IDR@IIT Indore
http://dspace.iiti.ac.in:8080/jspui
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 22 Jun 2018 22:57:00 GMT2018-06-22T22:57:00ZHomotopy perturbation method to solve non-linear differential equations
http://dspace.iiti.ac.in:8080/jspui/handle/123456789/1116
Title: Homotopy perturbation method to solve non-linear differential equations
Authors: Kumar, Rahul; Ahmad, Sk. Safique [Supervisor]; Manna, Santanu [Supervisor]
Abstract: The thesis contains a survey of the perturbation method [cf. Nayfeh, 1981] and
generalization of the perturbation method for the solution of linear and Nonlinear
differential equations. The generalization of perturbationmethod has been first introduced
by Ji-Huan He (1999) called Homotopy Perturbation Method (HPM). According to
Cheniguel and Reghioua (2013), Biazar and Eslami (2011), Mechee et al. (2017), etc.,
HPM is one of the new and excellent methods for solving the nonlinear differential
equation. It is well known that the perturbation theory is based on an assumption of an
equation (in the form of power series) with a small parameter. A perfect choice of small
parameter leads to the excellent result. However, if the choice of the small parameter is not
suitable then the solution is going to be a bad asset. In such cases, the HPM can find the
accurate approximate solution of the differential equation. This method does not depend
on the small parameter in the assumed equation. The HPM is a combination of homotopy
and perturbation method which provides an advantageous way to obtain an analytical
or approximate solution of the differential equations. Chapter 1, contains the literature
survey of perturbation, homotopy and generalized homotopy perturbation method. In
Chapter 2, we have discussed the basic theory of perturbation method and its application
from the books of Nayfeh (1981) and Liao (1995). The Chapter 3, started with the basic
idea of homotopy [cf. Ji-Huan He, 1999] and extended to the study of the HPM[He, 2005,
2006; Hemeda, 2012]. In this chapter, we have discussed Inviscid Burgers Nonlinear
problem and nonhomogeneous Advection Nonlinear problem using the HPM. In Chapter
4, we survey the literature of the generalization of the homotopy perturbation method
(GHPM) from the article of Hector, (2014). The last Chapter contains the conclusions
and future plan.
Keywords: Homotopy, Homotopy perturbation method, Linear, Nonhomogeneous,
Nonlinear, ODEs, PDEs, Perturbation method, Power series, Topology.Fri, 04 May 2018 00:00:00 GMThttp://dspace.iiti.ac.in:8080/jspui/handle/123456789/11162018-05-04T00:00:00ZA unified approach to problems on guessing, source coding and encoding of tasks
http://dspace.iiti.ac.in:8080/jspui/handle/123456789/1115
Title: A unified approach to problems on guessing, source coding and encoding of tasks
Authors: Thakre, Ashish; Kumar, M. Ashok [Supervisor]; Kumar, Ashisha [Supervisor]
Abstract: We study four problems namely, Campbell's source coding problem, Massey's guessing
problem, Huieihel et al.'s memoryless guessing problem, and Bunte and Lapidoth's
encoding of tasks problem. We observe a close relationship among these problems. In all
these problems, the objective function to minimize is moments of some functions of random
variables. R enyi entropy and the Sundaresan's divergence arise as optimal solutions.
This motivates us to establish a connection between these four problems. In this thesis
we nd a uni ed approach to solve all these problems. Indeed, we establish a general
problem where all the problems are particular ones. We also compare our results with
the existing ones. We strongly feel that this generalization would help us to understand
the problems better and might help us apply in real life situations.Tue, 22 May 2018 00:00:00 GMThttp://dspace.iiti.ac.in:8080/jspui/handle/123456789/11152018-05-22T00:00:00ZUnivalent functions and area problems
http://dspace.iiti.ac.in:8080/jspui/handle/123456789/1114
Title: Univalent functions and area problems
Authors: Mohanty, Sai Rasmi Ranjan; Sahoo, Swadesh Kumar [Supervisor]
Abstract: This thesis contains a survey of basic properties of univalent functions in the analytic
function theory. Mostly we focuses on the class of univalent functions in the unit disk in
which each of them has a Taylorâ€™s series expansion with a specific normalized form. This
class of functions is preserved under certain elementary transformations. The well-known
Bieberbach theorem, the growth theorem, the distortion theorem, the Koebe 1/4-theorem,
area theorems are presented in this thesis. The classical subclasses of univalent functions,
namely, the class of convex and starlike functions are also studied including their characterizations.
As a part of applications of above and other related properties considered in
this thesis, we compute areas of image domains of the unit disk and its subdisks under
functions of some special types looking into the fact that the image domains are bounded.
These are also examined through several examples of functions and their graphs. Finally,
in the line of area of regions, we expect that a number of problems can be studied to maximize
length of image of unit circle over the class of univalent functions. A few analysis
on the latter part are covered in the concluding chapter.Fri, 18 May 2018 00:00:00 GMThttp://dspace.iiti.ac.in:8080/jspui/handle/123456789/11142018-05-18T00:00:00ZMorphologically tailored CuO photocathode using aqueous solution technique for enhanced visible light driven water splitting
http://dspace.iiti.ac.in:8080/jspui/handle/123456789/1113
Title: Morphologically tailored CuO photocathode using aqueous solution technique for enhanced visible light driven water splitting
Authors: Kushwaha, Ajay Kumar
Abstract: Cupric oxide (CuO) nanostructures are grown on fluorine doped tin oxide (FTO) coated glass substrate using aqueous solution approach. The concentration of precursorâ€™s solution has significant impact on morphology of CuO nanostructure. By varying concentration of precursor, the growth of two different morphologies (oriented nanosheets and nanoleaves) is achieved. X-ray diffraction pattern and X-ray photoelectron spectroscopy reveals formation of pure CuO crystalline phase. Mott-Schottky characteristic confirms the p-type semiconducting nature. Ultrathin structures of nanoleaves lead to higher light trapping and light absorption in visible-NIR region. The nanoleaves film has lower bandgap in comparison with nanosheets film. Photoelectrochemical measurements result in 1.5 mA/cm2 photocurrent for nanoleaves electrode and 1.1 mA/cm2 for nanosheets electrode at a potential of 0 V v/s RHE. The photocurrent conversion efficiency is 1.8% and 1.4% in nanoleaves and nanosheets electrodes, respectively. Electrochemical impedance analyses endorse more efficient collection and separation of charge carriers in nanoleaves film.Sun, 01 Jan 2017 00:00:00 GMThttp://dspace.iiti.ac.in:8080/jspui/handle/123456789/11132017-01-01T00:00:00Z