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Item Image Segmentation using Euler Graphs(CCC Publications, 2010-09-01) Janakiraman, T.N.; Chandra Mouli, P.V.S.S.R.This paper presents a new algorithm for image segmentation problem using the concepts of Euler graphs in graph theory. By treating image as an undirected weighted non-planar finite graph (G), image segmentation is handled as graph partitioning problem. The proposed method locates region boundaries or clusters and runs in polynomial time. Subjective comparison and objective evaluation shows the efficacy of the proposed approach in different image domains. © 2006-2010 by CCC Publications.Item An application of semigroup theory to the coagulation-fragmentation models(TUBITAK, 2021-08-25) Das, Arijit; Das, Nilima; Saha, JitrajWe present the existence and uniqueness of strong solutions for the continuous coagulation-fragmentation equation with singular fragmentation and essentially bounded coagulation kernel using semigroup theory of operators. Initially, we reformulate the coupled coagulation-fragmentation problem into the semilinear abstract Cauchy problem (ACP) and consider it as the nonlinear perturbation of the linear fragmentation operator. The existence of the substochastic semigroup is proved for the pure fragmentation equation. Using the substochastic semigroup and some related results for the pure fragmentation equation, we prove the existence of global nonnegative, strong solution for the coagulation-fragmentation equation.Item Conservative finite volume schemes for multidimensional fragmentation problems(MDPI AG, 2021-03-17) Saha, Jitraj; Bück, AndreasIn this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problemsItem A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation(MDPI, 2023-02-09) Kharchandy, Farel William Viret; Das, Arijit; Thota, Vamsinadh; Saha, Jitraj; Singh, MehakpreetAbstract A new population balance model is introduced, in which a pair of particles can coagulate into a larger one if their encounter is a completely inelastic collision; otherwise, one of them breaks into multiple fragments (two or more) due to the elastic collision. Mathematically, coagulation and breakage models both manifest nonlinearity behavior. We prove the global existence and uniqueness of the solution to this model for the compactly supported kinetic kernels and an unbounded breakage distribution function. A further investigation dealt with the volume conservation property (necessary condition) of the solution.Item Applications of first order differential subordination for functions with positive real part(Babes-Bolyai University, 2018-09-26) Ahuja, Om P.; Kumar, Sushil; Ravichandran, VSeveral inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with lemniscate of Bernoulli are obtained by making use of the well-known theory of differential subordination. Further, these inclusions give sufficient conditions for normalized analytic functions to belong to some subclasses of starlike functions. The results also provide sharp version of some previously known results.Item Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes(MDPI AG, 2018-08-18) Cho, Nak Eun; Kumar, Virendra; Ravichandran, VHigher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction.Item Star-likeness associated with the exponential function(TUBITAK, 2019-03-22) Naz, Adiba; Nagpal, Sumit; Ravichandran, VGiven a domain Ω in the complex plane and a univalent function q defined in an open unit disk D[double-struck] with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions Ψ(Ω, q) so that the differential subordination Ψ (p(z), zp'(z), z2p''(z); z) ≺ h(z) implies p(z) ≺ q(z), where p is an analytic function in D[double-struck] with p(0) = 1, ψ: 3 ×D[double-struck] → and Ω = h(D[double-struck]) . This paper investigates the properties of this class for q(z) = ez . As application, several sufficient conditions for normalized analytic functions f to be in the subclass of star-like functions associated with the exponential function are obtained.Item Starlike functions related to the bell numbers(MDPI AG, 2019-02-13) Cho, Nak Eun; Kumar, Sushil; Kumar, Virendra; Ravichandran, V; Srivastava, H. M.The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined. © 2019 by the authors.Item Starlikeness of Analytic Functions with Subordinate Ratios(Hindawi Limited, 2021-10-29) Ali, Rosihan M.; Ravichandran, Vaithiyanathan; Sharma, KanikaLet h be a nonvanishing analytic function in the open unit disc with h0=1. Consider the class consisting of normalized analytic functions f whose ratios fz/gz, gz/zpz, and pz are each subordinate to h for some analytic functions g and p. The radius of starlikeness of order α is obtained for this class when h is chosen to be either hz=1+z or hz=ez. Further, starlikeness radii are also obtained for each of these two classes, which include the radius of Janowski starlikeness, and the radius of parabolic starlikeness. © 2021 Rosihan M. Ali et al.Item Differential subordination for Janowski functions with positive real part(Babes-Bolyai University, 2021-09-28) Anand, Swati; Kumar, Sushil; Ravichandran, VTheory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition. We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Janowski function with positive real part. As applications, we obtain sufficient conditions for normalized analytic functions to be Janowski starlike functions.Item Radius of starlikeness through subordination(Babes-Bolyai University, 2023-03-17) Sebastian, Asha; Ravichandran, VaithiyanathanA normalized function f on the open unit disc is starlike (or convex) univalent if the associated function (Formula Presented) is a function with positive real part. The radius of starlikeness or convexity is usually obtained by using the estimates for functions with positive real part. Using subordination, we examine the radius of various starlikeness, in particular, radii of Janowski starlikeness and starlikeness of order β, for the function f when the function f is either convex or (Formula Presented) lies in the right-half plane. Radii of starlikeness associated with lemniscate of Bernoulli and exponential functions are also considered. © 2023,Studia Universitatis Babes-Bolyai Mathematica. All Rights Reserved.Item Ma-Minda starlikeness of certain analytic functions(Babes-Bolyai University, 2025-02-25) Janani, Baskar Babujee; Ravichandran, VA normałized anałytic function defined on the open unit disc (Formula presented) is całłed Ma-Minda starłike if zf0(z)/f(z) is subordinate to the function ϕ. For a normałized convex function f defined on (Formula presented) and α > 0, we determine the radius of Ma-Minda starłikeness of the function g defined as (Formula presented) for certain choices of ϕ. In particułar, we investigate the radius of Janowski starłikeness of the function g. © Studia UBB MATHEMATICA. Published by Babeş-Bolyai University This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.