On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

Computer-assisted optimization of selectivity by tuning temperature and carrier gas pressure drop in two GC capillary columns coupled in series

The paper shows a computer-assisted procedure for the optimization of selectivity of two columns coupled in series by tuning the working temperature (using the isothermal mode) and columns coupling-point pressure at constant inlet and outlet carrier gas pressures. The optimization procedure validation was tested by the separation of 32 hydrocarbons in a column series with the aim to resolve the maximum number of components in the shortest possible analysis time.Dedicated to Professor J. F. K. Huber on the occasion of his 65th birthday     

Flow and heat transfer with prescribed skin friction in a rotating fluid

This paper investigates the rotating flow and heat transfer of a viscous fluid induced by a stretching surface. The nonlinear problem subject to a given skin friction at the boundary is solved. Analytic solution is obtained using homotopy analysis method. The velocity, temperature, and stretching velocity is calculated for different values of the rotation parameter (λ). The obtained results are compared with the well known results of rotating flow induced by a stretching surface by using four sets of boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Tuning the mesogenic properties of 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals: the effect of a phenoxy end-group in two sterically equivalent series

Two sterically equivalent series of phenoxy-terminated 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals were synthesised, and their mesogenic properties were characterised by polarised optical microscopy and differential scanning calorimetry (DSC). The phenoxy end-group causes a significant increase in melting point and inhibits – at least partially – the mesomorphism of these materials relative to the parent isomers; in most cases, the broad enantiotropic SmC phase formed by the parent isomers is suppressed by the addition of the phenoxy end-group. However, detailed analyses by small-angle X-ray scattering and monodomain 2D X-ray scattering suggest that these compounds form a SmA phase with a partially intercalated bilayer structure in which the phenoxy end-groups are nanosegregated. Such an intercalated bilayer structure might enable the tuning of smectogenic properties by appropriate substitution of the phenoxy end-groups.     

On the estimation of nonlinear time series models

In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates     

Automatic β-expansions of formal Laurent series over finite fields

We consider β-expansions of formal Laurent series over finite fields. If the base β is a Pisot or Salem series, we prove that the β-expansion of a Laurent series α is automatic if and only if α is algebraic.     

A Note on twin primes and the modular ring Z 6

The modular ring ?₆ defines integers via (6r _i + (i ? 3)) where i is the class and r _i the row when tabulated in an array. Since only Classes 2₆ and 4₆ contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.     

Signal modeling using the gradient search

This letter presents a new method for continuous signal modeling. Firstly, the continuous signal can be represented as a function of the trigonometric functional extension (Fourier series). Fourier series of the signal are parameterized by the fundamental frequency and unknown parameters. Then, the gradient-based iterative identification algorithm is derived, for estimating parameters of the signal model with known and unknown frequencies, separately. Finally, the simulation results indicate that the proposed algorithm is effective.     

Anion effects on the phase transition of N‐isopropylacrylamide hydrogels

NMR spectra were collected for poly(N‐isopropylacrylamide) (PNIPAAm) hydrogel using high‐resolution magic angle spinning (HRMAS) after gel pieces were hydrated in the presence of D₂O, NaF, NaCl, and NaI aqueous solutions. Changes in the peak height intensity of the spectra provide quantitative insight into the phase transition process. The thermodynamic values of the phase transition were calculated using a van't Hoff analysis of the NMR data. Unlike the trend observed for decreases in the (LCST), changes in the enthalpy and entropy did not clearly display a linear dependence with respect to salt concentration. Rather, it was observed that increases in salt concentration did not affect the enthalpy and entropy to the extent as the initial change observed between no salt and 100 mM solutions. Finally, the effect of salts on the hysteresis of the rehydrating process was observed. Hysteresis occurs due to the need for hydrophobic interactions to break down before water is able to infiltrate the polymer matrix. NaF stabilizes hydrophobic interactions while NaI destabilize hydrophobic interactions, causing them to break down at higher temperatures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Evaluation of mean and variance integrals without integration

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential calculus. The general nature of the technique has potential for wider applications.