S.M. Nikol’skii Mathematical Institute
S.M. Nikol’skii Mathematical Institute
S.M. Nikol’skii Mathematical Institute conducts research in the field of functional analysis, theory of functional spaces, ordinary differential equations, partial differential equations, nonlinear analysis, spectral theory of differential operators.
Director
Alexander Skubachevskii
Contacts
News All news
Science
06 Jul
A RUDN University chemist created anti-tumour compounds that are up to 80 times more effective than their counterparts

A chemist from RUDN University has created platinum complex compounds that are superior in activity to cisplatin, the drug for the treatment of tumour diseases. The new compounds turned out to be also less toxic to healthy cells.

Science
22 Jun
RUDN University biologist discovered that lavender enhances the immunity of carp

Biologist from RUDN University Morteza Yousefi has found that lavender extract added to the food reduces stress and improves immunity in carp in fish farms. The discovery may be used in fish farming.

Science
22 Jun
Leading oncologists release Russia's first encyclopedia of pediatric thoracoabdominal oncological surgery

Every year in Russia, about 4 thousand children need help of cancer surgeons. The lives of children depend on the professionalism and knowledge of surgeons. RUDN experts share relevant information and many years of experience for the first time in Russia, presenting systemic knowledge of pediatric thoracoabdominal oncological surgery in an encyclopedia published by a professor at the Faculty of Continuing Medical Education of RUDN University, Doctor of medical sciences Andrey Ryabov. The book is edited by the former chief oncologist of Russia, a brilliant oncologist surgeon, legendary academician Mikhail Davydov.

Research projects All projects
Construction of spherically symmetric stationary solutions of the Vlasov-Poisson system of equations describing the stationary distribution of particles in a gravitational field. Obtaining sufficient conditions for confining high-temperature plasma in a “mirror-trap” fusion reactor.

Project leader

Alexander Skubachevskii

In the problem of describing the asymptotic properties of generalized solutions of quasilinear parabolic equations in a neighborhood of the time of the singular exacerbation of the boundary regime (i.e. boundary data), at the present time, it were found limiting restrictions on the intensity of the exacerbation leading to solutions with a non zero but finite measure of the blow- up, i.e. the so-called S-modes are described.

Project leader

Andrey Shishkov

Laboratories and centers All laboratories

Scientific center of nonlinear problems of mathematical physics

The center is a structural subdivision of the S.M. Nikol’skii Mathematical Institute specializes in the field of mathematical physics.

TypeCenter

Interdisciplinary center for Mathematical modelling in Biomedicine

Mathematical modelling in biomedicine is one of rapidly developing scientific disciplines motivated by the fundamental research and by the applications to public health.

TypeCenter

Partners All partners

City

Giessen, Germany

Type of institution

University

Subject of cooperation:
Conducting joint research in the field of nonlinear functional-differential equations. Publication of joint works in high-rated journals.
Result of cooperation:

Joint research work with H.-O.-Walther, an employee of Justus Liebig University. Sufficient terms of hyperbolicity and stability of periodic solutions of nonlinear functional-differential equations were obtained. The results of the work are reflected in the articles: - Walter H.-O., Skubachevskii A. L. On hyperbolicity of rapidly oscillating periodic solutions to functional differential equations. // Journal “Functional analysis and its applications”, Vol. 39, is. 1, M., 2005, p. 82-85. - Walter X-Skubachevskii A. L. On hyperbolicity of solutions with irrational periods of some functional differential equations. // Journal “Proceedings of the Russian Higher School Academy of Sciences”, Vol. 402. №2, M., 2005, p. 151-154.

About partner:
Start of cooperation: 2003
Field of cooperation: hyperbolicity of periodic solutions of nonlinear functional-differential equations.

City

Munich, Germany

Type of institution

University

Subject of cooperation:
- Conducting joint research in the field of stationary solutions of the Vlasov-Poisson system describing the distribution of particles in the gravitational field.
- Publication of joint works in high-rated journals
Result of cooperation:

We are working on the joint article “Spherical symmetric stationary solutions of the Vlasov – Poisson equation” with J. Batt, an employee of Ludwig Maximilian University of Munich.

About partner:
Start of cooperation: 2017.

City

Jena, Germany

Type of institution

University

Subject of cooperation:
- Conducting joint research in the field of optimal embedding, estimates of continuity modules.
- Publication of joint works in high-rated journals.
Result of cooperation:

Joint research work with D. Haroske, an employee of Friedrich Schiller University Jena. Evaluation of the uniform modulus of continuity for Bessel potentials, accurate evaluation of the majorant of modules of continuity and optimal embedding for generalized Bessel potentials were obtained, optimal Calderon space for Bessel potentials and optimal Calderon space for generalized Bessel potentials were built.

Goldman M.L., Haroske D. Estimates for continuity envelopes and approximation numbers of Bessel potentials // Journal of Approximation Theory. 2013. Vol. 172. P. 58–85.

Goldman M.L., Haroske D. Optimal Calderon spaces for the generalized Bessel potentials / // Doklady Mathematics. 2015. Vol. 92. № 1. P. 404–407.

About partner:
Start of cooperation: 2013.

City

Hannover, Germany

Type of institution

University

Subject of cooperation:
- Conducting joint research in the field of the theory of elliptic operators, noncommutative geometry.
- Publication of joint papers in high-rated journals
Result of cooperation:

Mathematicians of RUDN University (Professor B. Yu. Sternin, Professor A. Y. Savin) with mathematicians of the University of Hannover (Prof. Dr. Elmar Schrohe) analyze actual problems of elliptic theory and noncommutative geometry in joint scientific works. In particular, an explicit uniformization for elliptic operators associated with groups of shift operators was found out. The terms for the Fredholm property of the operators associated with groups of quantized canonical transformations were obtained.

A.Yu. Savin, B.Yu. Sternin, E. Schrohe, “Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization”, Proceedings of the Russian Higher School Academy of Sciences, 441:5 (2011), 593–596; A.Yu. Savin, B.Yu. Sternin, E. Schrohe, “Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization”, Dokl. Math., 84:3 (2011), 846-849

A.Yu. Savin, B.Yu. Sternin, E. Schrohe, “On the Index Formula for an Isometric Diffeomorphism”, Journal of Mathematical Sciences, 201:6 (2014), 818–829

A.Yu. Savin, E. Schrohe, B. Sternin, “Uniformization and Index of Elliptic Operators Associated with Diffeomorphisms of a Manifold”, Russian Journal of Mathematical Physics, 22:3 (2015), “410–420”

About partner:
Start of cooperation: 2011.

City

Padova, Italy

Type of institution

University

Subject of cooperation:
- Conducting joint research in the field of spectral theory.
- Publication of joint works in high-rated journals.
Result of cooperation:

Accurate stability evaluation for the variation of eigenvalues of nonnegative selfadjoint elliptic operators of arbitrary even order when changing the open sets on which they are defined were obtain with P. D. Lamberti, M. Lanza de Cristoforis, Feleqi E. This evaluation is expressed in terms of Lebesgue measure of the symmetric difference of open sets. The boundary terms of Dirichlet and Neumann were analyzed.

A full list of joint works can be found here

About partner:
Start of cooperation: 2006.
Field of cooperation: spectral theory.

City

Baku, Azerbaijan

Type of institution

Research Institute

Subject of cooperation:
- Conducting joint research in the field of operator theory in Morrie type spaces.
- Publication of joint works in high-rated journals.

City

Ramat-Gan, Israel

Type of institution

University

Subject of cooperation:
- Conducting joint research in the field of operator theory in Morrie type spaces.
- Publication of joint works in high-rated journals.
Result of cooperation:

The terms that ensure the boundedness of Hausdorff operators in Morrie spaces were obtained together with E. Liflyand. The classes of Hausdorff operators for which the necessary and sufficient terms of boundedness coincide were described.

About partner:
Start of cooperation: 2017.

City

Praga, Czech Republic

Type of institution

Research Institute

Subject of cooperation:
- Conducting joint research in the field of operator theory in Morrie type spaces.
- Publication of joint works in high-rated journals.
Result of cooperation:

Necessary and sufficient terms for the boundedness of fractional maximal operators in general Morrie local spaces are for a wide class of admissible values of numerical parameters were obtained together with A. Gogatishvili. Sufficient and necessary terms for this kind of limitation for a certain range of parameters were obtained.

About partner:
Start of cooperation: 2010.

City

Nashville, USA

Type of institution

University

Subject of cooperation:
Mathematical modeling of erythropoiesis and blood cancers such as multiple myeloma. Development of optimal chemotherapy methods for patients with multiple myeloma.
Result of cooperation:

Joint research work with M. Koury. The mathematical model was developed, computer calculations and comparisons with experimental data of erythropoiesis functioning on the basis of erythroblastic islands were carried out. The development of multiple myeloma and its effect on erythropoiesis were investigated. Various treatment protocols of patients were modeled and compared with clinical data.

About partner:
Start of cooperation: 2012.

City

Barcelona, Spain

Type of institution

University

Subject of cooperation:
Multiscale and spatial models of immune response.
Result of cooperation:

Joint research work with A. Meyerhans. The study of the spread of viral infection in body tissues on the basis of reaction-diffusion and hybrid discrete-continuous models of immune response.

About partner:
Start of cooperation: 2016.

City

Lyon, France

Type of institution

University

Subject of cooperation:
Mathematical modeling of various diseases and clinical trials on virtual patients.
Result of cooperation:

Joint research work with C. Dumontet, P. Nony. Mathematical modeling of variousdiseases: leukaemia, lymphoma, lymphodema, mucoviscidosis, thrombosis. Simulation of clinical trials.

About partner:
Start of cooperation: 2012.

City

St. Gallen, Switzerland

Type of institution

Research Centre

Subject of cooperation:
Joint research with Prof. Ludwig Burkhardt's group on “Mathematical modeling of spatial structure and functioning of lymphoid organs”.
Result of cooperation:

Parametric models of the geometry of the lymph node were developed. Models were developed and topological properties of a network of fibroblastic reticular cells were analyzed. The features of lymph flow in the network of lymph node conduits were studied.

About partner:
Start of cooperation: 2000.

City

Heidelberg, Germany

Type of institution

Research Centre

Subject of cooperation:
Joint research with Prof. Willy Yeager on mathematical modeling of sepsis.
Result of cooperation:

The components of the system model describing the regulation of energy metabolism of cells in normoxia and hypoxia were developed.

About partner:
Start of cooperation: 2015.

Type of institution

University

Subject of cooperation:
Development of new modeling methods in Biomedicine based on discrete-continuous approaches in which biological cells are considered as individual objects, intracellular regulation is modeled by ordinary differential equations, and intercellular concentrations were described by partial differential equations. Application of these methods to modeling of various physiological processes.
Result of cooperation:

Joint research work with A. Bouchnita. Mathematical models and computer programs for describing the coagulation of blood in the stream considering biochemical reactions in the plasma and aggregation of platelets were developed. The terms of normal clot growth and thrombosis were obtained. Two articles are in print this year.

About partner:
Start of cooperation: 2018.
Events All events
2020
19 - 21 Aug
Online International Workshop “Differential Equations and Interdisciplinary Investigations”
The S.M. Nikol’skii Mathematical Institute holds the Online International Workshop “Differential Equations and Interdisciplinary Investigations” August 19-21, 2020 dedicated to the 60th anniversary of RUDN University. Within the framework of the conference leading scientists will give a course of lectures in a number of modern mathematical areas and their applications.
2020
9 Jul
Seminar “Investigation of cerebral hemodynamics based on intraoperative monitoring and mathematical models of complex media. Part 2”
We will talk about our multidisciplinary investigation of fluids and tissues in the brain: intraoperative monitoring of blood flows, laboratory and clinical simulation of blood flows and tissues of the brain, mathematical and computing simulation fluids and tissues of the brain.
2020
7 Jul
Seminar “Conservation laws with point constraint: analysis, approximation, modeling of road and pedestrian traffic”
We will briefly present classical LWR and ARZ macroscopic models of traffic flow (Lighthill-Whitham-Richards, Aw-Rascle and Zhang) and focus on their modification that permits to reproduce non-monotone features of traffic at bottlenecks, such as Faster-Is-Slower and Braess' Paradox.