sabyasachi mukherjee - Academia.edu (original) (raw)

Papers by sabyasachi mukherjee

Transactions of the American Mathematical Society, 2021

It is well known that baby Mandelbrot sets are homeomorphic to the original one. We study baby Tr... more It is well known that baby Mandelbrot sets are homeomorphic to the original one. We study baby Tricorns appearing in the Tricorn, which is the connectedness locus of quadratic anti-holomorphic polynomials, and show that the dynamically natural straightening map from a baby Tricorn to the original Tricorn is discontinuous at infinitely many explicit parameters. This is the first known example of discontinuity of straightening maps on a real two-dimensional slice of an analytic family of holomorphic polynomials. The proof of discontinuity is carried out by showing that all non-real umbilical cords of the Tricorn wiggle, which settles a conjecture made by various people including Hubbard, Milnor, and Schleicher.

Materials Today: Proceedings, 2019

This paper examining the impact of welding parameters, by parametric investigation of multi spot ... more This paper examining the impact of welding parameters, by parametric investigation of multi spot welded lap shear specimen, on the tensile shear strength of spot welded specimen. Further, study is carried out, to develop mathematical model by using regression analysis which shows relationship between selected welding parameters and weld strength. The design parameters considered are specimen thickness, number of spots and distance between the spots while process parameters are electrode force and weld current. As per Taguchi design of experiment approach, five welding parameters with three levels of each are considered for analysis. Experimentation is carried out as per L 27 orthogonal array to investigate the effect of process and design parameters on tensile shear strength. Particle swarm optimization (PSO) method was used to determine welding parameter has a significant impact on weld strength. Tests for confirmation have been conducted to validate the results. Confirmation tests exhibit that deviation between the results obtained by experimentation and regression is up to 0.571741%. Particle swarm optimization explore that maximum tensile shear strength 9399.55 N is obtained at 06 numbers of spot and 16 mm distance between the spots as optimum value for 1.22 mm galvanized steel sheets.

Nonlinearity, 2017

In [BE16], Bergweiler and Eremenko computed the number of critical points of the Green's function... more In [BE16], Bergweiler and Eremenko computed the number of critical points of the Green's function on a torus by investigating the dynamics of a certain family of antiholomorphic meromorphic functions on tori. They also observed that hyperbolic maps are dense in this family of meromorphic functions in a rather trivial way. In this paper, we study the parameter space of this family of meromorphic functions, which can be written as antiholomorphic perturbations of Weierstrass Zeta functions. On the one hand, we give a complete topological description of the hyperbolic components and their boundaries, and on the other hand, we show that these sets admit natural parametrizations by associated dynamical invariants. This settles a conjecture, made in [LW10], on the topology of the regions in the upper half plane H where the number of critical points of the Green's function remains constant.

2011 Fifth IEEE International Conference on Advanced Telecommunication Systems and Networks (ANTS), 2011

An important parameter for performance analysis of Routing and Wavelength Assignment (RWA) strate... more An important parameter for performance analysis of Routing and Wavelength Assignment (RWA) strategies in WDM networks is blocking probability. Past research has shown that the process in which RWA is carried out significantly affects the wavelength conversion requirements, which in turn affects blocking probability. In this paper we propose a new strategy GDWA (Graph Decomposition based Wavelength Assignment) for static

Transactions of the American Mathematical Society, 2021

It is well known that baby Mandelbrot sets are homeomorphic to the original one. We study baby Tr... more It is well known that baby Mandelbrot sets are homeomorphic to the original one. We study baby Tricorns appearing in the Tricorn, which is the connectedness locus of quadratic anti-holomorphic polynomials, and show that the dynamically natural straightening map from a baby Tricorn to the original Tricorn is discontinuous at infinitely many explicit parameters. This is the first known example of discontinuity of straightening maps on a real two-dimensional slice of an analytic family of holomorphic polynomials. The proof of discontinuity is carried out by showing that all non-real umbilical cords of the Tricorn wiggle, which settles a conjecture made by various people including Hubbard, Milnor, and Schleicher.

Materials Today: Proceedings, 2019

This paper examining the impact of welding parameters, by parametric investigation of multi spot ... more This paper examining the impact of welding parameters, by parametric investigation of multi spot welded lap shear specimen, on the tensile shear strength of spot welded specimen. Further, study is carried out, to develop mathematical model by using regression analysis which shows relationship between selected welding parameters and weld strength. The design parameters considered are specimen thickness, number of spots and distance between the spots while process parameters are electrode force and weld current. As per Taguchi design of experiment approach, five welding parameters with three levels of each are considered for analysis. Experimentation is carried out as per L 27 orthogonal array to investigate the effect of process and design parameters on tensile shear strength. Particle swarm optimization (PSO) method was used to determine welding parameter has a significant impact on weld strength. Tests for confirmation have been conducted to validate the results. Confirmation tests exhibit that deviation between the results obtained by experimentation and regression is up to 0.571741%. Particle swarm optimization explore that maximum tensile shear strength 9399.55 N is obtained at 06 numbers of spot and 16 mm distance between the spots as optimum value for 1.22 mm galvanized steel sheets.

Nonlinearity, 2017

In [BE16], Bergweiler and Eremenko computed the number of critical points of the Green's function... more In [BE16], Bergweiler and Eremenko computed the number of critical points of the Green's function on a torus by investigating the dynamics of a certain family of antiholomorphic meromorphic functions on tori. They also observed that hyperbolic maps are dense in this family of meromorphic functions in a rather trivial way. In this paper, we study the parameter space of this family of meromorphic functions, which can be written as antiholomorphic perturbations of Weierstrass Zeta functions. On the one hand, we give a complete topological description of the hyperbolic components and their boundaries, and on the other hand, we show that these sets admit natural parametrizations by associated dynamical invariants. This settles a conjecture, made in [LW10], on the topology of the regions in the upper half plane H where the number of critical points of the Green's function remains constant.

2011 Fifth IEEE International Conference on Advanced Telecommunication Systems and Networks (ANTS), 2011

An important parameter for performance analysis of Routing and Wavelength Assignment (RWA) strate... more An important parameter for performance analysis of Routing and Wavelength Assignment (RWA) strategies in WDM networks is blocking probability. Past research has shown that the process in which RWA is carried out significantly affects the wavelength conversion requirements, which in turn affects blocking probability. In this paper we propose a new strategy GDWA (Graph Decomposition based Wavelength Assignment) for static