### ?

## Стабильность резонансов оператора Дирака

Алгебра и анализ. 2022. Т. 34. № 6. С. 197-216.

Mokeev D.

Korotyaev E., Mokeev D., Asymptotic Analysis 2023 Vol. 132 No. 1-2 P. 83-130

We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems: in terms of zeros of reflection coefficient and in terms of poles of reflection coefficients (i.e. resonances). Moreover, we prove the following: 1) a zero of the reflection coefficient can be arbitrarily shifted, such that we obtain ...

Added: March 8, 2023

Korotyaev E., Mantile A., Mokeev D., SIAM Journal on Mathematical Analysis 2024 Vol. 56 No. 2 P. 2115-2148

We consider Schrödinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schrödinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. ...

Added: March 7, 2024

Evgeny Korotyaev, Mokeev D., Analysis and Mathematical Physics 2021 Vol. 11 Article 32

We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function and prove that a potential is uniquely determined by its resonances. Moreover, we prove the following: (1) resonances are free ...

Added: April 18, 2021

Людмила Ивановна Кузьмина, ОСИПОВ Ю. В., ЦАРЕВА В. И., Промышленное и гражданское строительство 2020 № 6 С. 64-68

Filtration problem for a suspension in a porous medium characterize the injection of a liquid grout into porous rock to strengthen loose soil or create waterproof partitions during the construction of tunnels and underground structures. The suspension is injected under pressure into an empty homogeneous porous medium and moves from inlet to outlet. Some particles ...

Added: July 2, 2020

Korotyaev E., Леонова Е. О., / arXive. Series arXie "Statistical mechanics". 2022.

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real ...

Added: September 26, 2022

Belomestny D., Morozova E., Panov V., / Cornell University. Series arXiv.org "math.ST". 2024. No. 2405.05419.

This study focuses on statistical inference for compound models of the form \(X=\xi_1+\ldots+\xi_N\), where \(N\) is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables \(\xi_1, \xi_2, \ldots\). The paper addresses the problem of reconstructing the distribution of \(\xi\) from observed samples of \(X\)'s distribution, a process ...

Added: May 10, 2024

Pogrebkov A., Symmetry 2019 Vol. 11 No. 436 P. 1-11

We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in R3. We demonstrated that specific properties of solutions of the HDE with respect to independent variables enabled introduction of an infinite set of discrete symmetries. We showed that degeneracy ...

Added: May 2, 2019

Inverse problems in Pareto’s demand theory and their applications to analysis of stock market crises

Klemashev N., Shananin A. A., Zhang S., Journal of Inverse and Ill-posed problems 2016 Vol. 26 No. 1 P. 95-108

We develop an approach to analysis of stock market crises based on the generalized nonparametric method. The generalized nonparametric method is based on solvability and regularization of ill-posed inverse problem in Pareto's demand theory. Our approach allows one to select a few companies that may be considered as the main reason for the crisis. We ...

Added: March 5, 2019

V.S. Samovol, Доклады Академии наук 2012 Vol. 85 No. 1 P. 122-124

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth ...

Added: November 27, 2012

Pogrebkov A., Boiti M., Pempinelli F., Theoretical and Mathematical Physics 2015 Vol. 185 No. 2 P. 1599-1613

We describe the properties of the Cauchy–Jost (also known as Cauchy–Baker–Akhiezer) function of the
Kadomtsev–Petviashvili-II equation. Using the ∂-method, we show that for this function, all equations
of the Kadomtsev–Petviashvili-II hierarchy are given in a compact and explicit form, including equations
for the Cauchy–Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential
of the ...

Added: September 9, 2016

Samovol V. S., Доклады Академии наук 2012 Vol. 85 No. 1 P. 122-124

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth ...

Added: November 27, 2012

Karasev M., Russian Journal of Mathematical Physics 2012 Vol. 19 No. 3 P. 299-306

For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quantization condition on the 2D-plane; the standard magnetic (symplectic) ...

Added: December 19, 2012

Klemashev N., Шананин А. А., Journal of Inverse and Ill-posed problems 2016 Vol. 24 No. 4 P. 367-391

According to Pareto's theory of consumer demand a rational representative consumer should choose their consumption bundle as the solution of mathematical programming problem of maximization of utility function under their budget constraint. The inverse problem of demand analysis is to recover the utility function from the demand functions. The answer to the question of solvability ...

Added: March 5, 2019

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.

We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...

Added: March 9, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016

Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291

The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...

Added: December 7, 2013

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014