Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.     

Fluorescein Hydrazide-Appended Metal–Organic Framework as a Chromogenic and Fluorogenic Chemosensor for Mercury Ions

In this work, we prepared a fluorescein hydrazide-appended Ni(MOF) (Metal–Organic Framework) [Ni₃(BTC)₂(H₂O)₃]·(DMF)₃(H₂O)₃ composite, FH@Ni(MOF). This composite was well-characterized by PXRD (powder X-ray diffraction), FT-IR (Fourier transform infrared spectroscopy), N₂ adsorption isotherm, TGA (thermogravimetric analysis), XPS (X-ray photoelectron spectroscopy), and FESEM (field emission scanning electron microscopy). This composite was then tested with different heavy metals and was found to act as a highly selective and sensitive optical sensor for the Hg²⁺ ion. It was found that the aqueous emulsion of this composite produces a new peak in absorption at 583 nm, with a chromogenic change to a pink color visible to the naked eye upon binding with Hg²⁺ ions. In emission, it enhances fluorescence with a fluorogenic change to green fluorescence upon complexation with the Hg²⁺ ion. The binding constant was found to be 9.4 × 10⁵ M⁻¹, with a detection limit of 0.02 μM or 5 ppb. This sensor was also found to be reversible and could be used for seven consecutive cycles. It was also tested for Hg²⁺ ion detection in practical water samples from ground water, tap water, and drinking water.     

Combined effects of heat and chemical reactions on the peristaltic flow of carreau fluid model in a diverging tube

The study of peristaltic flow of a Carreau fluid in a non‐uniform tube under the consideration of long wavelength in the presence of heat and mass transfer is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Two types of analytical solutions have been evaluated (i) perturbation method (ii) homotopy analysis method for velocity, temperature and concentration field. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves. Copyright © 2010 John Wiley & Sons, Ltd.     

On Smoothness of the Green Function for?the?Complement of a Rarefied Cantor-Type Set

Smoothness of the Green functions for the complement of rarefied Cantor-type sets is described in terms of the function j(d)=(1/log\frac1d)\varphi (\delta)=(1/\log\frac{1}{\delta}) that gives the logarithmic measure of sets. Markov’s constants of the corresponding sets are evaluated.     

Peristaltic flow of a Jeffrey‐six constant fluid in a uniform inclined tube

In this work, we studied the peristaltic flow of a Jeffrey‐six constant fluid in a uniform tube. The governing equations of the Jeffrey‐six constant fluid were simplified by using the assumptions of long wave length and low Reynolds number approximation. The simplified form of equations were solved using the perturbation, homotopy analysis and finite difference methods. The comparison of the three solutions are shown graphically. The variation of pressure rise and frictional forces with the different parameters were also examined numerically. Results are presented at the end of the article. Copyright © 2011 John Wiley & Sons, Ltd.     

Exact and numerical simulation of peristaltic flow of a non‐Newtonian fluid with inclined magnetic field in an endoscope

In the present article, we have studied the effects of inclined magnetic field on the peristaltic flow of Jeffrey fluid through the gap between two coaxial inclined tubes. The inner tube is rigid, whereas the outer tube has sinusoidal wave traveling down its wall. The governing equations are simplified using long wave length and low Reynolds number approximations. Exact and numerical solutions have been derived for velocity profile. The expressions for pressure rise and friction force are calculated using numerical integration. Graphical results and trapping phenomenon is presented at the end of the article to see the physical behavior of different parameters. Copyright © 2010 John Wiley & Sons, Ltd.