Towards a More General Type of Univariate Constrained Interpolation With Fractal Splines

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current article is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.Comment: 7 pages, 6 figure

Multi-epoch intra-night optical monitoring of 8 radio-quiet BL Lac candidates

For a new sample of 8 weak-line-quasars (WLQs) we report a sensitive search in 20 intranight monitoring sessions, for blazar-like optical flux variations on hour-like and longer time scale (day/month/year$-$like). The sample consists exclusively of the WLQs that are not radio$-$loud and have either been classified as `radio-weak probable BL Lac candidates' and/or are known to have exhibited at least one episode of large, blazar$-$like optical variability. Whereas only a hint of intra$-$night variability is seen for two of these WLQs, J104833.5$+$620305.0(z = 0.219) and J133219.6$+$622715.9 (z = 3.15), statistically significant inter$-$night variability at a few per cent level is detected for three of the sources, including the radio-intermediate WLQ J133219.6$+$622715.9 (z = 3.15) and the well known bona$-$fide radio$-$quiet WLQs J121221.5$+$534128.0 (z = 3.10) and WLQ J153259.9$-$003944.1 (z = 4.62). In the rest$-$frame, this variability is intra-day and in the far$-$UV band. On the time scale of a decade, we find for three of the WLQs large brightness changes, amounting to 1.655$\pm$0.009, 0.163$\pm$0.010 and 0.144$\pm$0.018 mag, for J104833.5$+$620305.0, J123743.1$+$630144.9 and J232428.4$+$144324.4, respectively. Whereas the latter two are confirmed radio-quiet WLQs, the extragalactic nature of J104833.5$+$620305.0 remains to be well established, thanks to the absence of any feature(s) in its available optical spectra. The present study forms a part of our ongoing campaign of intranight optical monitoring of radio quiet weak-line quasars, in order to improve the understanding of this enigmatic class of Active Galactic Nuclei and to look among them for a possible tiny, elusive population of radio-quiet BL Lacs.Comment: Accepted to MNRAS. 12 pages, 1 figure, 4 Tabl

Limits on the time variation of the electromagnetic fine-structure constant in the low energy limit from absorption lines in the spectra of distant quasars

Most of the successful physical theories rely on the constancy of few fundamental quantities (such as the speed of light, $c$, the fine-structure constant, \alpha, the proton to electron mass ratio, \mu, etc), and constraining the possible time variations of these fundamental quantities is an important step toward a complete physical theory. Time variation of \alpha can be accurately probed using absorption lines seen in the spectra of distant quasars. Here, we present the results of a detailed many-multiplet analysis performed on a new sample of Mg II systems observed in high quality quasar spectra obtained using the Very Large Telescope. The weighted mean value of the variation in \alpha derived from our analysis over the redshift range 0.4<z<2.3 is \Delta\alpha/\alpha = (-0.06+/-0.06) x 10^{-5}. The median redshift of our sample (z=1.55) corresponds to a look-back time of 9.7 Gyr in the most favored cosmological model today. This gives a 3\sigma limit, -2.5 x 10^{-16} yr^-1 <(\Delta\alpha/\alpha\Delta t) <+1.2x10^{-16} yr^-1, for the time variation of \alpha, that forms the strongest constraint obtained based on high redshift quasar absorption line systems.Comment: uses revtex, 4 pages 3 figures. Accepted for publication in Physical Review Letter

Optimisation of abrasive wear of rice husk reinforced epoxy composite by using response surface methodology

Wear is the disintegration or sideways uprooting of a material from its "derivative" and unique position on a solid surface performed by the movement of an alternate surface. The requirement for relative movement between two surfaces and mechanical contact between asperities is a paramount refinement between mechanical wear contrasted with different courses of action with comparative results. The wear analysis is possible by expository procedures like Response Surface Methodology. Response Surface Methodology (RSM) is an accumulation of statistical and mathematical techniques helpful for creating, enhancing, and upgrading methodologies. It additionally has important requisitions in the outline, advancement, and definition of new items, and also in the change of existing item plans. The broadest provisions of RSM are in the modern world, especially in circumstances where several input variables conceivably impact some performance measure or quality characteristic of the product or process

Stability of Coalescence Hidden variable Fractal Interpolation Surfaces

In the present paper, the stability of Coalescence Hidden variable Fractal Interpolation Surfaces(CHFIS) is established. The estimates on error in approximation of the data generating function by CHFIS are found when there is a perturbation in independent, dependent and hidden variables. It is proved that any small perturbation in any of the variables of generalized interpolation data results in only small perturbation of CHFIS. Our results are likely to be useful in investigations of texture of surfaces arising from the simulation of surfaces of rocks, sea surfaces, clouds and similar natural objects wherein the generating function depends on more than one variable