Neoteric optical media for refractive index determination of gems and minerals

Refractive index determination of minerals and gems often requires their immersion in fluids with the same refractive index. However, these natural materials frequently have refractive indices above the ranges of common organic solvents. Most available high refractive index immersion materials are solid at room temperature, toxic, noxious, corrosive, carcinogenic, or any combination thereof. Since the physical properties of ionic liquids can be tuned by varying the cation and/or anion, we have developed immersion fluids for mineralogical studies which are relatively benign. We report here the syntheses of a range of ionic liquids ( many novel) based on the 1-alkyl-3-methylimidazolium cation, which all have refractive indices greater than 1.4, and can be used as immersion fluids for optical mineralogy studies. We further show that for a series of ionic liquids with the same anion, the refractive indices can be adjusted by systematic changes in the cation.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

A hierarchical multiclass support vector machine incorporated with holistic triple learning units

This paper proposes a new hierarchical learning structure, namely the holistic triple learning (HTL), for extending the binary support vector machine (SVM) to multi-classification problems. For an N-class problem, a HTL constructs a decision tree up to a depth of A leaf node of the decision tree is allowed to be placed with a holistic triple learning unit whose generalisation abilities are assessed and approved. Meanwhile, the remaining nodes in the decision tree each accommodate a standard binary SVM classifier. The holistic triple classifier is a regression model trained on three classes, whose training algorithm is originated from a recently proposed implementation technique, namely the least-squares support vector machine (LS-SVM). A major novelty with the holistic triple classifier is the reduced number of support vectors in the solution. For the resultant HTL-SVM, an upper bound of the generalisation error can be obtained. The time complexity of training the HTL-SVM is analysed, and is shown to be comparable to that of training the one-versus-one (1-vs.-1) SVM, particularly on small-scale datasets. Empirical studies show that the proposed HTL-SVM achieves competitive classification accuracy with a reduced number of support vectors compared to the popular 1-vs-1 alternative.

Optical Fiber Refractive Index Sensor for Chloride Ion Monitoring

The development of a reflective, gold-coated long-period grating-based sensor for the measurement of chloride ions in solution is discussed. The sensor scheme is based around a long-period fiber grating (LPG)-based Michelson interferometer where the sensor was calibrated and evaluated in the laboratory using sodium chloride solutions, over a wide range of concentrations, from 0.01 to 4.00 M. The grating response creates shifts in the spectral characteristic of the interferometer, formed using the LPG and a reflective surface on the distal end of the fiber, due to the change of refracting index of the solution surrounding it. It was found that the sensitivity of the device could be enhanced over that obtained from a bare fiber by coating the LPG-based interferometer with gold nanoparticles and the results of a cross-comparison of performance were obtained and details discussed. The approach will be explored as a basis to create a portable, low-power device, developed with the potential for installation in concrete structures to determine the ingress of chloride ions, operating through monitoring the refractive index change.