Amperometric Detection of 4‐Chlorophenol on Two Types of Expanded Graphite Based Composite Electrodes

The assessment of an expanded graphite‐Ag‐zeolite‐epoxy composite (EG‐Z‐Ag‐Epoxy) electrode for the determination of 4‐chlorophenol (4‐CP) is described and compared to the corresponding expanded graphite‐epoxy composite (EG‐Epoxy) electrode. Cyclic voltammetry was used to characterize the electrochemical behavior and determination of 4‐CP at both electrodes in 0.1 M Na₂SO₄ and 0.1 M NaOH supporting electrolytes. A substantial enhancement of sensitivity for the determination of 4‐CP at the EG‐Z‐Ag‐Epoxy electrode was reached by applying a chemical preconcentration step prior to voltammetric quantification. Also, under these last conditions the lowest limit of detection of 1 μM illustrates the analytical versatility of this electrode in a concentration range where aquatic 4‐chlorophenol pollution is known to occur.     

Enzymatic Oxygen Microsensor Based on Bilirubin Oxidase Applied to Microbial Fuel Cells Analysis

A selective oxygen biosensor based on bilirubin oxidase (BOx) was developed. The sensor was used for determining oxygen profiles in a membraneless, single‐chamber microbial fuel cell (SCMFC), fed with raw wastewater. The linear response of the sensor was optimized by a diffusion layer of silica gel. A computer‐controlled stage was used to obtain accurate and precise measurements. Oxygen concentration in biofilms covering electrodes was measured, showing 3 mg L^?1 of O₂ in the bulk solution, decreasing to 0 mg L^?1 in the cathodic biofilm. The MFC generated power in the range of 0–0.08 mW, associated to the oxygen content.     

A complete 1H and 13C NMR data assignment for 3-phenylmethylene-1H,3H-naphtho-[1,8-c,d]-pyran-1-one

Complete assignments of the 1H and 13C NMR chemical shifts for 3-phenylmethylene-1H,3H-naphtho-[1,8-c,d]-pyran-1-one were done by means of one- and two-dimensional NMR techniques, including 1H-(1)H COSY, HMQC and HMBC spectra. Ab initio quantum chemistry calculations and a shift prediction by an incremental method provided values close to the proposed assignments. All mid-IR spectral bands are given as reference data. The DRIFT FTIR, ATR FTIR and Raman spectra are given as a Supplementary data in JCAMP-DX format, version 4.24. In addition, a method of compound's synthesis, that has the product yield higher as compared to already known data in the literature, is given.     

The central polynomials for the Grassmann algebra

In this paper we describe the central polynomials for the infinite-dimensional unitary Grassmann algebra G over an infinite field F of characteristic ≠ 2. We exhibit a set of polynomials that generates the vector space C(G) of the central polynomials of G as a T-space. Using a deep result of Shchigolev we prove that if charF = p > 2 then the T-space C(G) is not finitely generated. Moreover, over such a field F, C(G) is a limit T-space, that is, C(G) is not a finitely generated T-space but every larger T-space W ≩ C(G) is. We obtain similar results for the infinite-dimensional nonunitary Grassmann algebra H as well.     

A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES

A new method for Total Least Squares (TLS) problems is presented. It differs from previous approaches and is based on the solution of successive Least Squares problems.The method is quite suitable for Structured TLS (STLS) problems. We study mostly the case of Toeplitz matrices in this paper. The numerical tests illustrate that the method converges to the solution fast for Toeplitz STLS problems. Since the method is designed for general TLS problems, other structured problems can be treated similarly.     

Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

One dimensional Dirac operators $L_{bc}\left(v\right)y=i\left(\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill ?1\hfill \end{array}\right)\frac{dy}{dx}+v\left(x\right)y\text{,}y=\left(\begin{array}{c}\hfill y_1\hfill \\ \hfill y_2\hfill \end{array}\right)\text{,}x\in [0,\pi ]\text{,}$ considered with $L^2$-potentials $v\left(x\right)=\left(\begin{array}{cc}\hfill 0\hfill & \hfill P\left(x\right)\hfill \\ \hfill Q\left(x\right)\hfill & \hfill 0\hfill \end{array}\right)$ and subject to regular boundary conditions ($bc$), have discrete spectrum. For strictly regular $bc$, the spectrum of the free operator $L_{bc}\left(0\right)$ is simple while the spectrum of $L_{bc}\left(v\right)$ is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval $[0,\pi ]$. Analogous results are obtained for regular but not strictly regular $bc$.     

Accurate and efficient evaluation of Schur and Jack functions

We present new algorithms for computing the values of the Schur and Jack functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data ( 0$">) and run in time that is only linear in .

     

Heat kernel expansions on the integers and the Toda lattice hierarchy

We consider the heat equation u _t = Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients α _k (n, m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schr?dinger operator. We derive an explicit formula for α _k in terms of the wave and the adjoint wave functions of the Toda lattice hierarchy. As a first application of this result, we prove that the values of these coefficients on the diagonals n = m and n = m + 1 define a hierarchy of differential-difference equations which is equivalent to the Toda lattice hierarchy. Using this fact and the correspondence between commutative rings of difference operators and algebraic curves we show that the fundamental solution can be summed up, giving a finite formula involving only two Bessel functions with polynomial coefficients in the time variable t, if and only if the operator L belongs to the family of bispectral operators constructed in [18].