16 citations · 47 across the 21 of their papers we have counts for
22 papers
Inverse Scattering for Single Photons in Quantum Optics
Giovanni Covi, Matti Lassas, Medet Nursultanov +3
We study inverse problems for a time-harmonic one-photon model describing the interaction of a single photon with a medium of stationary two-level atoms. After time-harmonic reduct…
Negative eigenvalue estimates for polyharmonic Schrödinger operators with measure-potentials: the subcritical case
Medet Nursultanov, Grigori Rozenblum
We study spectral estimates for polyharmonic Schrödinger operators in the subcritical regime . The measure potential is assumed to satisfy a capacitary…
An inverse problem for semilinear wave equations on metric tree graphs
Sergei Avdonin, Matti Lassas, Jinpeng Lu +2
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unk…
Quantum field theory and inverse problems: Imaging with Entangled Photons
Matti Lassas, Medet Nursultanov, Lauri Oksanen +1
We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to u…
Negative eigenvalue estimates for the 1D Schr{ö}dinger operator with measure-potential
Robert Fulsche, Medet Nursultanov, Grigori Rozenblum
We investigate the negative part of the spectrum of the operator on , where a locally finite Radon measure is serving as a potential. We…
The backscattering problem for time-dependent potentials
Medet Nursultanov, Lauri Oksanen, Plamen Stefanov
We study the inverse backscattering problem for time-dependent potentials. We prove uniqueness and Lipshitz stability for the recovery of small potentials.
Introduction to inverse problems for hyperbolic PDEs
Medet Nursultanov, Lauri Oksanen
There are two main approaches to solve inverse coefficient determination problems for wave equations: the Boundary Control method and an approach based on geometric optics. These n…
Determining Lorentzian manifold from non-linear wave observation at a single point
Medet Nursultanov, Lauri Oksanen, Leo Tzou
We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evalu…
Eigenvalue Variations of the Neumann Laplace Operator Due to Perturbed Boundary Conditions
Medet Nursultanov, William Trad, Justin Tzou +1
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold under the singular perturbation. This perturbation involve…
Disjoint data inverse problem on manifolds with quantum chaos bounds
Matti Lassas, Medet Nursultanov, Lauri Oksanen +1
We consider the inverse problem to determine a smooth compact Riemannian manifold from a restriction of the source-to-solution operator, , for the wave e…
boundedness of Fourier multipliers
Medet Nursultanov
We investigate the boundedness of the Fourier multipliers. We obtain sufficient conditions, namely, we derive Hormander and Lizorkin type theorems. We also obtain…
The narrow capture problem on general Riemannian surfaces
Medet Nursultanov, William Trad, Justin C. Tzou +1
In this article, we study the narrow capture problem on a Riemannian 2-manifold. This involves the derivation of the mean first passage (sojourn) time of a surface-bound ion modell…
The strength of diversity: mathematical proof that collections of variable individuals are robust in the face of challenges
Julie Rowlett, Carl-Joar Karlsson, Medet Nursultanov
Can one demonstrate quantitative effects of diversity within a system comprised of distinct individuals on the performance of the system as a whole? Assuming that individuals can b…
Narrow escape problem in the presence of the force field
Medet Nursultanov, William Trad, Leo Tzou
This paper considers the narrow escape problem of a Brownian particle within a three-dimensional Riemannian manifold under the influence of the force field. We compute an asymptoti…
On the Mean First Arrival Time of Brownian Particles on Riemannian Manifolds
Medet Nursultanov, Justin C. Tzou, Leo Tzou
We use geometric microlocal methods to compute an asymptotic expansion of mean first arrival time for Brownian particles on Riemannian manifolds. This approach provides a robust wa…
Biodiversity of marine microbes is safeguarded by phenotypic variability in ecological traits
Susanne Menden-Deuer, Medet Nursultanov, Sinead Collins +2
Why, contrary to theoretical predictions, do marine microbe communities harbor tremendous phenotypic heterogeneity? How can so many marine microbe species competing in the same nic…
How to hear the corners of a drum
Medet Nursultanov, Julie Rowlett, David Sher
We announce a new result which shows that under either Dirichlet, Neumann, or Robin boundary conditions, the corners in a planar domain are a spectral invariant of the Laplacian. F…
Spectral Theory for Sturm-Liouville operators with measure potentials through Otelbaev's function
Robert Fulsche, Medet Nursultanov
We investigate the spectral properties of Sturm-Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues…
The heat kernel on curvilinear polygonal domains in surfaces
Medet Nursultanov, Julie Rowlett, David A. Sher
We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those…
Asymptotic expansion for the eigenvalues of a perturbed anharmonic oscillator
Ksenia Fedosova, Medet Nursultanov
In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise Hölder continuous perturbation and investiga…
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary
Lashi Bandara, Medet Nursultanov, Julie Rowlett
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metri…
Evolution of time-harmonic electromagnetic and acoustic waves along waveguides
Medet Nursultanov, Andreas Rosén
We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wav…