On a Zero-Sum Generalization of a Variation of Schur’s Equation

Let be a positive integer, and let denote the cyclic group of residues modulo m. Furthermore, let denote the minimum integer N such that for every function there exist m integers satisfying and (and ). It is shown that for every odd prime m. Daniel Schaal: Partially supported by a South Dakota Governor’s 2010 Individual Research Seed Grant.     

Porosity dependence of electron percolation in nanoporous TiO2 layers

The electron diffusion coefficient at varying porosity has been determined in a series of nanostructured TiO(2) films of different initial thicknesses. The porosity was changed by applying different pressures prior to sintering, thereby modifying the internal morphology of the films though not their chemical and surface conditions. A systematic increase of the effective diffusion coefficient was observed as the porosity was decreased, indicating the improvement of the internal connectivity of the network of nanoparticles. The experimental results have been rationalized using percolation theory. First of all, applying a power law dependence, the diffusion coefficient as a function of porosity from different films collapsed in a single master curve. In addition, application of the models of effective medium approximation (EMA) allows us to compare the experimental results with previous data from Monte Carlo simulation. The different data show a similar dependence in agreement with the EMA predictions, indicating that the geometrical effect of electron transport due to variation of porous morphology in TiO(2) nanoparticulate networks is well described by the percolation concept.     

Self-optimizing charge-transfer energy phenomena in metallosupramolecular complexes by dynamic constitutional self-sorting

In this paper we report an extended series of 2,6-(iminoarene)pyridine-type ZnII complexes [(Lii)2Zn]II, which were surveyed for their ability to self-exchange both their ligands and their aromatic arms and to form different homoduplex and heteroduplex complexes in solution. The self-sorting of heteroduplex complexes is likely to be the result of geometric constraints. Whereas the imine-exchange process occurs quantitatively in 1:1 mixtures of [(Lii)2Zn]II complexes, the octahedral coordination process around the metal ion defines spatial-frustrated exchanges that involve the selective formation of heterocomplexes of two, by two different substituents; the bulkiest ones (pyrene in principle) specifically interact with the pseudoterpyridine core, sterically hindering the least bulky ones, which are intermolecularly stacked with similar ligands of neighboring molecules. Such a self-sorting process defined by the specific self-constitution of the ligands exchanging their aromatic substituents is self-optimized by a specific control over their spatial orientation around a metal center within the complex. They ultimately show an improved charge-transfer energy function by virtue of the dynamic amplification of self-optimized heteroduplex architectures. These systems therefore illustrate the convergence of the combinatorial self-sorting of the dynamic combinatorial libraries (DCLs) strategy and the constitutional self-optimized function.     

Noncollinear double quasi phase matching in one-dimensional poled crystals

We demonstrate simultaneous phase matching of two different nonlinear processes, using a noncollinear interaction in periodically poled crystal with single grating. The noncollinear scheme provides phase-matching solutions over continuous regions of the optical spectrum and can be used for multiple-harmonic generation as well as all-optical effects. We have demonstrated experimentally third-harmonic generation of a 3 microm pump wavelength in a noncollinear configuration using a periodically poled LiNbO3 crystal. We observed, in good agreement with theoretical calculation, very broad spectral and thermal acceptance bandwidths, as well as a relatively narrow angular bandwidth.     

Determination of pesticides in river water using rotating disk sorptive extraction and gas chromatography-mass spectrometry

The rotating disk sorptive extraction (RDSE) technique was applied to the determination of pesticides in aqueous samples. Pesticides of different polarities were considered in this study: chlorpyrifos, diazinon, fenvalarate, cyhalothrin, cypermethrin, lindane and malathion. The sorptive/desorptive behavior of the pesticides was studied using a rotating disk containing a polydimethylsiloxane (PDMS) phase on one of its surfaces. The analyte polarity was a significant factor in the extraction time; shorter extraction times were required for the more apolar pesticides. The optimum variables for the extraction of all analytes were: extraction time of 3 h, sample volume of 25 mL, rotational velocity of the disk 1250 rpm, desorption time of 30 min using methanol. For pesticides with values of Log K_ow > 4, the extraction time can be reduced to 30 min for a quantitative extraction. Under these conditions, recoveries between 76% and 101% were obtained for the target pesticides, and the repeatability of the methodology, expressed as relative standard deviation, was determined to be between 10% and 20%. Additionally, the limits of detection of the analytes were lower than 3.1 μg L⁻¹. The extraction method developed using the RDSE was compared to a stir bar sorptive extraction (SBSE) under the same conditions. It can be observed that the extraction using the rotating disk offers higher recoveries because of its higher PDMS volume and its higher surface area to volume ratio that allows for improved mass transfer.     

Surface grafting of a thermoplastic polyurethane with methacrylic acid by previous plasma surface activation and by ultraviolet irradiation to reduce cell adhesion

The material performance, in a biological environment, is mainly mediated by its surface properties and by the combination of chemical, physical, biological, and mechanical properties required, for a specific application.In this study, the surface of a thermoplastic polyurethane (TPU) material (Elastollan^®1180A50) was activated either by plasma or by ultra-violet (UV) irradiation. After surface activation, methacrylic acid (MAA) was linked to the surface of TPU in order to improve its reactivity and to reduce cell adhesion. Grafted surfaces were evaluated by X-ray photoelectron spectroscopy (XPS), by atomic force microscopy (AFM) and by contact angle measurements. Blood compatibility studies and cell adhesion tests with human bone marrow cells (HBMC) were also performed.If was found that UV grafting method led to better results than the plasma activation method, since cell adhesion was reduced when methacrylic acid was grafted to the TPU surface by UV.     

The geometric phase in nonlinear frequency conversion

The geometric phase of light has been demonstrated in various platforms of the linear optical regime, raising interest both for fundamental science as well as applications, such as flat optical elements. Recently, the concept of geometric phases has been extended to nonlinear optics, following advances in engineering both bulk nonlinear photonic crystals and nonlinear metasurfaces. These new technologies offer a great promise of applications for nonlinear manipulation of light. In this review, we cover the recent theoretical and experimental advances in the field of geometric phases accompanying nonlinear frequency conversion. We first consider the case of bulk nonlinear photonic crystals, in which the interaction between propagating waves is quasi-phase-matched, with an engineerable geometric phase accumulated by the light. Nonlinear photonic crystals can offer efficient and robust frequency conversion in both the linearized and fully-nonlinear regimes of interaction, and allow for several applications including adiabatic mode conversion, electromagnetic nonreciprocity and novel topological effects for light. We then cover the rapidly-growing field of nonlinear Pancharatnam-Berry metasurfaces, which allow the simultaneous nonlinear generation and shaping of light by using ultrathin optical elements with subwavelength phase and amplitude resolution. We discuss the macroscopic selection rules that depend on the rotational symmetry of the constituent meta-atoms, the order of the harmonic generations, and the change in circular polarization. Continuous geometric phase gradients allow the steering of light beams and shaping of their spatial modes. More complex designs perform nonlinear imaging and multiplex nonlinear holograms, where the functionality is varied according to the generated harmonic order and polarization. Recent advancements in the fabrication of three dimensional nonlinear photonic crystals, as well as the pursuit of quantum light sources based on nonlinear metasurfaces, offer exciting new possibilities for novel nonlinear optical applications based on geometric phases.     

Hydrazine borane: synthesis, characterization, and application prospects in chemical hydrogen storage

Hydrazine borane (N(2)H(4)BH(3)) is the novel boron- and nitrogen-based material appearing to be a promising candidate in chemical hydrogen storage. It stores 15.4 wt% of hydrogen in hydridic and protic forms, and the challenge is to release H(2) with maximum efficiency, if possible all hydrogen stored in the material. An important step to realize this ambitious goal is to synthesize HB with high yields and high purity, and to characterize it fully. In this work, we report a 2-step synthesis (salt metathesis and solvent extraction-drying) through which N(2)H(4)BH(3) is successfully obtained in 3 days, with a yield of about 80% and a purity of 99.6%. N(2)H(4)BH(3) was characterized by NMR, IR, XRD, TGA and DSC, its stability in dioxane and water was determined, and its thermolysis by-products were characterized. We thus present a complete data sheet that should be very useful for future studies. Furthermore, we propose a discussion on the potential of HB (with H(2) released by either thermolysis or hydrolysis) in chemical hydrogen storage.