Switchable electrode controlled by Boolean logic gates using enzymes as input signals

Application of Boolean logic operations performed by enzymes to control electrochemical systems is presented. Indium–tin oxide (ITO) electrodes with the surface modified with poly-4-vinyl pyridine (P4VP) brush were synthesized and used as switchable electrochemical systems. The switch ON and OFF of the electrode activity were achieved by pH changes generated in situ by biocatalytic reactions in the presence of enzymes used as input signals. Two logic gates operating as AND/OR Boolean functions were designed using invertase and glucose oxidase or esterase and glucose oxidase as input signals, respectively. The electrode surface coated with a shrunk P4VP polymer at neutral pH values was not electrochemically active because of the blocking effect of the polymer film. The positive outputs of the logic operations yielded a pH drop to acidic conditions, resulting in the protonation and swelling of the P4VP polymer allowing penetration of a soluble redox probe to the conducting support, thus switching the electrode activity ON. The electrode interface was reset to the initial OFF state, with the inhibited electrochemical reaction, upon in situ pH increase generated by another enzymatic reaction in the presence of urease. Logically processed biochemical inputs of various enzymes allowed reversible activation–inactivation of the electrochemical reaction.     

{\mathbb{G}_a^ M} degeneration of flag varieties

Let ${\mathcal{F}_\lambda}$ be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module V _λ . We define a flat degeneration ${\mathcal{F}_\lambda^a}$ , which is a ${\mathbb{G}^M_a}$ variety. Moreover, there exists a larger group G ^a acting on ${\mathcal{F}_\lambda^a}$ , which is a degeneration of the group G. The group G ^a contains ${\mathbb{G}^M_a}$ as a normal subgroup. If G is of type A, then the degenerate flag varieties can be embedde‘d into the product of Grassmannians and thus to the product of projective spaces. The defining ideal of ${\mathcal{F}_\lambda}$ is generated by the set of degenerate Plücker relations. We prove that the coordinate ring of ${\mathcal{F}_\lambda^a}$ is isomorphic to a direct sum of dual PBW-graded ${\mathfrak{g}}$ -modules. We also prove that there exists bases in multi-homogeneous components of the coordinate rings, parametrized by the semistandard PBW-tableux, which are analogs of semistandard tableaux.     

ChemInform Abstract: Solving the Structure of Li Ion Battery Materials with Precession Electron Diffraction: Application to Li2CoPO4F.

The crystal structure of Li₂CoPO₄F is completely solved from precession electron diffraction data, including the location of the Li atoms.     

Research on the electrochemistry of oxygen ion conductors in the former Soviet Union

Following previous reviews of research results on oxygen ion-conducting materials obtained in the former USSR, this article addresses the case of Bi₂O₃-based compositions. Phase formation in oxide systems with Bi₂O₃, thermal expansion, stability, bulk transport properties and oxygen exchange of bismuth oxide solid electrolytes are briefly discussed. Primary attention is focused on oxides with high ionic and mixed conductivity, including stabilized fluorite-type (δ) and sillenite (γ) phases of Bi₂O₃, γ-Bi₄V₂O₁₁ and other compounds of the aurivillius series. Another major point being addressed is on the applicability of these materials in high-temperature electrochemical cells, which is limited by numerous specific disadvantages of Bi₂O₃-based ceramics. The electrochemical properties of various electrode systems with bismuth oxide electrolytes are also briefly analyzed. Electronic Publication     

Combinatorics of q-Characters of Finite-Dimensional Representations of Quantum Affine Algebras

We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from [FR] and derive some of their corollaries. In particular, we prove that the tensor product of fundamental representations is reducible if and only if at least one of the pairwise normalized R-matrices has a pole. Received: 16 December 1999 / Accepted: 12 July 2000     

Research on the electrochemistry of oxygen ion conductors in the former Soviet Union

This review is focused on the analysis of experimental results on oxygen ion-conducting ceramic materials based on HfO₂, CeO₂, and ThO₂, published in the former Soviet Union. In particular, the physicochemical and transport properties of fluorite-related oxides and the characteristics of electronic conduction in these solid electrolytes are briefly reviewed. Emphasis is given to electrocatalytic and electrochemical properties of cerium-containing oxides, which are promising materials for electrodes of electrochemical cells operating in reducing atmospheres, and mixed-conducting membranes. A comparative analysis of specific features of the solid-electrolyte ceramics based on hafnia, zirconia, ceria, and thoria is performed in order to reveal basic tendencies of oxygen ionic transport in fluorite-type oxides, and to identify the potential applicability of these materials in various high-temperature electrochemical devices. Received: 23 September 1999 / Accepted: 10 October 1999     

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy).     

Linearizable Abel equations and the Gurevich–Pitaevskii problem

Applying symmetry reduction to a class of $\mathrm{SL}(2,\mathbb{R})$-invariant third-order ordinary differential equations (ODEs), we obtain Abel equations whose general solution can be parameterized by hypergeometric functions. Particular case of this construction provides a general parametric solution to the Kudashev equation, an ODE arising in the Gurevich–Pitaevskii problem, thus giving the first term of a large-time asymptotic expansion of its solution in the oscillatory (Whitham) zone.     

Recent advances in laser self-injection locking to high-Q microresonators

The stabilization and manipulation of laser frequency by means of an external cavity are nearly ubiquitously used in fundamental research and laser applications. While most of the laser light transmits through the cavity, in the presence of some back-scattered light from the cavity to the laser, the self-injection locking effect can take place, which locks the laser emission frequency to the cavity mode of similar frequency. The self-injection locking leads to dramatic reduction of laser linewidth and noise. Using this approach, a common semiconductor laser locked to an ultrahigh-Q microresonator can obtain sub-Hertz linewidth, on par with state-of-the-art fiber lasers. Therefore it paves the way to manufacture high-performance semiconductor lasers with reduced footprint and cost. Moreover, with high laser power, the optical nonlinearity of the microresonator drastically changes the laser dynamics, offering routes for simultaneous pulse and frequency comb generation in the same microresonator. Particularly, integrated photonics technology, enabling components fabricated via semiconductor CMOS process, has brought increasing and extending interest to laser manufacturing using this method. In this article, we present a comprehensive tutorial on analytical and numerical methods of laser self-injection locking, as well a review of most recent theoretical and experimental achievements.