Spectral Optimization: From Mathematics to Physics and Advanced Technology

Deliverables

Open Research Data Pilot

Explanation of vertex coupling influence

Analysis of spectral properties depending on the network geometry and topology, spectral optimization and control. Two or three published journal articles or preprints.

1-d perturbations and controllability

Explanation of the interplay of 1-d perturbations and controllability of the spectrum of DAE's. Two or three published journal articles or preprints.Extension to operators (which corresponds to partial differential equations).

Localization properties of bases and frames on the multivariate torus

Localization properties of bases and frames on the multivariate torus. Two or three published journal articles or preprints.

Dissemination, exploitation and outreach

Permanent tasks

Publications

PT-symmetric dynamical confinement: Fermi acceleration, quantum force, and Berry phase

Author(s): Rakhmanov, S., Trunk, C., Znojil, M., Matrasulov, D.
Published in: Physical Review A, Issue 109, 2024, Page(s) 053519, ISSN 2469-9926
Publisher: American Physical Society

Dirac particle under dynamical confinement: Fermi acceleration, trembling motion and quantum force

Author(s): J. Dittrich, S. Rakhmanov, D. Matrasulov
Published in: Physics Letters A, Issue 503, 2024, Page(s) 129408, ISSN 0375-9601
Publisher: Elsevier BV
DOI: 10.1016/j.physleta.2024.129408

Elliptic problems with rough boundary data in generalized Sobolev spaces

Author(s): Anna Anop, Robert Denk and Aleksandr Murach
Published in: Comm. Pure Appl. Anal., Issue Volume 20, Issue 2, 2021, Page(s) 697-735, ISSN 1534-0392
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2020286

Quantum lattice transport along an infinitely extended perturbation

Author(s): Marzieh Baradaran, Pavel Exner, Andrii Khrabustovskyi
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 58, 2025, Page(s) 145203, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/adc646

Vertex coupling interpolation in quantum chain graphs

Author(s): Pavel Exner, Jan Pekař
Published in: Journal of Mathematical Physics, Issue 65, 2024, Page(s) 092102, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0208361

Boundary-value problems for weakly singular integral equations

Author(s): Oleksandr Boichuk and Victor Feruk
Published in: Discrete and Continuous Dynamical Systems – Series, Issue Volume 27, Issue 3, 2022, 2022, Page(s) 1379-1395, ISSN 1531-3492
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcdsb.2021094

Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals

Author(s): Serdyuk, A.S., Stepanyuk, T.A.
Published in: FILOMAT, Issue Volume 34, Issue 14, 2020, 2020, Page(s) 4697–4707, ISSN 0354-5180
Publisher: Universitet of Nis
DOI: 10.2298/fil2014697s

On the Approximate Solution of Weakly Nonlinear Boundary-Value Problems by the Newton–Kantorovich Method

Author(s): A. A. Boichuk & S. M. Chuiko
Published in: Journal of Mathematical Sciences, Issue Volume 261, Number 2, 2022, 2022, Page(s) 228–240, ISSN 1072-3374
Publisher: Plenum Publishers
DOI: 10.1007/s10958-022-05748-5

Multi-interval Sturm-Liouville problems with distributional coefficients

Author(s): Andrii Goriunov
Published in: Methods Funct. Anal. Topology, Issue Vol. 26, no. 2, 2020, Page(s) 103-110, ISSN 2415-7503
Publisher: Methods of Functional Analysis and Topology (MFAT)
DOI: 10.31392/mfat-npu26_2.2020.02

A Multi-Point Problem for a system of Differential Equations with Piecewise-Constant a Argument of generalized Type as a Neural Network Model.

Author(s): A. Abildayeva, A. Assanova, A. Imanchiyev
Published in: Eurasian Mathematical Journal, Issue Volume 13, Number 2 (2022),, 2022, Page(s) 08 – 17., ISSN 2077-9879
Publisher: L. N. Gumilyov Eurasian National University
DOI: 10.32523/2077-9879-2022-13-2-08-17

Asymptotic Estimates for the Best Uniform Approximations of Classes of Convolution of Periodic Functions of High Smoothness

Author(s): Anatolii S. Serdyuk and Igor V. Sokolenko
Published in: Journal of Mathematical Sciences, Issue Volume 252, Number. 4, 2021, 2021, ISSN 1072-3374
Publisher: Plenum Publishers
DOI: 10.1007/s10958-020-05178-1

Riemann problem for multiply connected domain in Besov spaces

Author(s): Nazarbay Bliev & Nurlan Yerkinbayev
Published in: Boundary Value Problems, Issue Article number: 70 (2024), 2024, ISSN 1687-2770
Publisher: Springer Nature
DOI: 10.1186/s13661-024-01883-x

Asymptotic estimates for the widths of classes of functions of high smoothness

Author(s): A.S. Serdyuk, I.V. Sokolenko
Published in: Carpathian Mathematical Publications, Issue Volume 15, Number 1, 2023, 2023, Page(s) 246-259, ISSN 2313-0210
Publisher: Precarpathian National University
DOI: 10.15330/cmp.15.1.246-259

Novel approach for solving multipoint boundary value problem for integro-differential equation

Author(s): Assanova A.T., Bakirova E.A, and Uteshova R.E.
Published in: Kazakh Mathematical Journal, Issue Vol. 20 No. 1, 2020, 2020, ISSN 2413-6468
Publisher: Institute of Mathematics and Mathematical Modeling

Elliptic problems with additional unknowns in boundary conditions and generalized Sobolev spaces

Author(s): A. Anop, I. Chepurukhina, A. Murach,
Published in: Axioms, Special Issue Boundary-Value and Spectral Problems, Issue 10(4), 2021, Page(s) article no. 292, 23 pp., ISSN 2075-1680
Publisher: MDPI
DOI: 10.3390/axioms10040292

A singular boundary value problem for evolution equations of hyperbolic type

Author(s): Anar T. Assanovaa, Roza E. Uteshova
Published in: Chaos, Solitonen und Fraktale, Issue Volume 143, 2021, ISSN 0000-0000
Publisher: ELSEVIER
DOI: 10.1016/j.chaos.2020.110517

Elliptic problems with unknowns on the boundary and irregular boundary data

Author(s): Iryna Chepurukhina, Aleksandr Murach
Published in: Methods Funct. Anal. Topology, Issue 26, no. 2, 2020, Page(s) 91-102, ISSN 1029-3531
Publisher: Methods of Functional Analysis and Topology (MFAT)
DOI: 10.48550/arxiv.2006.08379

Direct and inverse approximation theorems of functions in the MusielakOrlicz type spaces

Author(s): Fahreddin Abdullayev, Stanislav Chaichenko, Andrii Shidlich
Published in: Mathematical Inequalities & Applications, Issue Volume 24, Number 2, 2021, 2021, Page(s) 323–336, ISSN 1331-4343
Publisher: Element d.o.o.
DOI: 10.7153/mia-2021-24-23

Autonomous nonlinear boundary-value problems for the Lyapunov equation in the Hilbert space

Author(s): D. S. Bihun, O. O. Pokutnyi, E. V. Panasenko.
Published in: Ukrainian Mathematical Journal, Issue Volume 73, Number 7, 2021, 2021, Page(s) 1009–1022, ISSN 0041-5995
Publisher: Consultants Bureau
DOI: 10.1007/s11253-021-01973-4

Approximation of generalized Poisson integrals by interpolating trigonometric polynomials

Author(s): A. Serdyuk, T. Stepaniuk
Published in: Ukrains’kyi Matematychnyi Zhurnal, Issue Volume 75, Number 7, 2023, 2023, Page(s) 946 - 969, ISSN 0041-6053
Publisher: Institute of Mathematics NAS of Ukraine
DOI: 10.37863/umzh.v75i7.7523

Approximation on hexagonal domains by Taylor-Abel-Poisson means

Author(s): Jürgen Prestin Viktor Savchuk Andrii Shidlich
Published in: Journal of Mathematical Analysis and Applications, Issue Volume 528, Issue 2, 2023, 2023, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.1016/j.jmaa.2023.127536

Parabolic problems in generalized Sobolev spaces

Author(s): Valerii Los, Vladimir Mikhailets, and Aleksandr Murach
Published in: Comm. Pure Appl. Anal., Issue Volume 20, Issue 10, 2021, Page(s) 3589-3620, ISSN 1534-0392
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/cpaa.2021123

Representation of the Mittag-Leffler function through the exponential functions in the case of rational derivatives

Author(s): Fikret A. Aliev , N.A .Aliev , N.A. Safarova
Published in: Proceedings of the 7th International Conference on Control and Optimization with Industrial Applications, Issue Volume 1, 2020, Page(s) 80-82, ISBN 9789952378610
Publisher: COIA
DOI: 10.48550/arxiv.1904.12737

Asymptotic behavior of the widths of classes of the generalized Poisson integrals

Author(s): A.S. Serdyuk, I. V. Sokolenko
Published in: International scientific online conference «Algebraic and geometric methods of analysis» May 29 - June 1, 2023, dedicated to 160th anniversary of D.O.Grave, Issue Book of Abstracts, 2023, Page(s) 109-110
Publisher: Institute of Mathematics of NAS of Ukraine

Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

Author(s): A.S. Serdyuk, I.V. Sokolenko
Published in: "International scientific conference ""Theory of approximations and its application"" is dedicated to the 100th anniversary of the birth of Mykola Pavlovich Korneychuk (September 16-19, 2020, Dnipro, Ukraine)", Issue Book of Abstracts, 2020, Page(s) P. 25
Publisher: Oles Honchar Dnipro National University

A weakly perturbed linear boundary value problem for a system of differential equations of fractional order

Author(s): A. Boichuk, V. Feruk
Published in: International scientific conference «MATHEMATICS AND INFORMATION TECHNOLOGIES» dedicated to the 55th anniversary of the faculty mathematics and informatics of Yuri Fedkovich Chernivtsi National University, (Chernivtsi, September 28-30, 2023), Issue Book of Abstracts, 2023, Page(s) 159-160
Publisher: Yuri Fedkovich Chernivtsi National University

Approximation by interpolation trigonometric polynomials in the classes of Weyl-Nagy differentiable functions with high exponent of smoothness

Author(s): A.S. Serdyuk, I. V. Sokolenko
Published in: International scientific conference «MATHEMATICS AND INFORMATION TECHNOLOGIES» dedicated to the 55th anniversary of the faculty mathematics and informatics of Yuri Fedkovich Chernivtsi National University, (Chernivtsi, September 28-30, 2023), Issue Book of Abstracts, 2023, Page(s) 303-304
Publisher: Yuri Fedkovich Chernivtsi National University

Estimates for best uniform approximations of classes of convolutions of periodic functions of high smoothness

Author(s): Anatolii Serdyuk, Igor Sokolenko
Published in: XI International Skorobohatko mathematical conference (October 26 – 30, 2020, Lviv, Ukraine), Issue Book of Abstracts, 2020, Page(s) P. 103, ISBN 978-966-02-9390-8
Publisher: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics

A nonlocal problem for hyperbolic equations with impulse discrete memory

Author(s): Assanova Anar T., Imanchiyev Askarbek E.
Published in: International scientific conference «MATHEMATICS AND INFORMATION TECHNOLOGIES» dedicated to the 55th anniversary of the faculty mathematics and informatics of Yuri Fedkovich Chernivtsi National University, (Chernivtsi, September 28-30, 2023), Issue Book of Abstracts, 2023, Page(s) 11-12
Publisher: Yuri Fedkovich Chernivtsi National University

On asymptotic equations for the widths of classes of the generalized Poisson integrals

Author(s): A.S. Serdyuk, I. V. Sokolenko
Published in: Current problems of Mechanics and Mathematics-2023, Issue Collection of Scientific Papers, 2023, Page(s) 307-308
Publisher: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine

On asymptotic estimates for the widths of classes of functions of high smoothness

Author(s): A.S. Serdyuk, I. V. Sokolenko
Published in: International Online Workshop on Approximation Theory (IOWAT-2021) (March 1921, 2021), Issue Book of Abstracts, 2021, Page(s) 34-35, ISBN 978-617-8011-11-6
Publisher: Vasyl Stefanyk Precarpathian National University

Asymptotical method to solution the identification problem for determining the parameters of discrete dynamical systems

Author(s): Aliev, F. A., Hajiyeva, N. S., Namazov, A. A., Safarova, N. A.
Published in: Proceedings of the7th International Conference on Control and Optimization with Industrial Applications, Issue VOL. 1, 2020, Page(s) 92-94, ISBN 9789952378603
Publisher: COIA

On asymptotic equations for the widths of classes of the generalized Poisson integrals

Author(s): A.S. Serdyuk, I. V. Sokolenko
Published in: International Conference Mathematical Analysis, Differential Equations & Applications (MADEA-9) (Bishkek, Kyrgyz Republic, June 21-25, 2021), Issue Book of Abstracts, 2021, Page(s) P. 73, ISSN 978-9967-9294-4-9-978-9967-9294-5-6
Publisher: Kyrgyz-Turkish Manas University

Cauchy problem of the fractional order linear ordinary differential equations

Author(s): Aliev, N. A., Safarova, N. A., Aliev, F. A., Velieva, N. I.
Published in: Proceedings of the7th International Conference on Control and Optimization with Industrial Applications, Issue VOL. 1, 2020, Page(s) 101-103
Publisher: COIA

Self-adjoint operators with nonlocal potential

Author(s): L. Nizhnik
Published in: Proceedings of 7th International Conference on Control and Optimization with Industrial Applications, Issue V1, 2022, 2022, Page(s) p,20-22, ISBN 9789952378610
Publisher: Baku State University

Larin Parameterization to Solve the Problem of Analytical Construction of the Optimal Regulator of Oscillatory Systems with Liquid Dampers

Author(s): Fikret A. Aliev, N.A. Aliev , N.I. Velieva, N.A. Safarova.
Published in: Journal of Applied and Computational Mechanics, Issue 6(SI) (2020), 2020, Page(s) Pages 1426-1430, ISSN 2383-4536
Publisher: Shahid Chamran University of Ahvaz
DOI: 10.22055/jacm.2020.34950.2548

An extended Hilbert scale and its applications

Author(s): Vladimir Mikhailets, Aleksandr Murach, Tetiana Zinchenko
Published in: ArXiv, 2021, Page(s) 43 pages
Publisher: arxiv
DOI: 10.48550/arxiv.2102.08089

Tunneling in soft waveguides: closing a book

Author(s): P. Exner, D. Spitzkopf
Published in: arXiv, submitted to J. Phys. A: Math. Gen., 2023
Publisher: arXiv

CORRESPONDENCEComments on “On a transformation of the *-congruence Sylvester equation for theleast squares optimization” by Satake, Y., Sogabe, T., Kemmochi, T., Zhang, S.L.

Author(s): Aliev, F.A., Larin , V.B., Mammadova, G.H.
Published in: TWMS Journal of Pure and Applied Mathematics, Issue V.12, N.2, 2021, 2021, Page(s) pp.289-290
Publisher: TWMS Journal of Pure and Applied Mathematics

Some Mathematical Problems and their Solutions for the Oscillating Systems with Liquid Dampers: A Review.

Author(s): Aliev Fikret , Aliyev N.A. , Hajiyeva N.S., , Mahmudov N.I
Published in: Journal of Applied and Computational Mathematics, Issue V.20, N.3, 2021, 2021, Page(s) pp.339-365.
Publisher: ?

A new look at old theorems of Fejér and Hardy

Author(s): Vladimir Mikhailets, Aleksandr Murach, Oksana Tsyhanok
Published in: ArXiv, 2023, Page(s) 12 Pages
Publisher: arXiv
DOI: 10.48550/arxiv.2307.15511

Elliptic problems in Besov and Sobolev-Triebel-Lizorkin spaces of low regularity

Author(s): I.S. Chepurukhina, A.A. Murach
Published in: Reports of the National Academy of Sciences of Ukraine, Issue no. 6, 2021, Page(s) 3-11
Publisher: Arxiv
DOI: 10.48550/arxiv.2108.08741

Povzner-Wienholtz-type theorems for Sturm-Liouville operators with singular coefficients

Author(s): Andrii Goriunov, Vladimir Mikhailets, Volodymyr Molyboga
Published in: ArXiv, 2021, Page(s) 10 Pages
Publisher: ArXiv
DOI: 10.48550/arxiv.2110.11750

Scattering problem for Dirac system with nonlocal potentials

Author(s): P. A. Cojuhari, L. P. Nizhnik
Published in: Methods Funct. Anal. Topology, Issue Vol. 25 (2019), no. 3, 2019, Page(s) 211–218, ISSN 2415-7503
Publisher: Methods of Functional Analysis and Topology (MFAT)

On the solvability of boundary value problems for linear differential-algebraic equations with constant coefficients

Author(s): Carsten Trunk, Anar Assanova, and Roza Uteshova
Published in: In Serie: Preprint/Technische Universität Ilmenau, Institut für Mathematik, Issue Bd. 23-06, 2023, Page(s) 7 pages
Publisher: dbt

Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

Author(s): Serdyuk, A. S.; Sokolenko, I. V.
Published in: ArXiv, 2020, Page(s) 19 Pages
Publisher: ArXiv
DOI: 10.48550/arxiv.2008.01450

Deliverables

Publications

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