A5102997234- Spectral Theory in Mathematical Physics
- Mathematical Dynamics and Fractals
- Mathematical Analysis and Transform Methods
- Advanced Operator Algebra Research
- Advanced Topics in Algebra
- Advanced Banach Space Theory
- Advanced Mathematical Physics Problems
- Quantum, superfluid, helium dynamics
- Structural Load-Bearing Analysis
- Geometric Analysis and Curvature Flows
- Geometry and complex manifolds
- Atomic and Subatomic Physics Research
- advanced mathematical theories
- Differential Equations and Boundary Problems
- Advanced Computational Techniques in Science and Engineering
- Topological and Geometric Data Analysis
- Cold Atom Physics and Bose-Einstein Condensates
- Quasicrystal Structures and Properties
- Advanced Data Processing Techniques
- Digital Image Processing Techniques
- Quantum Chromodynamics and Particle Interactions
- Holomorphic and Operator Theory
- Nuclear physics research studies
- Complexity and Algorithms in Graphs
- Algebraic structures and combinatorial models
Massachusetts Institute of Technology
2022-2023
Tashkent University of Information Technology
2021
Pomona College
2021
North Carolina Agricultural and Technical State University
2002
We have studied the (pi(-),K+) reaction on a silicon target to investigate sigma-nucleus potential. The inclusive spectrum was measured at beam momentum of 1.2 GeV/c with an energy resolution 3.3 MeV (FWHM) by employing superconducting kaon spectrometer system. compared theoretical calculations within framework distorted-wave impulse approximation, which demonstrates that strongly repulsive potential nonzero size imaginary part reproduces observed spectrum.
Quantum cat maps are toy models in quantum chaos associated to hyperbolic symplectic matrices $A\in \operatorname{Sp}(2n,\mathbb{Z})$. The macroscopic limits of sequences eigenfunctions a map characterized by semiclassical measures on the torus $\mathbb{R}^{2n}/\mathbb{Z}^{2n}$. We show that if characteristic polynomial every power $A^k$ is irreducible over rationals, then measure has full support. proof uses an earlier strategy Dyatlov-J\'ez\'equel [arXiv:2108.10463] and higher-dimensional...
In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto C*-subalgebras.We begin by showing that these generalize the Frobenius norm, and we provide explicit formulas for C*-subalgebras of finite-dimensional C*-algebras.This allows us compare to operator norm finding equivalence constants.In particular, find constants standard Effros-Shen algebras vary continuously with respect their given irrational parameters.
This article discusses the use and development of a mathematical model for calculating items balance flow information, example, water supply economic facilities.
We construct a new version of the dual Gromov--Hausdorff propinquity that is sensitive to strongly Leibniz property. In particular, this distance complete on class quantum compact metric spaces. Then, given an inductive limit C*-algebras for which each C*-algebra equipped with L-seminorm, we provide sufficient conditions placing L-seminorm such sequence converges in propinquity. As application, place L-seminorms AF-algebras using Frobenius--Rieffel norms, have convergence Effros--Shen...
We study $\ell^\infty$ norms of $\ell^2$-normalized eigenfunctions quantum cat maps. For maps with short periods (constructed by Bonechi and de Bi\`evre), we show that there exists a sequence $u$ $\|u\|_{\infty}\gtrsim (\log N)^{-1/2}$. general the upper bound $\|u\|_\infty\lesssim Here semiclassical parameter is $h=(2\pi N)^{-1}$. Our analogous to one proved B\'{e}rard for compact Riemannian manifolds without conjugate points.
Abstract We study ℓ ∞ norms of 2 -normalized eigenfunctions quantum cat maps. For maps with short periods (constructed by Bonechi and de Biévre in F S De Bièvre (2000, Communications Mathematical Physics , 211 659–686)) we show that there exists a sequence u <?CDATA $\parallel u{\parallel }_{\infty }\gtrsim {\left(\mathrm{log}N\right)}^{-1/2}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">∥</mml:mo> <mml:mi>u</mml:mi> <mml:msub>...
The complex Green operator $\mathcal{G}$ on CR manifolds is the inverse of Kohn-Laplacian $\square_b$ orthogonal complement its kernel. In this note, we prove Schatten and Sobolev estimates for unit sphere $\mathbb{S}^{2n-1}\subset \mathbb{C}^n$. We obtain these by using spectrum asymptotics eigenvalues usual Laplace-Beltrami operator.
Let $A$ be a set of finite integers, define $$A+A \ = \{a_1+a_2: a_1,a_2 \in A\}, A-A \{a_1-a_2: A\},$$ and for non-negative integers $s$ $d$ $$sA-dA\ =\ \underbrace{A+\cdots+A}_{s} -\underbrace{A-\cdots-A}_{d}.$$ A More Sums than Differences (MSTD) is an where $|A+A| > |A-A|$. It was initially thought that the percentage subsets $[0,n]$ are MSTD would go to zero as $n$ approaches infinity addition commutative subtraction not. However, in surprising 2006 result, Martin O'Bryant proved...
The Erd\H{o}s distance problem concerns the least number of distinct distances that can be determined by $N$ points in plane. integer lattice with is known as \textit{near-optimal}, it spans $\Theta(N/\sqrt{\log(N)})$ distances, lower bound for a set (Erd\H{o}s, 1946). only previous non-asymptotic work related to has been done was $N \leq 13$. We take new approach this model case, studying distribution, or other words, plot frequencies each $N\times N$ lattice. In order fully characterize we...
We obtain an analog of Weyl's law for the Kohn Laplacian on lens spaces. also show that two 3-dimensional spaces with fundamental groups equal prime order are isospectral respect to if and only they CR isometric.
Let $M= \Gamma \setminus \mathbb{H}_d$ be a compact quotient of the $d$-dimensional Heisenberg group $\mathbb{H}_d$ by lattice subgroup $\Gamma$. We show that eigenvalue counting function $N(\lambda)$ for any fixed element family second order differential operators $\left\{\mathcal{L}_\alpha\right\}$ on $M$ has asymptotic behavior $N\left(\lambda\right) \sim C_{d,\alpha} \operatorname{vol}\left(M\right) \lambda^{d + 1}$, where $C_{d,\alpha}$ is constant only depends dimension $d$ and...
In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto C*-subalgebras. We begin by showing that these generalize the Frobenius norm, and we provide explicit formulas for C*-subalgebras of finite-dimensional C*-algebras. This allows us compare to operator norm finding equivalence constants. particular, find constants standard Effros-Shen algebras vary continuously with respect their given irrational parameters.