Determination of the surface parameters for aspheric aphakic lenses

Two methods are proposed for aspherical surface evaluation — scanning and interferometry. Each of these methods enables the determination of the radius of curvature at the lens vertex, the asphericity, astigmatism, rotation asymmetry, surface topography and the deviation of the surface from following the theoretically stated shape. While the scanning technique is low cost and simple, the interferometric technique (which needs optical arrangements) gives more information about the surface quality. These methods, combined with a computer, establish powerful instruments for controlling lens production.     

Abelian varieties and the general Hodge conjecture

We investigate the relationship between the usual and general Hodgeconjectures for abelian varieties. For certain abelian varieties A, weshow that the usual Hodge conjecture for all powers of A implies thegeneral Hodge conjecture for A.     

Method Development and Quantitative Elemental Analysis of Mentha Longifolia L. Leaves from Saudi Arabia by Total Reflection X-Ray Fluorescence

A method has been developed for the quantitative elemental analysis of Mentha longifolia L. leaves collected from different cities in Saudi Arabia using total reflection X-ray fluorescence. Using a microwave digestion system, 100?mg of each sample was completely digested using 3?mL of nitric acid and 2?mL of hydrogen peroxide. The stabilization of the digested samples on the silicon reflectors was studied using a silicone solution and polyvinyl alcohol. 5?µL of either silicone solution or polyvinyl alcohol (1% m/v) was pipetted and dried on the silicon reflector prior to the deposition of the digested samples. It was recognized that there is some enhancement on the intensity of the peak area with the silicone solution at photon energies less than 11?keV. However, the obtained results confirm the ability of using silicone solution or polyvinyl alcohol (1% m/v) as the stabilizer prior to the deposition of the sample droplet on the quartz reflector. However, the silicone solution was more applicable. Based on the developed method, 15 elements were quantified, namely, P, S, Cl, K, Ca, Ti, Cr, Mn, Fe, Cu, Zn, Br, Rb, Sr, and Ba. Based on the present quantitative analysis results, M. longifolia samples collected from Al-Madina city had the highest concentration of P, Cl, K, Ti, Fe, Ni, and Cu. The lowest concentrations of P, S, Cl, K, Mn, Ni, and Br were found in Taif-Shafa.     

Molecular interaction of N-formylmorpholine with alkanols,a spectroscopic study

The interactions of N-formylmorpholine (NFM) with different alkanols were monitored using proton nuclear magnetic resonance and IR spectroscopy. It was found that the NFM interaction with alkanols decreases with increasing length and branching of the alkanols. A good correlation was obtained between the proton chemical shift and the volume of mixing of alkanols with NFM.     

Long-chain ammonium fluoride salts as universal analytical reagents for total anion determination

Lipophilic quaternary ammonium cations are insoluble in water when paired with any anion except fluoride or hydroxide. This phenomenon is the basis for a novel method for total anion determination. Tetra-n-octylammonium fluoride (TOAF) is used for the direct titration of any anion or mixture of anions with the exception of hydroxide. Anions for which no direct analytical method exists, e.g., nitrate or hydrogenfluoride (HF₂^?), are simply assayed by conductimetric titration with TOAF reagent.     

Studying the effect of using low-discrepancy sequences to initialize population-based optimization algorithms

In this paper, we investigate the use of low-discrepancy sequences to generate an initial population for population-based optimization algorithms. Previous studies have found that low-discrepancy sequences generally improve the performance of a population-based optimization algorithm. However, these studies generally have some major drawbacks like using a small set of biased problems and ignoring the use of non-parametric statistical tests. To address these shortcomings, we have used 19 functions (5 of them quasi-real-world problems), two popular low-discrepancy sequences and two well-known population-based optimization methods. According to our results, there is no evidence that using low-discrepancy sequences improves the performance of population-based search methods.     

Solving bilinear tensor least squares problems and application to Hammerstein identification

Bilinear tensor least squares problems occur in applications such as Hammerstein system identification and social network analysis. A linearly constrained problem of medium size is considered, and nonlinear least squares solvers of Gauss–Newton‐type are applied to numerically solve it. The problem is separable, and the variable projection method can be used. Perturbation theory is presented and used to motivate the choice of constraint. Numerical experiments with Hammerstein models and random tensors are performed, comparing the different methods and showing that a variable projection method performs best.