Functions averages over the roots of unity,cauchy problems and addition formulas

An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions.     

Analytical layer-element solutions of Biot’s consolidation with anisotropic permeability and incompressible fluid and solid constituents

Based on the governing equations of 2D plane-strain Biot’s consolidation, the relationship between generalized displacements and stresses of a single soil layer with anisotropic permeability and incompressible fluid and solid constituents is described by an analytical layer-element, which is deduced in the Laplace–Fourier transform domain by using the eigenvalue approach. Taking the boundary conditions and the continuity of the soil layers into consideration, a global stiffness matrix is subsequently assembled and solved. As to the 3D case, the same derivation is employed after the application of a decoupling transformation. The actual solutions in the physical domain can further be acquired by inverting the Laplace–Fourier transform. Finally, numerical examples are carried out to verify the presented theory and discuss the influence of the anisotropic permeability on the consolidation behavior.     

Convergence results for a self-dual regularization of convex problems

We study a one-parameter regularization technique for convex optimization problems whose main feature is self-duality with respect to the Legendre–Fenchel conjugation. The self-dual technique, introduced by Goebel, can be defined for both convex and saddle functions. When applied to the latter, we show that if a saddle function has at least one saddle point, then the sequence of saddle points of the regularized saddle functions converges to the saddle point of minimal norm of the original one. For convex problems with inequality and state constraints, we apply the regularization directly on the objective and constraint functions, and show that, under suitable conditions, the associated Lagrangians of the regularized problem hypo/epi-converge to the original Lagrangian, and that the associated value functions also epi-converge to the original one. Finally, we find explicit conditions ensuring that the regularized sequence satisfies Slater's condition.     

An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Characterisation of PDO olive oil Chianti Classico by non-selective (UV–visible,NIR and MIR spectroscopy) and selective (fatty acid composition) analytical techniques

An authentication study of the Italian PDO (protected designation of origin) extra virgin olive oil Chianti Classico was performed; UV–visible (UV–vis), Near-Infrared (NIR) and Mid-Infrared (MIR) spectroscopies were applied to a set of samples representative of the whole Chianti Classico production area.     

A support for the identification of non-tryptic peptides based on low resolution tandem and sequential mass spectrometry data: The INSPIRE software

A simple software, to be used as an aid in the identification of non-tryptic peptides based on low resolution (3D-ion trap) tandem (MS/MS) and sequential (MS³) mass spectrometry data, is presented.     

A cation trap for anodic stripping voltammetry: NH3–plasma treated carbon nanotubes for adsorption and detection of metal ions

NH₃–plasma treated multi-walled carbon nanotubes (pn-MWCNTs) with cation traps for the detection of ultratrace quantities of Zn(II), Cd(II), Cu(II), and Hg(II) using square wave anodic stripping voltammetry (SWASV) is described. The pn-MWCNTs use their adsorption performance to enhance the sensitivity. It is found that under optimized conditions Zn(II), Cd(II), Cu(II) and Hg(II) were individually detected at potentials of −1.16, −0.78, −0.268 and 0.108 V, respectively. The detection limit (3σ method) of 0.314, 0.0272, 0.2263, and 0.1439 nM toward Zn(II), Cd(II), Cu(II), and Hg(II) is achievable, respectively. No interference could be seen during the simultaneous detection of Zn(II), Cd(II), Cu(II), and Hg(II). The pn-MWCNTs exhibit excellent selectivity owing to the different ability of adsorption. A study of the ability of pn-MWCNTs in practical application is carried out using a sample of water collected from Dongpu Reservoir in Hefei City, Anhui, China. It is found that the results were favorable when compared against inductively coupled plasma atomic emission spectrometry (ICP-AES) analysis.     

Studies of Space and Time Resolved Emission Measurements of an ArF Excimer Laser Ablated Plasma

Abstract

A laser ablated plasma created by an ArF excimer laser of wavelength of 193 nm, laser power of 150-200 mJ, repetition rate of 1 Hz, and zinc, copper, iron and nickel targets was studied. Quantitative emission studies are reported that are both space and time resolved. The space results of the laser ablated plasma suggest a confined plasma with a gaussian type distribution of atoms and ions. The time resolved studies show a maximum emission signal occurring at approximately 20 μs with a lifetime of less than 100 μs.     

Fluorescence Sensitization of Aqueous Terbium and Europium Ions Without Aromatic Donors or Synergistic Agents

Abstract

EDTA and DTPA complexes of terbium and europium are excited at wavelengths below 250 nm. producing the typical lanthanide emission through energy transfer from the complex to the coordinated metal. This allows determination of these rare earth ions in water without solvent extraction, the use of synergistic agents, or aromatic sensitizers. Terbium-EDTA has the most efficient energy transfer, 31%, giving a 165-fold emission enhancement and a limit of detection of 6 × 10^?7 M. Calibration curves are linear over a concentration range spanning three orders of magnitude. The characteristic lanthanide ion emission is obtained in all cases, but the excitation of the complexes is pH dependent, showing intensity increases up to pH 12. Mild interference by alkali and alkaline earth metals was overcome by increasing the ligand concentration, but transition metal interference was more severe. Only minor enhancement was observed at higher ligand/metal ratios.     

A numerical analysis of a class of generalized Boussinesq‐type equations using continuous/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ²ⁿ⁺²) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P₂ Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd.