30 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- St Petersburg UniversityRU6 papers
- Växjö KommunSE4 papers
- North-Eastern Federal UniversityRU2 papers
- Peter the Great St. Petersburg Polytechnic UniversityRU2 papers
- Universidad Nacional Autónoma de MéxicoMX2 papers
- University of BathGB2 papers
- Czech Academy of Sciences, Institute of MathematicsCZ1 paper
- Institute of MathematicsPL1 paper
- Institute of Mathematics and InformaticsBG1 paper
- Institute of Problems of Mechanical EngineeringRU1 paper
- Peoples' Friendship University of RussiaRU1 paper
- Saarland UniversityDE1 paper
19 papers
Differential geometry in the theory of Hessian operators
N. M. Ivochkina, N. V. Filimonenkova
The paper introduces a new differential-geometric system which originates from the theory of -Hessian operators. The core of this system is a new notion of invariant differentia…
In Search of Shadows: the First Topological Conference, Moscow 1935
D. E. Apushkinskaya, A. I. Nazarov, G. I. Sinkevich
We discuss some mistakes and curiosities concerned with the celebrated First International Topological Conference in Moscow, 1935.
Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I
Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev
A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotic…
Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media
Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev +1
A novel approach to critical-contrast homogenisation is proposed. Norm-resolvent asymptotics are explicitly constructed. An essential feature of our approach is that it relates hom…
Large-Scale Fluctuations in the Number Density of Galaxies in Independent Surveys of Deep Fields
S. I. Shirokov, N. Yu. Lovyagin, Yu. V. Baryshev +1
New arguments supporting the reality of large-scale fluctuations in the density of the visible matter in deep galaxy surveys are presented. A statistical analysis of the radial dis…
Probabilistic counterparts of nonlinear parabolic PDE systems
Ya. I. Belopolskaya
We extend the results of the FBSDE theory in order to construct a probabilistic representation of a viscosity solution to the Cauchy problem for a system of quasilinear parabolic e…
On the history of nested intervals: from Archimedes to Cantor
Galina Sinkevich
The idea of the principle of nested intervals or the concept of convergent sequences which is equivalent to this idea dates back to the ancient world. Archimedes calculated the unk…
On the History of Number Line
Galina Sinkevich
The notion of number line was formed in XX c. We consider the generation of this conception in works by M. Stiefel (1544), Galilei (1633), Euler (1748), Lambert (1766), Bolzano (18…
On the history of analysis. The formation of definitions
G. Sinkevich
The mathematical analysis was conceived in XVII century in Newton and Leibniz works. The problem of logical rigor in definitions was considered by Arnauld and Nicole in "Logique ou…
Georg Cantor from St. Petersburg. Childhood and history of the family. Archival research
G. I. Sinkevich
Georg Cantor (1845-1918) was born, and spent the first 11 years of his life in St. Petersburg. The present lecture is devoted to his childhood and his family. Most of these documen…
Cycle slipping in nonlinear circuits under periodic nonlinearities and time delays
Vera Smirnova, Anton Proskurnikov, Natalia V. Utina
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general…
Distributions associated to homogeneous distributions
A. V. Kosyak, V. I. Polischook, V. M. Shelkovich
In this paper we continue to study {\it quasi associated homogeneous distributions \rm{(}generalized functions\rm{)}} which were introduced in the paper by V.M. Shelkovich, Associa…
Wavelet analysis on adeles and pseudo-differential operators
A. Yu. Khrennikov, A. V. Kosyak, V. M. Shelkovich
This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize fi…
Non-Haar -adic wavelets and their application to pseudo-differential operators and equations
A. Yu. Khrennikov, V. M. Shelkovich
In this paper a countable family of new compactly supported {\em non-Haar} -adic wavelet bases in ${\cL}^2(\bQ_p^n)$ is constructed. We use the wavelet bases in the following ap…
Asymptotical behavior of one class of -adic singular Fourier integrals
A. Yu. Khrennikov, V. M. Shelkovich
We study the asymptotical behavior of the -adic singular Fourier integrals $$ J_{π_α,m;ϕ}(t) =\bigl< f_{π_α;m}(x)χ_p(xt), ϕ(x)\bigr> =F\big[f_{π_α;m}ϕ\big](t), \quad |t|_p \to \…
p-Adic refinable functions and MRA-based wavelets
A. Yu. Khrennikov, V. M. Shelkovich, M. Skopina
We described a wide class of -adic refinable equations generating -adic multiresolution analysis. A method for the construction of -adic orthogonal wavelet bases within th…
Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes
S. Albeverio, Ya. Belopolskaya
We reduce the construction of a weak solution of the Cauchy problem for the Navier-Stokes system to the construction of a solution to a stochastic problem. Namely, we construct dif…
-Adic Haar multiresolution analysis and pseudo-differential operators
V. M. Shelkovich, M. Skopina
The notion of {\em -adic multiresolution analysis (MRA)} is introduced. We discuss a ``natural'' refinement equation whose solution (a refinable function) is the characteristic…
Associated and quasi associated homogeneous distributions (generalized functions)
V. M. Shelkovich
In this paper analysis of the concept of {\it associated homogeneous distributions} (generalized functions) is given, and some problems related to these distributions are solved. I…