A5046956215- Spectral Theory in Mathematical Physics
- Analytic Number Theory Research
- Advanced Harmonic Analysis Research
- Graph theory and applications
- Matrix Theory and Algorithms
- Mathematical Dynamics and Fractals
- Algebraic Geometry and Number Theory
- Mathematical Inequalities and Applications
- Advanced Mathematical Theories and Applications
- Mathematical Approximation and Integration
- Nonlinear Partial Differential Equations
- Numerical methods in inverse problems
- Advanced Mathematical Modeling in Engineering
- Chaos-based Image/Signal Encryption
- Sleep and related disorders
- Limits and Structures in Graph Theory
- Sleep and Work-Related Fatigue
- Mathematics and Applications
- Health and Lifestyle Studies
- Differential Equations and Boundary Problems
- Graph Labeling and Dimension Problems
- Fuzzy and Soft Set Theory
- Random Matrices and Applications
- Sleep and Wakefulness Research
- Functional Equations Stability Results
University of California, San Diego
2025
Imperial College London
2017-2024
Homi Bhabha National Institute
2022
Harish-Chandra Research Institute
2021-2022
Columbia University
1963
Sleep deprivation is common among university students, and has been associated with poor academic performance physical dysfunction. However, current literature a narrow focus in regard to domains tested, this study aimed investigate the effects of night sleep on cognitive students. A randomized controlled crossover was carried out 64 participants [58% male (
Journal Article Some inequalities on characteristic roots of matrices Get access T. W. ANDERSON, ANDERSON Department Mathematical Statistics, Columbia University Search for other works by this author on: Oxford Academic Google Scholar S. DAS GUPTA Biometrika, Volume 50, Issue 3-4, December 1963, Pages 522–524, https://doi.org/10.1093/biomet/50.3-4.522 Published: 01 1963
In this paper, we study the asymptotic behaviour of sharp constant in discrete Hardy and Rellich inequality on lattice $\mathbb{Z}^d$ as $d \rightarrow \infty$. process, proved some Hardy-type inequalities for operators $\Delta^m$ $\nabla(\Delta^m)$ non-negative integers $m$ a $d$ dimensional torus. It turns out that grows $d^2$ respectively $ d
Abstract In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights the form $$n^\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>n</mml:mi> <mml:mi>α</mml:mi> </mml:msup> </mml:math> . We prove inequality when $$\alpha is an even natural number sharp constant and remainder terms. also find explicit constants in standard Rellich inequalities(with ) which are asymptotically as \rightarrow \infty...
In this thesis, we study problems at the interface of analysis and discrete mathematics. We discuss analogues well known Hardy-type inequalities Rearrangement on lattice graphs $\mathbb{Z}^d$, with a particular focus behaviour sharp constants optimizers.In first half analyse Hardy for $d=1$ then $d \geq 3$. prove weighted inequality integers power weights form $n^\alpha$. This is done via two different methods, namely super-solution Fourier method. also use method to type higher order...
Abstract The Polya–Szegő inequality in states that, given a nonnegative function , its spherically symmetric decreasing rearrangement is ‘smoother’ the sense of for all . We study analogues on lattice grid graph spiral known to satisfy Wang‐Wang satisfies it and no can develop robust approach show that both these rearrangements up constant In particular, also existence (many) such
In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights the form $n^α$. We prove inequality when $α$ is an even natural number sharp constant and remainder terms. also find explicit constants in standard Rellich its higher order versions. As by-product work derive combinatorial identity using purely analytic methods. This suggests correlation between identities functional identities.
We study Hardy inequalities for antisymmetric functions in three different settings: euclidean space, torus and the integer lattice. In particular, we show that under condition sharp constant inequality increases substantially grows as d^4 d \rightarrow \infty all cases. As a side product, prove on domain whose boundary forms corner at point of singularity x=0.