Dinkar Patil - Academia.edu (original) (raw)

Papers by Dinkar Patil

In recent years, a lot of interest has been shown in the study of symmetry properties of solution... more In recent years, a lot of interest has been shown in the study of symmetry properties of solutions of nonlinear elliptic equations, reflecting the symmetry of domain. Linear elliptic equations arise in several models describing various phenomena in the Applied sciences. It is an important goal in mathematical analysis to establish symmetry property of solutions of differential equations both from a theoretical point of view and for the applications .In 1979 Gidas, Ni and Nirenberg [9, 10] introduced the method of moving planes to obtain the symmetry results and monotonicity for positive solutions of nonlinear elliptic equations. Li and Ni[19] proved the symmetry results for the conformal scaler curvature equation Δu + K(x)u = 0 in R; n ≥ 3. Recently, Naito [16] studied the problem of radial symmetry of classical solutions of semilinear elliptic equations Δu+V (|x|) e = 0 in R, by the moving plane method. Recently Dhaigude and Patil [2] studied the radial symmetry of positive solutio...

The International Journal of Acoustics and Vibration, 2002

Journal of Scientific & Industrial Research, 2002

To restore fertility and productivity of saline soil through bioremediation, a farm-scale trial w... more To restore fertility and productivity of saline soil through bioremediation, a farm-scale trial was undertaken by exploring the effect of three factors, viz, soil conditioner (SC, recycled agrowaste), halophiles culture, and a plant growth regulator (PGR), modified industrial byproduct. A three factor factorial design was used with each factor at two levels - the lower level indicated no treatment, while the upper level indicated treatment, and there were eight experiments in all, which were replicated thrice. One out of the eight treatment combinations was without SC, PGR, or halophiles inputs served as control. The plantation and growth of Casuarina equisetifolia, in the treated soils as per the design, was monitored through various relevant parameters that included soil characteristics, level of (micro) nutrients, and exchangeable cations, and growth-related parameters. The analysis of data thus generated through appropriate ANOVA indicated an overwhelming role of SC in the biore...

Journal of the Indian Institute of Science, 2012

In this article the shuffling of cards is studied by using the concept of a group action. We use ... more In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

Proceedings Mathematical Sciences, 2004

Physical Review B, 2012

We present scanning tunneling microscopy and spectroscopy measurements of the charge-density wave... more We present scanning tunneling microscopy and spectroscopy measurements of the charge-density wave state in 1T-TiSe2, Cu0.05TiSe2 and Cu0.06TiSe2 single crystals. Topography images at 4.2 K reveal that the charge density waves are present in all samples studied, although the amplitude of the charge modulation decreases with the Cu-doping. Moreover, the chiral phase of the charge density wave is preserved also in Cu-doped samples. Tunneling spectroscopy shows that there is only a partial gap in the pure compound, with bands crossing the Fermi surface. In the Cu-doped samples the system becomes more metallic due to the increase of the chemical potential.

The aim of this paper is to study the symmetry properties of positive solutions of nonlinear elli... more The aim of this paper is to study the symmetry properties of positive solutions of nonlinear elliptic boundary value problems of type Du + f(|x|,u,ru) = 0 in R n . u(x) ! 0 as |x| ! ¥ We employ the moving plane method based on maximum principle on unbounded domains to obtain the

The aim of this paper is to study the symmetry properties of solutions of bi-harmonic differentia... more The aim of this paper is to study the symmetry properties of solutions of bi-harmonic differential equations of the type ∆ u + α u = 0 and ∆ u + f(u) = 0 in Ω ⊂ R We employ the method of moving planes, which is based on the Maximum principles in bounded domains to obtain the result of symmetry of solutions of the bi-harmonic problems. Index Terms – Moving Plane Method, Symmetry, Bi-harmonic equations, Maximum Principles.

Resonance, 2006

Riemann had revolutionized the fields of analysis, geometry and mathematical physics. His ideas c... more Riemann had revolutionized the fields of analysis, geometry and mathematical physics. His ideas concerning geometry of space had a profound effect on the development of modern theoretical physics. Riemannian manifolds, Riemann surfaces, the Cauchy—Riemann equations, the Riemann hypothesis-all these and more are packed into his one-volume collected works. Riemann clarified the notion of integration by defining, a little over 135