Explanipedia

A Regularization for Time-Fractional Backward Heat Conduction Problem with Inhomogeneous Source Function Open

Vighnesh V. Alavani, P. Danumjaya, M. Thamban Nair · 2024

Recently, Nair and Danumjaya (2023) introduced a new regularization method for the homogeneous time-fractional backward heat conduction problem (TFBHCP) in a one-dimensional space variable, for determining the initial value function. In th…

Sentiment analysis model for cryptocurrency tweets using different deep learning techniques Open

M. Thamban Nair, Laila A. Abd-Elmegid, Mohamed I. Marie · 2024

Bitcoin (BTC) is one of the most important cryptocurrencies widely used in various financial and commercial transactions due to the fluctuations in the price of this currency. Recent research in large data analytics and natural language pr…

A source identification problem in a bi-parabolic equation: convergence rates and some optimal results Open

Subhankar Mondal, M. Thamban Nair · 2023

This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Du…

A new regularisation for time-fractional backward heat conduction problem Open

M. Thamban Nair, P. Danumjaya · 2023

It is well-known that the backward heat conduction problem of recovering the temperature $u(\cdot, t)$ at a time $t\geq 0$ from the knowledge of the temperature at a later time, namely $g:= u(\cdot, τ)$ for $τ>t$, is ill-posed, in the sens…

Prediction of Cryptocurrency Price using Time Series Data and Deep Learning Algorithms Open

M. Thamban Nair, Mohamed I. Marie, Laila A. Abd-Elmegid · 2023

One of the most significant and extensively utilized cryptocurrencies is Bitcoin (BTC). It is used in many different financial and business activities. Forecasting cryptocurrency prices are crucial for investors and academics in this indus…

On truncated spectral regularization for an ill-posed evolution equation Open

M. Thamban Nair · 2021

Conforming and Nonconforming Finite Element Methods for Biharmonic Inverse Source Problem Open

Devika Shylaja, M. Thamban Nair · 2021

This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconfor…

Identification of matrix diffusion coefficients in a parabolic PDE Open

Subhankar Mondal, M. Thamban Nair · 2020

We consider an inverse problem of identifying the diffusion coefficient in matrix form in a parabolic PDE. In 2006, Cao and Pereverzev, used a \textit{natural linearisation} method for identifying a scalar valued diffusion coefficient in a…

A new regularization method for a parameter identification problem in a non-linear partial differential equation Open

M. Thamban Nair, Samprita Das Roy · 2020

We consider a parameter identification problem associated with a quasi-linear elliptic Neumann boundary value problem involving a parameter function a(⋅) and the solution u(⋅), where the problem is to identify a(⋅) on an interval $I:= g(\G…

Regularization of linear ill-posed problems involving multiplication operators Open

Peter Mathé, M. Thamban Nair, Bernd Hofmann · 2020

We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function. Such equations naturally arise fr…

Regularization of linear ill-posed problems involving multiplication\n operators Open

Peter Mathé, M. Thamban Nair, Bernd Hofmann · 2019

We study regularization of ill-posed equations involving multiplication\noperators when the multiplier function is positive almost everywhere and zero\nis an accumulation point of the range of this function. Such equations\nnaturally arise…

A PROJECTION BASED REGULARIZED APPROXIMATION METHOD FOR ILL-POSED OPERATOR EQUATIONS Open

Laurence Grammont, M. Thamban Nair · 2018

Problem of solving Fredholm integral equations of the first kind is a prototype of an ill-posed problem of the form T (x) = y, where T is a compact operator between Hilbert spaces. Regularizations and discretizations of such equations are …

Referee report. For: Statistical analysis plan for the WOMAN-ETAPlaT study: Effect of tranexamic acid on platelet function and thrombin generation [version 2; referees: 4 approved] Open

M. Thamban Nair · 2017

Referee report. For: Statistical analysis plan for the WOMAN-ETAPlaT study: Effect of tranexamic acid on platelet function and thrombin generation [version 1; referees: 2 approved, 2 approved with reservations] Open

M. Thamban Nair · 2017

A Discrete Regularization Method for Ill-Posed Operaror Equations Open

M. Thamban Nair · 2016

Discrete regularization methods are often applied for obtaining stable approximate solutions for ill-posed operator equations $Tx=y$, where $T: X\to Y$ is a bounded operator between Hilbert spaces with non-closed range $R(T)$ and $y\in R(T…

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