# preferredTitle
Arthur George and Mary Emolene Owen Chair, Distinguished Professor

# positions[].label
Arthur George and Mary Emolene Owen Chair

# overview
Major research articles, books, surveys, and presentations around the world on inverse problems (with applications to medical and homeland security imaging), material science (photonic crystals, nanostructures), spectral theory 9with math physics applications), and quantum graphs.

# researchAreas[].label
Human Resource Development, Workplace Incivility, Crisis Management, Work-life Issues

# researchAreas[].label
Human Resource Development and African Americans

# keywords[]
Propagation Of Electromagnetic And Acoustic Waves

# keywords[]
4.1 Discovery And Preclinical Testing Of Markers And Technologies

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
Machine Learning And Artificial Intelligence

# keywords[]
Propagation Of Electromagnetic And Acoustic Waves

# keywords[]
4.1 Discovery And Preclinical Testing Of Markers And Technologies

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
Propagation Of Electromagnetic And Acoustic Waves

# keywords[]
16 Peace, Justice And Strong Institutions

# keywords[]
4.1 Discovery And Preclinical Testing Of Markers And Technologies

# educationAndTraining[].organization.label
University of Kharkiv - (Kharkiv, Ukraine)

# educationAndTraining[].organization.label
Voronezh State University - (Voronezh, Russia)

# educationAndTraining[].organization.label
National Academy of Sciences of Ukraine - (Kiev, Ukraine)

# awardsAndHonors[].label
Fellow of the Society for Industrial and Applied Mathematics

# publications[].label
Singularities of the boundary of the stability region in the infinite-dimensional case

# publications[].label
BAND-GAP STRUCTURE OF THE SPECTRUM OF PERIODIC MAXWELL OPERATORS

# publications[].label
THE SUPPORT THEOREM FOR THE SINGLE RADIUS SPHERICAL MEAN TRANSFORM

# publications[].label
On a problem concerning affine-invariant points of convex sets

# publications[].label
On occurrence of spectral edges for periodic operators inside the Brillouin zone

# publications[].label
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior

# publications[].label
Band-gap structure of spectra of periodic dielectric and acoustic media .2. Two-dimensional photonic crystals

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Auxiliary Statements and Proofs of Technical Lemmas

# publications[].label
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography

# publications[].label
INVERSION OF WEIGHTED DIVERGENT BEAM AND CONE TRANSFORMS

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Three-Dimensional Image Reconstruction from Compton Camera Data

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
REPRESENTATIONS OF SOLUTIONS OF PERIODIC PARTIAL DIFFERENTIAL EQUATIONS

# publications[].label
Range conditions for a spherical mean transform

# publications[].label
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

# publications[].label
Spectral properties of high contrast band-gap materials and operators on graphs

# publications[].label
The support theorem for the single radius spherical mean transform

# publications[].label
(): Mikhail Aleksandrovich Shubin (obituary)

# publications[].label
Remembering Carlos A. Berenstein (19442019)

# publications[].label
Differential and pseudo-differential operators on graphs as models of mesoscopic systems

# publications[].label
Compton camera imaging and the cone transform: a brief overview

# publications[].label
On the structure of spectra of periodic elliptic operators

# publications[].label
Critical partitions and nodal deficiency of billiard eigenfunctions

# publications[].label
Floquet representation of solutions of linear hypoelliptic systems of partial differential equations

# publications[].label
Dispersion relations and spectra of periodically perforated structures

# publications[].label
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

# publications[].label
Floquet theory for partial differential equations

# publications[].label
On resonant spectral gap opening in quantum graph networks

# publications[].label
Some binomial formulas for non-commuting operators

# publications[].label
A Bayesian approach to the detection of small low emission sources.

# publications[].label
Range descriptions for the spherical mean Radon transform

# publications[].label
Band-gap structure of spectra of periodic dielectric and acoustic media .1. Scalar model

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
AN OVERVIEW OF PERIODIC ELLIPTIC OPERATORS

# publications[].label
Liouville-Riemann-Roch Theorems on Abelian Coverings Preface

# publications[].label
An asymptotic model for wave propagation in thin high contrast 2D acoustic media.

# publications[].label
Passive Detection of Small Low-Emission Sources: Two-Dimensional Numerical Case Studies

# publications[].label
(    ): Boris Rufimovich Vainberg (on his 80th birthday)

# publications[].label
Master's-level certificate program in nuclear forensics at Texas A&M University

# publications[].label
Spectral shift via "lateral" perturbation

# publications[].label
Book Review: Climate modeling for scientists and engineers

# publications[].label
Spectral shift via "lateral" perturbation

# publications[].publisher
European Mathematical Society - EMS - Publishing House

# publications[].label
Some Major CT Modalities and Their Features to Watch for

# publications[].label
On guided electromagnetic waves in photonic crystal waveguides

# publications[].label
Coincidence of length spectra does not imply isospectrality

# publications[].label
Integral representations of solutions of periodic elliptic equations

# publications[].label
Differential operators on graphs and photonic crystals

# publications[].label
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed

# publications[].label
Detecting small low emission radiating sources

# publications[].label
Spectra of "fattened" open book structures

# publications[].label
Spectra of fattened open book structures

# publications[].label
Call for papers for a special issue on Quantum Graphs and their Applications

# publications[].label
Mikhail Aleksandrovich Shubin. December 19, 1944 -- May 13, 2020

# publications[].label
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs

# publications[].label
Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds

# publications[].label
On Reconstruction Formulas and Algorithms for the Thermoacoustic Tomography

# publications[].label
Detection of small low emission sources - case studies

# publications[].label
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media

# publications[].label
Stabilizing inverse problems by internal data. II. Non-local internal data and generic linearized uniqueness

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Range descriptions for the spherical mean Radon transform

# publications[].label
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior

# publications[].publisher
European Mathematical Society - EMS - Publishing House

# publications[].label
Range conditions for the exponential radon transform

# publications[].label
Coincidence of length spectra does not imply isospectrality

# publications[].label
Some binomial formulas for non-commuting operators

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
On Parseval frames of exponentially decaying composite Wannier functions

# publications[].label
Generalized transforms of Radon type and their applications

# publications[].label
Generic properties of dispersion relations for discrete periodic operators

# publications[].label
Deep learning for 2D passive source detection in presence of complex cargo

# publications[].label
Convergence of spectra of mesoscopic systems collapsing onto a graph

# publications[].label
On the spectral synthesis in the spaces of solutions of invariant differential equations

# publications[].label
2D and 3D reconstructions in acousto-electric tomography

# publications[].label
Selim Grigor'evich Krein (on his seventieth birthday)

# publications[].label
Tight frames of exponentially decaying Wannier functions

# publications[].label
On the injectivity of the circular Radon transform arising in thermoacoustic tomography

# publications[].label
Identities for sin x that Came from Medical Imaging

# publications[].label
Inverse Problems with Interior Information

# publications[].label
On the spectra of carbon nano-structures

# publications[].label
Mathematics of Hybrid Imaging. A Brief Review

# publications[].label
Reconstructions in ultrasound modulated optical tomography

# publications[].label
Homogeneous trees of second order SturmLiouville equations: A general theory and program

# publications[].label
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown

# publications[].label
The exponential X-ray transform and Fritz Johns equation. I. Range description

# publications[].label
Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds

# publications[].label
Bloch solutions of periodic partial differential equations

# publications[].label
On absence of embedded eigenvalues for Schrodinger operators with perturbed periodic potentials

# publications[].label
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs

# publications[].label
2D and 3D reconstructions in acousto-electric tomography

# publications[].label
A survey in mathematics for industry mathematics of thermoacoustic tomography

# publications[].label
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

# publications[].label
A Bayesian Approach to Detection of Small Low Emission Sources

# publications[].label
DETECTING SMALL LOW EMISSION RADIATING SOURCES

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
RANGE CONDITIONS FOR THE MULTIDIMENSIONAL EXPONENTIAL X-RAY TRANSFORM

# publications[].label
Quantum graph spectra of a graphyne structure

# publications[].label
Quantum graphs: an introduction and a brief survey

# publications[].label
Stabilizing inverse problems by internal data

# publications[].label
2d photonic crystals with cubic structure: asymptotic analysis

# publications[].label
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

# publications[].label
A range description for the planar circular Radon transform

# publications[].label
Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs

# publications[].label
A range description for the planar circular radon transform

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Mikhail Aleksandrovich Shubin. December 19, 1944 -- May 13, 2020

# publications[].label
Boris R. Vainberg (on his 80th birthday)

# publications[].label
On a problem concerning affine-invariant points of convex sets

# publications[].label
On some spectral problems of mathematical physics

# publications[].label
Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs

# publications[].label
CBMS-NSF Regional Conference Series in Applied Mathematics: Preface

# publications[].label
DEPSCoR Project Mathematical Analysis of Photonic Band-Gap Materials 1997-2000

# publications[].label
Boris R. Vainberg (on his 80th birthday)

# publications[].label
Approximation by spherical waves inLp-spaces

# publications[].label
On the injectivity of the circular Radon transform

# publications[].label
Three-Representation Problem in Banach Spaces

# publications[].label
Spectral shift via "lateral" perturbation

# publications[].label
RANGE CONDITIONS FOR A SPHERICAL MEAN TRANSFORM

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Functional Analysis and Geometry: Selim Grigorievich Krein Centennial Preface

# publications[].label
Identities for sin(x) that came from medical imaging

# publications[].label
Stability of spectral partitions with corners

# publications[].publisher
European Mathematical Society - EMS - Publishing House

# publications[].label
On Reconstruction Formulas and Algorithms for the Thermoacoustic Tomography

# publications[].label
Graph models for waves in thin structures

# publications[].label
Mathematics of Photoacoustic and Thermoacoustic Tomography

# publications[].label
On absence of embedded eigenvalues for Schrdinger operators with perturbed periodic potentials

# publications[].label
The support theorem for the single radius spherical mean transform

# publications[].label
Dispersion relations and spectra of periodically perforated structures

# publications[].label
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

# publications[].label
Integral representations of solutions of periodic elliptic equations

# publications[].label
Detection of small low emission sources - case studies

# publications[].label
An efficient finite element method for computing spectra of photonic and acoustic band-gap materials - I. Scalar case

# publications[].label
Stability of spectral partitions with corners

# publications[].label
Deep learning for 2D passive source detection in presence of complex cargo

# publications[].label
On guided waves in photonic crystal waveguides

# publications[].label
Paley-Wiener theorem for exponential Radon transform

# publications[].label
On Parseval frames of exponentially decaying composite Wannier functions

# publications[].label
Spectra of "fattened" open book structures

# publications[].label
"Standard" CT and X-ray and Radon Transforms

# publications[].label
ON THE BEHAVIOR OF FLOQUET EXPONENTS OF A KIND OF PERIODIC EVOLUTION PROBLEMS

# publications[].label
On the location of spectral edges in Z-periodic media

# publications[].label
On positivity problems for the Radon transform and some related transforms

# publications[].label
Functional Analysis and Geometry: Selim Grigorievich Krein Centennial Introduction

# publications[].label
On guided electromagnetic waves in photonic crystal waveguides

# publications[].label
Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness

# publications[].label
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

# publications[].label
Stabilizing Inverse Problems by Internal Data

# publications[].label
Asymptotic methods for thin high-contrast two-dimensional PBG materials

# publications[].publisher
Institute of Electrical and Electronics Engineers (IEEE)

# publications[].label
Some binomial formulas for non-commuting operators

# publications[].label
Boris Rufimovich Vainberg (on his 80th birthday)

# publications[].label
Synthetic focusing in ultrasound modulated tomography

# publications[].label
On absolute continuity of spectra of periodic elliptic operators

# publications[].label
Mathematics of Photoacoustic and Thermoacoustic Tomography

# publications[].label
Thermo-, Photo-, and Optoacoustic Tomography (TAT/PAT/OAT)

# publications[].label
On resonant spectral gap opening in quantum graph networks

# publications[].label
Generic properties of dispersion relations for discrete periodic operators

# publications[].label
On embedded eigenvalues of perturbed periodic Schrodinger operators

# publications[].label
To the memory of Selim Grigor'evich Krein (1917-1998)

# publications[].label
Asymptotics of spectra of Neumann Laplacians in thin domains

# publications[].label
Integral representations and Liouville theorems for solutions of periodic elliptic equations

# publications[].label
3D Image Reconstruction from Compton camera data

# publications[].label
Some inversion formulas in the single photon emission computed tomography

# publications[].label
Reconstruction of a continuous representation with respect to a subrepresentation and a factor representation

# publications[].label
More about 3D Radon and X-ray Transforms

# publications[].label
Integral representations and Liouville theorems for solutions of periodic elliptic equations

# publications[].label
CONTEMPORARY MATHEMATICS Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial Preface

# publications[].label
Half-time Range description for the free space wave operator and the spherical means transform

# publications[].label
Green's function asymptotics near the internal edges of spectra of   periodic elliptic operators. Spectral edge case

# publications[].label
On inversion and range characterization of one transform arising in emission tomography

# publications[].label
THE ABSENCE OF L2-SOLUTIONS FOR PERIODIC PARTIAL DIFFERENTIAL EQUATIONS

# publications[].label
On reconstruction formulas and algorithms for the thermoacoustic tomography

# publications[].label
On occurrence of spectral edges for periodic operators inside the Brillouin zone

# publications[].label
On the location of spectral edges in $mathbb{Z}$-periodic media

# publications[].label
ON THE FLOQUET THEORY FOR PERIODIC LINEAR DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

# publications[].label
Tight frames of exponentially decaying Wannier functions

# publications[].label
On absolute continuity of spectra of periodic elliptic operators

# publications[].label
Some sufficient conditions for the existence of nonhomogeneous flows in networks

# publications[].label
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown

# publications[].label
On resonant spectral gaps in quantum graphs

# publications[].publisher
European Mathematical Society - EMS - Publishing House

# publications[].label
Inversion of Weighted Divergent Beam and Cone Transforms

# publications[].label
SPHERICAL REPRESENTATION OF SOLUTIONS OF INVARIANT DIFFERENTIAL EQUATIONS ON A RIEMANNIAN SYMMETRIC SPACE OF NONCOMPACT TYPE

# publications[].label
Functions on symmetric spaces which are periodic in the mean

# publications[].label
The Radon Transform and Medical Imaging Preface

# publications[].label
An overview of periodic elliptic operators

# publications[].label
Numerical harmonic analysis on the hyperbolic plane

# publications[].label
Quantum graph spectra of a graphyne structure

# publications[].label
CONTEMPORARY MATHEMATICS Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial Introduction

# publications[].label
Spectral properties of classical waves in high-contrast periodic media

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Quantum graphs: an introduction and a brief survey

# publications[].label
3D Image Reconstruction from Compton camera data

# publications[].label
CRITICAL PARTITIONS AND NODAL DEFICIENCY OF BILLIARD EIGENFUNCTIONS

# publications[].label
Quantum graphs: I. Some basic structures

# publications[].label
Selim Krein and Voronezh Winter Mathematical Schools

# publications[].label
On the spectra of carbon nano-structures

# publications[].label
Leon Ehrenpreis, Recollections from the Recent Decades

# publications[].tags
16 Peace, Justice and Strong Institutions

# publications[].label
Mathematics of Hybrid Imaging: A Brief Review

# publications[].label
Artifacts, Incomplete Data, Microlocal Analysis, and Such

# publications[].label
SYNTHETIC FOCUSING IN ULTRASOUND MODULATED TOMOGRAPHY

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Mathematics of Photoacoustic and Thermoacoustic Tomography

# publications[].label
On reconstruction formulas and algorithms for the thermoacoustic tomography

# publications[].label
Floquet Theory for Partial Differential Equations

# editorOf[].label
Tomography and Inverse Transport Theory International Workshop on Mathematical Methods in Emerging Modalities of Medical Imaging, October 25-30, 2009, Banff, Canada : International Workshop on Inverse Transport Theory and Tomography, May 16-21, 2010, Banff, Canada

# editorOf[].label
Waves in Periodic and Random Media Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Waves in Periodic and Random Media, June 22-28, 2002, Mount Holyoke College, South Hadley, MA

# editorOf[].label
Analysis on Graphs and Its Applications Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 8-June 29, 2007

# editorOf[].label
Quantum Graphs and Their Applications Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 19-23, 2005, Snowbird, Utah

# editorOf[].label
Tomography, Impedance Imaging, and Integral Geometry 1993 AMS-SIAM Summer Seminar on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry, June 7-18, 1993, Mount Holyoke College, Massachusetts

# researcherOn[].label
Spectral Problems of Mathematical Physics Related to Novel Materials Science and Photonics

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Inverse Problems For Biomedical Imaging and Homeland Security

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Collaborative Research: Mathematics of Emerging Imaging Methods In Medicine and Homeland Security

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Spectral problems of mathematical physics and material science

# researcherOn[].awardedBy.label
Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# etdChairOf[].label
Do, Ngoc Thanh (2016-08). Some Spectral Problems in Mathematical Physics. Doctoral Dissertation.

# etdChairOf[].label
Allmaras, Moritz (2011-12). Modeling Aspects and Computational Methods for Some Recent Problems of Tomographic Imaging. Doctoral Dissertation.

# etdChairOf[].label
Weyand, Tracy Kathleen (2014-08). Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator. Doctoral Dissertation.

# etdChairOf[].label
Terzioglu, Fatma (2018-05). Compton Camera Imaging and the Cone Transform. Doctoral Dissertation.

# etdChairOf[].label
Kha, Minh Tuan (2017-08). Spectral Edge Properties of Periodic Elliptic Operators. Doctoral Dissertation.

# etdChairOf[].label
Ong, Beng Seong (2006-08). Spectral problems of optical waveguides and quantum graphs. Doctoral Dissertation.

# etdChairOf[].label
Nguyen, Linh V. (2010-08). Mathematical Problems of Thermoacoustic Tomography. Doctoral Dissertation.

# etdChairOf[].label
Moon, Sunghwan (2013-12). Properties of Some Integral Transforms Arising in Tomography. Doctoral Dissertation.

# etdChairOf[].label
Georgieva-Hristova, Yulia Nekova (2010-08). Mathematical Problems of Thermoacoustic and Compton Camera Imaging. Doctoral Dissertation.

# etdChairOf[].label
Ambartsoumian, Gaik (2006-08). Spherical radon transforms and mathematical problems of thermoacoustic tomography. Doctoral Dissertation.