Normal sequences over finite abelian groups

In this note, we obtain the structure of short normal sequences over a finite abelian p-group or a finite abelian group of rank two, thus answering positively a conjecture of Gao and Zhuang for various groups. The results obtained here improve all known results on this conjecture.     

A simple four-unknown refined theory for bending analysis of functionally graded plates

In the present paper, a refined trigonometric higher-order plate theory is simply derived, which satisfies the free surface conditions. Moreover, the number of unknowns of this theory is the least one comparing with other shear theories. The effects of transverse shear strains as well as the transverse normal strain are taken into account. The number of unknown functions involved in the present theory is only four as against six or more in case of other shear and normal deformation theories. The bending response of FG rectangular plates is presented. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory. Additional results for all displacements and stresses are investigated through-the-thickness of the FG rectangular plate.     

Bayesian Growth Curves Using Normal Mixtures With Nonparametric Weights

Reference growth curves estimate the distribution of a measurement as it changes according to some covariate, often age. We present a new methodology to estimate growth curves based on mixture models and splines. We model the distribution of the measurement with a mixture of normal distributions with an unknown number of components, and model dependence on the covariate through the weights, using smooth functions based on B-splines. In this way the growth curves respect the continuity of the covariate and there is no need for arbitrary grouping of the observations. The method is illustrated with data on triceps skinfold in Gambian girls and women.     

Quaternionic Cayley transform revisited

A Cayley type transform in the context of quaternions (previously introduced by the author) is revisited. A simplified definition is given and shorter proofs are exhibited. As new results, the range of this transform restricted to a class of unbounded normal operators is described, and an application to a moment problem with constraints is given. The extension problem to normal operators in this new context is also revisited.     

Powers and direct sums

This paper investigates when a bounded operator on Hilbert space has the property that its square is similar to to the direct sum of it with itself. A few general results are obtained and the normal operators and unilateral shifts having this property are characterized. Several additional examples are explored.     

Individual loss reserving using paid–incurred data

This paper develops a stochastic model for individual claims reserving using observed data on claim payments as well as incurred losses. We extend the approach of Pigeon et al. (2013), designed for payments only, towards the inclusion of incurred losses. We call the new technique the individual Paid and Incurred Chain (iPIC) reserving method. Analytic expressions are derived for the expected ultimate losses, given observed development patterns. The usefulness of this new model is illustrated with a portfolio of general liability insurance policies. For the case study developed in this paper, detailed comparisons with existing approaches reveal that iPIC method performs well and produces more accurate predictions.     

Evaluation of new silica‐based humic acid stationary phase for the separation of tocopherols in cold‐pressed oils by normal‐phase high‐performance liquid chromatography

A new humic acid stationary phase was prepared by immobilizing humic acid onto aminopropyl silica via an amide linkage formation and used, for the first time, for the separation and quantification of the tocopherol compounds in cold‐pressed oil samples under normal‐phase high‐performance liquid chromatography conditions. Parameters affecting the chromatographic separation such as mobile phase composition and flow rate were optimized. By evaluating the calculations of capacity factor, asymmetry factor, resolution, selectivity factor, and theoretical plate number, the best separation was obtained with isocratic elution of n‐hexane and isopropyl alcohol (99:1% v/v) at a flow rate of 1.0 mL/min. The effluent was monitored by a fluorescence detector set at excitation and emission wavelengths 295 and 330 nm, respectively. All compounds were separated in 20 min. The method was validated according to international guidelines and found to be linear in a wide concentration range, also the mean recovery of the compounds ranged from 97.9 to 99.2%, with a CV less than 2.7% in all cases. The results showed that the developed stationary phase is suitable for the separation and quantification of the tocopherol compounds in real oil samples.     

Limit theorems for functionals of two independent Gaussian processes

Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. A new and interesting phenomenon is that, in comparison with the results for fractional Brownian motion, extra randomness appears in the limiting distributions for Gaussian processes with nonstationary increments, say sub-fractional Brownian motion and bi-fractional Brownian. The results are obtained based on the method of moments, in which Fourier analysis, the chaining argument introduced in [11] and a pairing technique are employed.     

The observation of sonic range velocities of normal zone propagation in high current density superconductor

The sonic range velocities of normal zone propagation in high current density superconductor were observed. The experimental results were obtained on samples of 0.16–0.11 mm thickness of a monofilamentary NbTi wire with critical current density J_c about 10⁶ A/cm². The s→n change of the sample sections was recorded after the normal zone stimulation by the magnetic field impulse. The voltage increasing speed reached 1.5×10⁷ V/s, and the normal zone propagation velocity exceeded 5±1 km/s. This high velocity can be caused by the detonation-like propagation of normal phase in superconductor with high current density.     

NACE–ESI-MS/MS method for separation and characterization of phosphorylation and acylation isomers of lipid A

Lipid A represents a heterogeneous group of bacterial outer membrane phosphoglycolipids, which play a major role in the pathogenesis of Gram-negative sepsis. The number and position of phosphoryl and acyl groups in lipid A molecules are key structural determinants in their bioactivities. In this study, a NACE–ESI-MS/MS method was developed for the simultaneous analysis of lipid A isomers possessing a different degree of phosphorylation and acylation. Various C4’- and C1-monophosphorylated lipid A isobars, as well as acylation isomers, were baseline separated within 43 min in a separation medium of methanol/dichloromethane/triethylamine/acetic acid 60:40:1.08:0.36 (v/v/v/v). Both normal and reverse CE polarities could be applied for proper detection of the analytes owing to the combination of a suction effect caused by the nebulizer gas at the outlet end of the capillary and external pressure applied on the inlet vial. The separated lipid A species could be identified unequivocally by their characteristic fragmentation patterns through CID performed in both negative- and positive-ionization modes. The uniqueness of the NACE–ESI-MS/MS method lies in its simplicity and reliability for proving the phosphorylation isomerism (C1 or C4’) and acylation pattern of native lipid A species or those designed for therapeutic applications.