A technique for multicoloring triangle-free hexagonal graphs

In order to avoid interference in cellular telephone networks, sets of radio frequencies are to be assigned to transmitters such that adjacent transmitters are allotted disjoint sets of frequencies. Often these transmitters are laid out like vertices of a triangular lattice in a plane. This problem corresponds to the problem of multicoloring an induced subgraph of a triangular lattice with integer demands associated with each vertex. We deal with the simpler case of triangle-free subgraphs of the lattice. [Frédéric Havet, Discrete Math. 233 (2001) 1–3] uses inductive arguments to prove that triangle-free hexagonal graphs can be colored with colors where ω_d is the maximum demand on a clique in the graph. We give a simpler proof and hope that our techniques can be used to prove the conjecture by [McDiarmid and Reed, Networks Suppl. 36 (2000) 114–117] that these graphs are -multicolorable.     

Finite element approximation to global stabilization of the Burgers’ equation by Neumann boundary feedback control law

In this article, we discuss global stabilization results for the Burgers’ equation using nonlinear Neumann boundary feedback control law. As a result of the nonlinear feedback control, a typical nonlinear problem is derived. Then, based on C ⁰-conforming finite element method, global stabilization results for the semidiscrete solution are analyzed. Further, introducing an auxiliary projection, optimal error estimates in \(L^{\infty }(L^{2})\), \(L^{\infty }(H^{1})\) and \(L^{\infty }(L^{\infty })\)-norms for the state variable are obtained. Moreover, superconvergence results are established for the first time for the feedback control laws, which preserve exponential stabilization property. Finally, some numerical experiments are conducted to confirm our theoretical findings.     

Fluorinated Boron Nitride Quantum Dots: A New 0D Material for Energy Conversion and Detection of Cellular Metabolism

Quantum dots encompass a broad spectrum of optical, catalytic, and electrochemical properties bringing in novel applications in catalysis, imaging, displays, and optoelectronics. Herein, the unanticipated broad‐spectrum light absorption and high fluorescence quantum yield in fluorinated boron nitride (FBN) quantum dots are discussed. A heterostructure of FBN quantum dots with a wide‐bandgap semiconductor, titania nanotube arrays, exhibits high photocatalytic activity as evidenced by high external quantum efficiency extending from ultraviolet to green region of the solar spectrum (≈24% at 400 nm). The high activity is confirmed using photoelectrochemical hydrogen evolution experiments. Further, it is demonstrated that high fluorescence quantum yield could be tapped for the detection of glycolytic activity in cancer cells compared to normal cells. This finding could shift the paradigm of molecular detection using quantum dots. The 0D structure and the gap states introduced through fluorination are believed to be responsible for these unprecedented characteristics of boron nitride.     

Black Phosphorus@Laser-Engraved Graphene Heterostructure-Based Temperature–Strain Hybridized Sensor for Electronic-Skin Applications

Smart electronic skin (e-skin) requires the easy incorporation of multifunctional sensors capable of mimicking skin-like perception in response to external stimuli. However, efficient and reliable measurement of multiple parameters in a single functional device is limited by the sensor layout and choice of functional materials. The outstanding electrical properties of black phosphorus and laser-engraved graphene (BP@LEG) demonstrates a new paradigm for a highly sensitive dual-modal temperature and strain sensor platform to modulate e-skin sensing functionality. Moreover, the unique hybridized sensor design enables efficient and accurate determination of each parameter without interfering with each other. The cationic polymer passivated BP@LEG composite material on polystyrene-block-poly(ethylene-ran-butylene)-block-polystyrene (SEBS) substrate outperforms as a positive temperature coefficient material, exhibiting a high thermal index of 8106 K (25–50  ° C) with high strain sensitivity (i.e., gauge factor, GF) of up to 2765 ( > 19.2%), ultralow strain resolution of 0.023%, and longer durability ( > 18 400 cycles), satisfying the e-skin requirements. Looking forward, this technique provides unique opportunities for broader applications, such as e-skin, robotic appendages, and health monitoring technologies.     

Surface structure of magnetite (111) under hydrated conditions by crystal truncation rod diffraction

X-ray crystal truncation rod (CTR) diffraction under hydrated conditions at circum-neutral pH was used to determine the surface structure of Fe₃O₄(111) following a wet chemical mechanical polishing (CMP) preparation method. The best-fit model to the CTR data shows the presence of two oxygen terminated domains that are chemically inequivalent and symmetrically distinct in the surface contribution ratio of 75% oxygen octahedral-iron (OOI) termination (^aO_2.61–^aO_1.00–^oh1Fe_2.55–^bO_1.00–^bO_3.00–^td1Fe_1.00–^oh2Fe_1.00–^td2Fe_1.00–R) to 25% oxygen mixed-iron (OMI) termination (^bO_1.00–^bO_3.00–^td1Fe₀–^oh2Fe_1.00–^td2Fe_1.00–^aO_3.00–^aO_1.00–^oh1Fe_3.00–R). An adsorbed water layer could not be constrained in the best-fit model. However, bond-valence analyses suggest that both of the surfaces are hydro-oxo terminated. Furthermore, the topmost iron layers of both domains are inferred to be occupied with the redox active Fe²⁺ and Fe³⁺ cations indicating that these irons are the principle irons involved in controlling the surface reactivity of magnetite in industrial and environmentally relevant conditions.     

Nanoscale Mapping of the Conductivity and Interfacial Capacitance of an Electrolyte-Gated Organic Field-Effect Transistor under Operation

Probing nanoscale electrical properties of organic semiconducting materials at the interface with an electrolyte solution under externally applied voltages is key in the field of organic bioelectronics. It is demonstrated that the conductivity and interfacial capacitance of the active channel of an electrolyte-gated organic field-effect transistor (EGOFET) under operation can be probed at the nanoscale using scanning dielectric microscopy in force detection mode in liquid environment. Local electrostatic force versus gate voltage transfer characteristics are obtained on the device and correlated with the global current–voltage transfer characteristics of the EGOFET. Nanoscale maps of the conductivity of the semiconducting channel show the dependence of the channel conductivity on the gate voltage and its variation along the channel due to the space charge limited conduction. The maps reveal very small electrical heterogeneities, which correspond to local interfacial capacitance variations due to an ultrathin non-uniform insulating layer resulting from a phase separation in the organic semiconducting blend. Present results offer insights into the transduction mechanism at the organic semiconductor/electrolyte interfaces at scales down to ≈100 nm, which can bring substantial optimization of organic electronic devices for bioelectronic applications such as electrical recording on excitable cells or label-free biosensing.     

Layer structure preservation during swelling, pillaring, and exfoliation of a zeolite precursor

MCM-22(P), the precursor to zeolite MCM-22, consists of stacks of layers that can be swollen and exfoliated to produce catalytically active materials. However, the current swelling procedures result in significant degradation of crystal morphology along with partial loss of crystallinity and dissolution of the crystalline phase. Fabrication of polymer nanocomposites and coatings with MCM-22 for separation, barrier, and other applications requires a swelling method that does not alter drastically the crystal morphology and layer structure and preserves the high aspect ratio of the layers. Here, we demonstrate such a method by swelling MCM-22(P) at room temperature. The low-temperature process does not disrupt the framework connectivity present in the parent MCM-22(P) material. By extensive washing with water, the swollen material, MCM-22(PS-RT), evolves to a new ordered layered structure. Interestingly, the swelling procedure is reversible and the swollen material can be restored back to MCM-22(P) by acidification of the sample. The swollen material can also be pillared to produce an MCM-36 analogue. It can also be exfoliated, and layers can be incorporated in a polymer matrix to make nanocomposites.     

Multifunctional Hybrids Based on 2D Fluorinated Graphene Oxide and Superparamagnetic Iron Oxide Nanoparticles

Carbon‐based nanomaterials have garnered a lot of attention in the research of yesteryear. Here this study reports a composite based on fluorinated graphene oxide—a multifunctional subsidiary of graphene; and iron oxide nanoparticles as a contrast agent for magnetic resonance imaging (MRI). Extensive structural and functional characterization is carried out to understand composite behavior toward biotoxicity and its performance as a contrast agent. The electron withdrawing fluorine group decreases the charge transfer to iron oxide increasing the magnetic saturation of the composite thus enhancing the contrast. The interaction of paramagnetic and superparamagnetic systems yields a superior contrast agent for MRI and fluorescent imaging.     

RP-LC Resolution of (R,S)-Atenolol via Diastereomerization with Marfey’s Reagent and Its Structural Variants Under Conventional and Microwave Heating

(R,S)-Atenolol was derivatized with Marfey’s reagent, (MR; 1-fluoro-2,4-dinitrophenyl-5-l-alanine amide or FDNP-l-Ala-NH₂) and its four structural variants (FDNP-l-Phe-NH₂, FDNP-l-Val-NH₂, FDNP-l-Leu-NH₂ and FDNP-l-Pro-NH₂). MR reacts quantitatively with 1° and 2° amino groups and atenolol has a secondary amino group. The derivatization reactions were carried out under conventional and microwave heating and compared. The resulting diastereomers were separated on RP-TLC and on a C18 column with detection at 340 nm. (R)-Isomer eluted before (S). The conditions of derivatization and chromatographic separation were optimized. The method was validated for linearity, repeatability, limits of detection and limit of quantification.