Browsing by Author "Balaji, S."

Now showing 1 - 9 of 9

Convergence of operators with closed range
(2019) Johnson, P.S.; Balaji, S.
Izumino has discussed a sequence of closed range operators (Tn) that converges to a closed range operator T on a Hilbert space to establish the convergence of Tn ? T for Moore-Penrose inverses. In general, if Tn ? T uniformly and each Tn has a closed range, then T need not have a closed range. Some sufficient conditions have been discussed on Tn and T such that T has a closed range whenever each Tn has a closed range. 2019 Khayyam Journal of Mathematics.
Convergence of operators with closed range
(Tusi Mathematical Research Group (TMRG) moslehian@memeber.ams.org, 2019) Johnson, P.S.; Balaji, S.
Izumino has discussed a sequence of closed range operators (Tn) that converges to a closed range operator T on a Hilbert space to establish the convergence of Tn† ? T† for Moore-Penrose inverses. In general, if Tn ? T uniformly and each Tn has a closed range, then T need not have a closed range. Some sufficient conditions have been discussed on Tn and T such that T has a closed range whenever each Tn has a closed range. © 2019 Khayyam Journal of Mathematics.
Dense Sense: a novel approach utilizing electron density augmented machine learning paradigm to understand the complex odour landscape
(Royal Society of Chemistry, 2025) Saha, P.; Sharma, M.; Balaji, S.; Barsainyan, A.A.; Kumar, R.; Steuber, V.; Schmuker, M.
Olfaction is a complex process where multiple nasal receptors interact to detect specific odorant molecules. Elucidating structure–activity-relationships for odorants and their receptors remains difficult since crystallization of the odor receptors is an extremely difficult process. Therefore, ligand-based approaches that leverage machine learning remain the state of the art for predicting odorant properties for molecules, such as the graph neural network approach used by Lee et al. In this paper we explored how information from quantum mechanics (QM) could synergistically improve the results obtained with the graph neural network. Our findings underscore the possibility of this methodology in predicting odor perception directly from QM data, offering a novel approach in the machine learning space to understand olfaction. This journal is © The Royal Society of Chemistry, 2025
Hyers-Ulam stability of linear operators in Frechet spaces
(2012) Sam, Johnson, P.; Balaji, S.
Hyers-Ulam stability of a linear operator between Frechet spaces is defined. Necessary and sufficient conditions for the existence of Hyers-Ulam stability of a continuous linear operator from a Frechet space to another Frechet space are given. 2012 NSP Natural Sciences Publishing Cor.
Hyers-Ulam stability of linear operators in Frechet spaces
(2012) Johnson, P.S.; Balaji, S.
Hyers-Ulam stability of a linear operator between Frechet spaces is defined. Necessary and sufficient conditions for the existence of Hyers-Ulam stability of a continuous linear operator from a Frechet space to another Frechet space are given. © 2012 NSP Natural Sciences Publishing Cor.
Inverse approach for estimating boundary properties in a transient fin problem
(2018) Gnanasekaran, N.; Balaji, S.
A solution methodology is proposed for an inverse estimation of boundary conditions from the knowledge of transient temperature data. A forward model based on prevalent time-dependent heat conduction fin equation is solved using a fully implicit finite volume method. First, the inverse model is formulated and accomplished for time-invariant heat flux at the fin base, and later extended to transient heat flux, base temperature and average heat transfer coefficient. Secondly, the Nusselt number is then replaced with Rayleigh number in the forward model to realistically estimate the base temperature, which varies with respect to time, based on in-house transient fin heat transfer experiments. This scenario further corroborates the validation of the proposed inverse approach. The experimental set-up consists of a mild steel 250 150 6mm3 fin mounted centrally on an aluminium base 250 150 8mm3 plate. The base is attached to an electrical heater and insulated with glass-wool to prevent heat loss to surroundings. Five calibrated K-type thermocouples are used to measure temperature along the fin. The functional form of the unknown parameters is not known beforehand; sensitivity studies are performed to determine suitability of the estimation and location of sensors for the inverse approach. Conjugate gradient method with adjoint equation is chosen as the inverse technique and the study is performed as a numerical optimization; subsequently, the estimates show satisfactory results. 2018, Indian Academy of Sciences.
Inverse approach for estimating boundary properties in a transient fin problem
(Springer, 2018) Gnanasekaran, N.; Balaji, S.
A solution methodology is proposed for an inverse estimation of boundary conditions from the knowledge of transient temperature data. A forward model based on prevalent time-dependent heat conduction fin equation is solved using a fully implicit finite volume method. First, the inverse model is formulated and accomplished for time-invariant heat flux at the fin base, and later extended to transient heat flux, base temperature and average heat transfer coefficient. Secondly, the Nusselt number is then replaced with Rayleigh number in the forward model to realistically estimate the base temperature, which varies with respect to time, based on in-house transient fin heat transfer experiments. This scenario further corroborates the validation of the proposed inverse approach. The experimental set-up consists of a mild steel 250×150×6mm3 fin mounted centrally on an aluminium base 250×150×8mm3 plate. The base is attached to an electrical heater and insulated with glass-wool to prevent heat loss to surroundings. Five calibrated K-type thermocouples are used to measure temperature along the fin. The functional form of the unknown parameters is not known beforehand; sensitivity studies are performed to determine suitability of the estimation and location of sensors for the inverse approach. Conjugate gradient method with adjoint equation is chosen as the inverse technique and the study is performed as a numerical optimization; subsequently, the estimates show satisfactory results. © 2018, Indian Academy of Sciences.
On semiclosed subspaces of Hilbert spaces
(2012) Johnson, P.S.; Balaji, S.
Semiclosed subspaces possess many special features that distinguish them from arbitrary subspaces. Few properties of proper dense semiclosed subspaces of Hilbert spaces are discussed. 2012 Academic Publications, Ltd.
On semiclosed subspaces of Hilbert spaces
(2012) Johnson, P.S.; Balaji, S.
Semiclosed subspaces possess many special features that distinguish them from arbitrary subspaces. Few properties of proper dense semiclosed subspaces of Hilbert spaces are discussed. © 2012 Academic Publications, Ltd.