Search results for: S. Behl

Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

Abstract:

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Hölder continuity condition, Fréchet derivative, fifth order convergence, recurrence relations.

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Authors: Ramandeep Behl, S. S. Motsa

Abstract:

The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: M. Jarrar, S. Behl, N. Shaheen, A. Fatima, R. Nasab

Abstract:

Skin aging is a slow multifactorial process influenced by both internal as well as external factors. Ultra-violet radiations (UV), diet, smoking and personal habits are the most common environmental factors that affect skin aging. Fat contents and fibrous proteins as collagen and elastin are core internal structural components. The direct influence of UV on elastin integrity and health is central on aging of skin especially by time. The deposition of abnormal elastic material is a major marker in a photo-aged skin. Searching for compounds that may protect against cutaneous photodamage is exceedingly valued. Retinoids and alpha hydroxy acids have been endorsed by some researchers as possible candidates for protecting and or repairing the effect of UV damaged skin. For consolidating a better system of anti- and protective effects of such anti-aging agents, we evaluated the combinatory effects of various dosages of lactic acid and retinol on the dermal fibroblast’s elastin levels exposed to UV. The UV exposed cells showed significant reduction in the elastin levels. A combination of drugs with a higher concentration of lactic acid (30 -35 mM) and a lower concentration of retinol (10-15mg/mL) showed to work better in maintaining elastin concentration in UV exposed cells. We assume this preservation could be the result of increased tropo-elastin gene expression stimulated by retinol whereas lactic acid probably repaired the UV irradiated damage by enhancing the amount and integrity of the elastin fibers.

Keywords: Alpha Hydroxy Acid, Elastin, Retinol, Ultraviolet radiations.

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