A Mediator‐Free Bienzyme Amperometric Biosensor Based on Horseradish Peroxidase and Glucose Oxidase Immobilized on Carbon Nanotube Modified Electrode

Multiwalled carbon nanotube (CNT) modified glassy carbon electrode immobilized with horseradish peroxidase (HRP) in Nafion coating showed direct electron transfer between HRP enzyme and the CNT‐modified electrode. A mediator‐free bienzyme glucose biosensor based on horseradish peroxidase and glucose oxidase was constructed. The bienzyme biosensor exhibited a high sensitivity for glucose detection at zero applied potential.     

Electrochemically Induced Free‐Radical Polymerization for the Fabrication of Amperometric Glucose Biosensors

Electrochemically induced free radical polymerization was employed for the fabrication of amperometric glucose biosensors. Based on the electrochemical reduction of persulfate anion, an ultrathin poly(acrylic acid) (PAA) hydrogel coating was generated on both the bare and glucose oxidase (GOD) crosslinked platinum electrodes in a neutral phosphate buffer solution under a low ionic strength condition. This electrosynthetic approach offers a flexible and controllable way to prepare functional coatings for biosensors under a wide range of highly biocompatible conditions, significantly different from other electropolymerization technologies that usually cause the enzyme deactivation. Negatively charged PAA hydrogel coating not only results in a biosensor with good permselectivity and long‐term stability, but also remarkably enhances its sensitivity by improving the oxygen recycle supply and the enzyme activity. Combined with a simple drop‐evaporation procedure to control the GOD loading, the present method offers a versatile and biocompatible way for fabricating highly sensitive biosensor.     

Maximal resonance of cubic bipartite polyhedral graphs

Let H{\mathcal{H}} be a set of disjoint faces of a cubic bipartite polyhedral graph G. If G has a perfect matching M such that the boundary of each face of H{\mathcal{H}} is an M-alternating cycle (or in other words, G-H{G-\mathcal{H}} has a perfect matching), then H{\mathcal{H}} is called a resonant pattern of G. Furthermore, G is k-resonant if every i (1 \leqslant i \leqslant k){i\,(1\,\leqslant\, i\, \leqslant\, k)} disjoint faces of G form a resonant pattern. In particular, G is called maximally resonant if G is k-resonant for all integers k \geqslant 1{k\,\geqslant\, 1}. In this paper, all the cubic bipartite polyhedral graphs, which are maximally resonant, are characterized. As a corollary, it is shown that if a cubic bipartite polyhedral graph is 3-resonant then it must be maximally resonant. However, 2-resonant ones need not to be maximally resonant.     

Some results on the Laplacian eigenvalues of unicyclic graphs

In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value. And also give an “asymptotically good” upper bounds for the second largest Laplacian eigenvalues of unicyclic graphs. Using this results, we can determine unicyclic graphs with maximum Laplacian separator. And unicyclic graphs with maximum Laplacian spread will also be determined.     

On the spectral radius of graphs with connectivity at most <Emphasis Type="Italic">k</Emphasis>

In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at , which is the graph obtained by joining k edges from k vertices of K _n-1 to an isolated vertex. We also show that the spectral radius of will be very close to n − 2 for a fixed k and a sufficiently large n.     

Synthesis,Characterization and Photophysical Properties of Iridium(III) Bis‐cyclometallated Complexes Containing 1,1‐Dithiolates

A series of neutral Ir(III)‐based heteroleptic complexes with a formula of [Ir(η²‐(C^∧N))₂(η²‐(S^∧S))] ((C^∧N)^‐ = ppy^‐, (S^∧S)^‐ = Et₂NCS₂^‐ ( 2a ), MeOCS₂^‐ ( 2b ), EtOCS₂^‐ ( 2c ), ⁱPrOCS₂^‐ ( 2d ); (C^∧N)^‐ = tpy^‐, (S^∧S) = Et₂NCS₂^‐ ( 3a ), MeOCS₂^‐ ( 3b ), EtOCS₂^‐ ( 3c ), ⁱPrOCS₂^‐ ( 3d ); (C^∧N)^‐ = epb^‐ , (S^∧S)^‐ = Et₂NCS₂^‐ ( 4a ), MeOCS₂^‐ ( 4a ), EtOCS₂^‐ ( 4a ); ppyH = 2‐phenylpyridine; tpyH = 2‐(4′‐tolyl)pyridine; epbH = ethyl 4‐(2′‐pyridyl)benzate) was synthesized and characterized. The crystal structure of complex 2d was also determined. The electron‐releasing substituents on (C^∧N)^‐ or (S^∧S)^‐ blueshift λ_max values.     

On the chaotic character of the stochastic heat equation, II

Consider the stochastic heat equation ${\partial_t u = (\varkappa/2)\Delta u+\sigma(u)\dot{F}}$ , where the solution u := u _t (x) is indexed by ${(t, x) \in (0, \infty) \times {\bf R}^d}$ , and ${\dot{F}}$ is a centered Gaussian noise that is white in time and has spatially-correlated coordinates. We analyze the large- ${\|x\|}$ fixed-t behavior of the solution u in different regimes, thereby study the effect of noise on the solution in various cases. Among other things, we show that if the spatial correlation function f of the noise is of Riesz type, that is ${f(x)\propto \|x\|^{-\alpha}}$ , then the “fluctuation exponents” of the solution are ${\psi}$ for the spatial variable and ${2\psi-1}$ for the time variable, where ${\psi:=2/(4-\alpha)}$ . Moreover, these exponent relations hold as long as ${\alpha \in (0, d \wedge 2)}$ ; that is precisely when Dalang’s theory [Dalang, Electron J Probab 4:(Paper no. 6):29, 1999] implies the existence of a solution to our stochastic PDE. These findings bolster earlier physical predictions [Kardar et al., Phys Rev Lett 58(20):889–892, 1985; Kardar and Zhang, Phys Rev Lett 58(20):2087–2090, 1987].     

Relaxed cutting plane method with convexification for solving nonlinear semi-infinite programming problems

In this paper, we present an algorithm to solve nonlinear semi-infinite programming (NSIP) problems. To deal with the nonlinear constraint, Floudas and Stein (SIAM J. Optim. 18:1187?C1208, 2007) suggest an adaptive convexification relaxation to approximate the nonlinear constraint function. The ??BB method, used widely in global optimization, is applied to construct the convexification relaxation. We then combine the idea of the cutting plane method with the convexification relaxation to propose a new algorithm to solve NSIP problems. With some given tolerances, our algorithm terminates in a finite number of iterations and obtains an approximate stationary point of the NSIP problems. In addition, some NSIP application examples are implemented by the method proposed in this paper, such as the proportional-integral-derivative controller design problem and the nonlinear finite impulse response filter design problem. Based on our numerical experience, we demonstrate that our algorithm enhances the computational speed for solving NSIP problems.     

Mode correlation of product pairs in the reaction OH+CD4-->HOD+CD3

The hydrogen abstraction reaction from methane by a hydroxyl radical produces two polyatomic molecules. Each product has several vibrational modes that characterize distinct, concerted motions of the constituent atoms of the molecule. This communication describes the first measurement that maps out the coincident information on how the mode of excitation of one product varies with that of the other co-product. Such information on mode correlation of product pairs is particularly appealing in that it provides intuitively a glimpse of the reaction paths by which the chemical transformation occurs.