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Effect of smoothing on robust chaos.
Deshpande, Amogh,Chen, Qingfei,Wang, Yan,Lai, Ying-Cheng,Do, Younghae Published by the American Physical Society through 2010 Physical review. E, Statistical, nonlinear, and so Vol.82 No.2
<P>In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.</P>
Deshpande, Bhavana,Handa, Amrish The Youngnam Mathematical Society 2016 East Asian mathematical journal Vol.32 No.5
We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.
Deshpande, Nupoor,Jadhav, Anendd,Bhola, Nitin,Gupta, Manan The Korean Dental Society of Anesthsiology 2020 Journal of Dental Anesthesia and Pain Medicine Vol.20 No.4
Background: Palatal injection of local anesthetics is the most painful injection. To obviate the need for palatal injections, local anesthetic agents with diffusibility are being investigated. Hence the present study was designed to analyze the anesthetic efficacy of 2% lidocaine hydrochloride (HCl) with 1:100,000 adrenaline and 4% articaine hydrochloride (HCl) with 1:100,000 adrenaline using single buccal infiltration for the extraction of maxillary premolars. Methods: A prospective, double-blind, crossover, randomized clinical study was performed on 60 consecutive systemically healthy patients with an age range of 15-30 years, requiring extraction of asymptomatic bilateral maxillary premolars for orthodontic purposes. They received 1ml buccal infiltration of 4% articaine HCl with 1:100,000 adrenaline on one side and 2% lidocaine HCl with 1:100,000 adrenaline on the other side. The extraction procedure on either side was scheduled 14 days apart. Parameters assessed were the time of onset of anesthesia, intraoperative discomfort, hemodynamic parameters, and the duration of analgesia. Analysis of the data was done using the Mann-Whitney test, the Wilcoxon test, the Kruskal-Wallis ANOVA test, and the chi-square test. Statistical significance was established at P < 0.05. Results: Articaine showed a faster time of onset and longer duration of analgesia than lidocaine. However, the difference in the intraoperative discomfort and hemodynamic parameters was statistically insignificant. Conclusion: Within the limitations of the study, it can be concluded that the extraction of maxillary premolars can be performed with a single buccal infiltration of 2% lidocaine HCl with 1:100,000 adrenaline, which is one of the most commonly used local anesthetic agent.
Deshpande, Bhavana,Chouhan, Suresh The Youngnam Mathematical Society 2012 East Asian mathematical journal Vol.28 No.5
The aim of this paper is to prove a common fixed point theorem in normed linear spaces for discontinuous, occasionally weakly biased mappings without assuming completeness of the space. We give an example to illustrare our theorem. We also give an application of our theorem to best approximation theory. Our theorem improve the results of Gregus [9], Jungck [12], Pathak, Cho and Kang [22], Sharma and Deshpande [26]-[28].
Low temperature magneto-transport properties in bilayered magnetic anti-dot mircoarrays
Deshpande, N.G.,Hwang, J.S.,Seo, M.S.,Yoo, Y.J.,Rhee, J.Y.,Kim, K.W.,Shao, Y.C.,Chen, K.H.,Pong, W.F.,Lee, Y.P. New York] ; North-Holland 2014 APPLIED SURFACE SCIENCE - Vol.314 No.-
Magneto-transport study on the photolithographically-patterned anti-dot micro-arrays of cobalt upper-layer over a uniform thin nickel under-layer has been carried out. Circular anti-dots in rhomboidal symmetry were fabricated. The magnetoresistance (MR) curves were recorded for magnetically-easy and -hard axes of the bilayer structure at various temperatures. In addition to anisotropic MR, at low temperatures, the MR data shows anomalous behavior with several kinks and plateau regions, indicating complex reversal phenomena. Further, decrease in temperature results in increase of MR average peak height, double splitting of MR peaks and broadening of MR peaks. Additionally, the exchange bias behavior was found in the transverse MR curve; while no significant exchange effect was seen in the longitudinal MR curve. Using energy dispersive spectrum and X-ray absorption spectra taken at Co L<SUB>3,2</SUB>-edge, the presence of CoO layer over the bilayer structure was detected; while the Ni under-layer remained deoxidized.
Optimization of GMAW Process Parameters to Improve the Length of Penetration in EN 10025 S 235 Grade
Deshpande, M.U.,Kshirsagar, J.M.,Dharmadhikari, Dr. H.M. The Korean Welding and Joining Society 2017 대한용접·접합학회지 Vol.35 No.1
In auto ancillary fabrication industry, GMAW is a very useful & important welding process and EN10025 S 235 Grade is common material used for manufacturing of two wheeler chassis. This research gives the detail influence of welding process parameters such as welding current, welding voltage, wire speed on the penetration in EN10025 S 235 Grade mild steel material. The experimentation of this research has been carried out by using three factors, three level Taguchi DOE method. To analyze & optimize the welding parameters & characteristics, analysis of variance, L9 orthogonal array & signal to noise ratio are used. Length of Penetration in addition to the depth of penetration is major concern in fillet welded joints, as the penetration decides the strength of the welded joint. After analysis of penetration in all 9 welded samples, optimize parameters readings verified & found probability value within 0.05.From this research it is come to know that welding current & welding voltage is major parameters which affects the penetration in welded joints.
COMMON COUPLED FIXED POINT FOR HYBRID PAIR OF MAPPINGS UNDER GENERALIZED NONLINEAR CONTRACTION
Deshpande, Bhavana,Handa, Amrish The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.1
We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under generalized non-linear contraction. An example supporting to our result has also been cited. We improve, extend and generalize several known results.
EXISTENCE OF COINCIDENCE POINT UNDER GENERALIZED NONLINEAR CONTRACTION WITH APPLICATIONS
Deshpande, Bhavana,Handa, Amrish,Thoker, Shamim Ahmad The Youngnam Mathematical Society 2016 East Asian mathematical journal Vol.32 No.3
We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.