD), glaucoma, and diabetes. Coumestrol exhibited K_i values of 10.25 ± 1.94, 5.99 ± 1.79, 25.41 ± 1.10, and 30.56 ± 3.36 nM towards these enzymes, respectively.     

Phenolysis of hexachlorocyclotriphosphazatriene

The reactions of hexachlorocyclotriphosphazatriene N₃P₃Cl₆ ( 1 ) with the sodium salts of 2,4,6‐trimethylphenol ( 2a ), 4‐tert‐butyl‐2‐methylphenol ( 2b ), 2‐tert‐butyl‐4‐methylphenol ( 2c ) have been investigated, and monoaryloxy‐substituted phosphazenes N₃P₃Cl₅OAr ( 3–5 ) were obtained. © 2005 Wiley Periodicals, Inc. 16:308–310, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20127     

Topochemical Path in High Lithiation of MoS2

Lithiation of MoS₂/RGO (reduced graphite oxide) electrodes repeatedly reached experimental capacities larger than 1000 mA · g^–1, corresponding to at least 6 lithium equivalents per gram of MoS₂. At our best knowledge, a convincing explanation is still missing in literature. In most cases, phase separation into Li₂S and elemental Mo was assumed to occur. However, this can only explain capacities up to 669 mA · g^–1, corresponding to an exchange of four Li. Formation of LiMo alloys could resolve the problem but the Li/Mo system does not contain any binary phases. If signs for Li₂S formation were found, indeed experimental capacities were below 700 mAh · g^–1. Here we present a topochemical mechanism, which sustains multiple charge/discharge cycles at 1000 mAh · g^–1, corresponding to an exchange of at least 6 Li per formula unit MoS₂. This topochemical reaction route prevents decomposition into binary phases and thus avoids segregation of the components of MoS₂. Throughout the whole lithiation/delithiation process, distinct layers of Mo are preserved but extended or shrunk by slight movements and reshuffling of sulfur and lithium atoms. On addition of 6 Li per formula unit to MoS₂, all central sulfur atoms are hosted in mutual Mo–S layers such that formal S^2– and Mo^2– anions appear coordinated by lithium cations. Indeed, similar structures are known in the field of Zintl phases. Our first‐principles crystal structure prediction study describes this topological path through conversion reactions during the lithiation/delithiation processes. All optimized phases along the topological path exhibit a distinct Mo layering giving rise to a series of dominant scattering into pseudo 001 reflections perpendicular to these Mo planes. The mechanism we present here explains why such high capacities can be reached reversibly for MoS₂/RGO nano composites     

Identification of Natural Compounds as Inhibitors of Pyruvate Kinase M2 for Cancer Treatment

The reliance of tumor cells on aerobic glycolysis is one of the emerging hallmarks of cancer. Pyruvate kinase M2 (PKM2), an important enzyme of glycolytic pathway, is highly expressed in a number of cancer cells. Tumor cells heavily depend on PKM2 to fulfill their divergent energetic and biosynthetic requirements, suggesting it as novel drug target for cancer therapies. Based on this context, we performed enzymatic-assay-based screening of the in-house phenolic compounds library for the identification of PKM2 inhibitors. This screening identified silibinin, curcumin, resveratrol, and ellagic acid as potential inhibitors of PKM2 with IC₅₀ values of 0.91 µM, 1.12 µM, 3.07 µM, and 4.20 µM respectively. For the determination of Ki constants and the inhibition type of hit compounds, Lineweaver–Burk graphs were plotted. Silibinin and ellagic acid performed the competitive inhibition of PKM2 with Ki constants of 0.61 µM and 5.06 µM, while curcumin and resveratrol were identified as non-competitive inhibitors of PKM2 with Ki constants of 1.20 µM and 7.34 µM. The in silico screening of phenolic compounds against three binding sites of PKM2 provided insight into the binding pattern and functionally important amino residues of PKM2. Further, the evaluation of cytotoxicity via MTT assay demonstrated ellagic acid as potent inhibitor of cancer cell growth (IC₅₀ = 20 µM). These results present ellagic acid, silibinin, curcumin, and resveratrol as inhibitors of PKM2 to interrogate metabolic reprogramming in cancer cells. This study has also provided the foundation for further research to validate the potential of identified bioactive entities for PKM2 targeted-cancer therapies.     

Toughness enhancers for bone scaffold materials based on biocompatible photopolymers

Providing access to the benefits of additive manufacturing technologies in tissue engineering, vinyl esters recently came into view as appropriate replacements for (meth)acrylates as precursors for photopolymers. Their low cytotoxicity and good biocompatibility as well as favorable degradation behavior are their main assets. Suffering from rather poor mechanical properties, particularly in terms of toughness, several improvements have been made over the last years. Especially, thiol–ene chemistry has been investigated to overcome those shortcomings. In this study, we focused on additional means to further improve the toughness of an already established biocompatible vinyl ester‐thiol formulation, eligible for digital light processing‐based stereolithography. All molecules were based on poly(ε‐caprolactone) as building block and the formulations were tested regarding their reactivity and the resulting mechanical properties. They all performed well as toughness enhancer, ultimately doubling the impact resistance of the reference system. © 2018 The Authors. Journal of Polymer Science Part A: Polymer Chemistry published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 110–119     

Magnetodielectric coupling by exchange striction in Y<Subscript>2</Subscript>Cu<Subscript>2</Subscript>O<Subscript>5</Subscript>

We have studied the magnetodielectric response of Y₂Cu₂O₅, the so-called blue phase in the Y₂O₃-CuO-BaO phase diagram. Based on symmetry principles, we predict and demonstrate magneto-dielectric coupling on a single crystal sample. We report an anomaly in the dielectric constant at the ordering temperature of the Cu spins. We probe the magnetic field-induced phase transitions between four different magnetic phases using magneto-capacitance measurements, demonstrating relatively strong magnetodielectric coupling. We observe an increase in dielectric constant in the spin-flip phase where there exists spontaneous magnetization. We construct a detailed magnetic phase diagram. The magnetodielectric coupling is analyzed in terms of striction induced by symmetric superexchange and optical phonon frequency shifts.     

RAFT‐mediated synthesis of poly[(oligoethylene glycol) methyl ether acrylate] brushes for biological functions

The synthesis of poly[(oligoethylene glycol) methyl ether acrylate] [poly(OEGA)] brushes was achieved via reversible addition‐fragmentation chain transfer (RAFT) polymerization and used to selectively immobilize streptavidin proteins. Initially, gold surfaces were modified with a trithiocarbonate‐based RAFT chain transfer agent (CTA) by using an ester reaction involving a gold substrate modified with 11‐mercapto‐1‐undecanol and bis(2‐butyric acid)trithiocarbonate. poly(OEGA) brushes were then prepared via RAFT‐mediated polymerization from the surface‐immobilized CTA. The immobilization of CTA on the gold surface and the subsequent polymer formation were followed by ellipsometry, X‐ray photoelectron spectroscopy, grazing angle‐Fourier transform infrared spectroscopy, atomic force microscopy, and water contact‐angle measurements. RAFT‐mediated polymerization method gave CTA groups to grafted poly(OEGA) termini, which can be converted to various biofunctional groups. The terminal carboxylic acid groups of poly(OEGA) chains were functionalized with amine‐functionalized biotin units to provide selective attachment points for streptavidin proteins. Fluorescence microscopy measurements confirmed the successful immobilization of streptavidin molecules on the polymer brushes. It is demonstrated that this fabrication method may be successfully applied for specific protein recognition and immobilization. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

On smoothers for multigrid of the second kind

We study smoothers for the multigrid method of the second kind arising from Fredholm integral equations. Our model problems use nonlocal governing operators that enforce local boundary conditions. For discretization, we utilize the Nyström method with the trapezoidal rule. We find the eigenvalues of matrices associated to periodic, antiperiodic, and Dirichlet problems in terms of the nonlocality parameter and mesh size. Knowing explicitly the spectrum of the matrices enables us to analyze the behavior of smoothers. Although spectral analyses exist for finding effective smoothers for 1D elliptic model problems, to the best of our knowledge, a guiding spectral analysis is not available for smoothers of a multigrid of the second kind. We fill this gap in the literature. The Picard iteration has been the default smoother for a multigrid of the second kind. Jacobi‐like methods have not been considered as viable options. We propose two strategies. The first one focuses on the most oscillatory mode and aims to damp it effectively. For this choice, we show that weighted‐Jacobi relaxation is equivalent to the Picard iteration. The second strategy focuses on the set of oscillatory modes and aims to damp them as quickly as possible, simultaneously. Although the Picard iteration is an effective smoother for model nonlocal problems under consideration, we show that it is possible to find better than ones using the second strategy. We also shed some light on internal mechanism of the Picard iteration and provide an example where the Picard iteration cannot be used as a smoother.