Controlling X‐ray deformable mirrors during inspection

The X‐ray deformable mirror (XDM) is becoming widely used in the present synchrotron/free‐electron laser facilities because of its flexibility in correcting wavefront errors or modification of the beam size at the sample location. Owing to coupling among the N actuators of an XDM, (N + 1) or (2N + 1) scans are required to learn the response of each actuator one by one. When the mirror has an important number of actuators (N) and the actuator response time including stabilization or the necessary metrology time is long, the learning process can be time consuming. In this work, a fast and accurate method is presented to drive an XDM to a target shape usually with only three or four measurements during inspection. The metrology data are used as feedback to calculate the curvature discrepancy between the current and the target shapes. Three different derivative estimation methods are introduced to calculate the curvature from measured data. The mirror shape is becoming close to the target through iterative compensations. The feasibility of this simple and effective approach is demonstrated by a series of experiments.     

Efficient removal of cadmium and 2-chlorophenol in aqueous systems by natural clay: Adsorption and photo-Fenton degradation processes

Adsorption and photo-Fenton processes were used as handy tools to ascertain the capability of natural clays to remove cadmium (Cd) and 2-chlorophenol (2-CP) from aqueous solution. Natural Fe-rich clay collected from Tejera-Esghira in Medenine area, south Tunisia, was used as a catalyst in the heterogeneous photo-Fenton oxidation of 2-CP in aqueous solution. Clay samples were acid activated to improve their adsorptive capacity for the removal of Cd. Experimental results indicated that the adsorption of Cd ions onto natural red clay of Tejera-Esghira followed the pseudo-second-order kinetic model. Langmuir model was found to describe the equilibrium data with the calculated maximum adsorption capacity of 23.59 mg g^?1 for acid-activated clay. Photo-Fenton experiments proved high activity of the natural clay catalyst, which was able to completely degrade the phenol present in the treated solution after 30 min and in the presence of ultraviolet light C (UV-C). Total organic carbon and gas chromatography analysis confirmed a 2-CP degradation mechanism toward an almost complete mineralization of the organic compound.     

Electrochemical Properties of Substituted 2‐Methyl‐1,4‐Naphthoquinones: Redox Behavior Predictions

In the context of the investigation of drug‐induced oxidative stress in parasitic cells, electrochemical properties of a focused library of polysubstituted menadione derivatives were studied by cyclic voltammetry. These values were used, together with compatible measurements from literature (quinones and related compounds), to build and evaluate a predictive structure–redox potential model (quantitative structure–property relationship, QSPR). Able to provide an online evaluation (through Web interface) of the oxidant character of quinones, the model is aimed to help chemists targeting their synthetic efforts towards analogues of desired redox properties     

The Dunkl Oscillator in the Plane II: Representations of the Symmetry Algebra

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger–Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra \({\mathfrak{u}(2)}\) . Two of the symmetry generators, J ₃ and J ₂, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J ₃ is diagonal and the operator J ₂ acts in a tridiagonal fashion. In the circular basis, the operator J ₂ is block upper-triangular with all blocks 2 × 2 and the operator J ₃ acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J ₂ in the circular basis are generated by the Heun polynomials, and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J ₂ are generated by little ?1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J ₂ is diagonal is considered. In this basis, the defining relations of the Schwinger–Dunkl algebra imply that J ₃ acts in a block tridiagonal fashion with all blocks 2 × 2. The matrix elements of J ₃ in this basis are given explicitly.     

Isomerization mechanism in hydrazone-based rotary switches: lateral shift, rotation, or tautomerization?

Two intramolecularly hydrogen-bonded arylhydrazone (aryl = phenyl or naphthyl) molecular switches have been synthesized, and their full and reversible switching between the E and Z configurations have been demonstrated. These chemically controlled configurational rotary switches exist primarily as the E isomer at equilibrium and can be switched to the protonated Z configuration (Z-H(+)) by the addition of trifluoroacetic acid. The protonation of the pyridine moiety in the switch induces a rotation around the hydrazone C=N double bond, leading to isomerization. Treating Z-H(+) with base (K(2)CO(3)) yields a mixture of E and "metastable" Z isomers. The latter thermally equilibrates to reinstate the initial isomer ratio. The rate of the Z → E isomerization process showed small changes as a function of solvent polarity, indicating that the isomerization might be going through the inversion mechanism (nonpolar transition state). However, the plot of the logarithm of the rate constant k vs the Dimroth parameter (E(T)) gave a linear fit, demonstrating the involvement of a polar transition state (rotation mechanism). These two seemingly contradicting kinetic data were not enough to determine whether the isomerization mechanism goes through the rotation or inversion pathways. The highly negative entropy values obtained for both the forward (E → Z-H(+)) and backward (Z → E) processes strongly suggest that the isomerization involves a polarized transition state that is highly organized (possibly involving a high degree of solvent organization), and hence it proceeds via a rotation mechanism as opposed to inversion. Computations of the Z ? E isomerization using density functional theory (DFT) at the M06/cc-pVTZ level and natural bond orbital (NBO) wave function analyses have shown that the favorable isomerization mechanism in these hydrogen-bonded systems is hydrazone-azo tautomerization followed by rotation around a C-N single bond, as opposed to the more common rotation mechanism around the C=N double bond.     

Further prenylated flavonols from Platanus acerifolia’s unripe buds

In addition to the methylated and prenylated flavonoids previously reported from Platanus acerifolia, the multistep chromatographic processing of the toluene extract of defatted fresh unripe buds resulted in the isolation of 8 metabolites. They corresponded to 5,7-dihydroxychromone, strobopinin [(2S)-5,7-dihydroxy-6-C-methylflavanone] as well as to six prenylated flavonols. Divided into two groups of three isomers, these C₅-substituted flavonols are derived from either galangin (5,7-dihydroxyflavonol) or kaempferide (5,7-dihydroxy-4′-methoxyflavonol). Four of them, unknown in the plant kingdom and with either open or cyclized C₅ chain, are discussed for the ¹³C NMR chemical shift variations when going from the open side C₅ chain to the cyclized chain isomers.     

Electrodialytic desalination of brackish water: effect of process parameters and water characteristics

The aim of this work is to study the desalination of brackish water using a laboratory scale electrodialysis cell. The influence of several parameters, such as flow rates, initial feed concentration, applied voltage and circulation mode on process efficiency were studied. This efficiency is evaluated by the demineralization rate, ionic flux transport and current efficiency. In this study, experiments were carried out on synthetic brackish water solutions prepared from sodium chloride salts. The concentrations of these solutions are varying from 0.5 to 3 g L^?1. The process was applied for the treatment of real brackish water sample with total dissolved salts ～5 g L^?1. The concentrations of different species in the obtained treated water are below the amounts recommended by World Health Organization for drinking water.     

Strong asymptotics for Krawtchouk polynomials

We determine the strong asymptotics for the class of Krawtchouk polynomials on the real line. We show how our strong asymptotics describes the limiting distribution of the zeros of the Krawtchouk polynomials.     

Discriminants and Functions of the Second Kind of Orthogonal Polynomials

We consider the problem of evaluating discriminants of general orthogonal polynomials. It is shown that for a general class of weight functions, the functions of the second kind and the orthogonal polynomials are linear independent solutions of the same second order differential equation. We derive a linear fourth-order differential equation satisfied by the numerator polynomials and give two additional linear independent solutions.     

Scheduling: Agreement graph vs resource constraints

We investigate two scheduling problems. The first is scheduling with agreements (SWA) that consists in scheduling a set of jobs non-preemptively on identical machines in a minimum time, subject to constraints that only some specific jobs can be scheduled concurrently. These constraints are represented by an agreement graph. We extend the NP-hardness of SWA with three distinct values of processing times to only two values and this definitely closes the complexity status of SWA on two machines with two fixed processing times. The second problem is the so-called resource-constrained scheduling. We prove that SWA is polynomially equivalent to a special case of the resource-constrained scheduling and deduce new complexity results of the latter.