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Multicriteria problems with importance-ordered criteria groups
Automation and Remote Control. 2022. Vol. 83. No. 7. P. 1108–1122.
A. P. Nelyubin, V. V. Podinovski
We develop a statement of the decision-making problem in the presence of information about the importance of criteria groups, give definitions of the relationships of the importance of criteria groups, and introduce coefficients of importance and preference relations based on such information. Methods for checking the consistency of information about importance are indicated, and ways of constructing the introduced preference relations are shown. The interrelation of qualitative importance and qualitative probability are revealed.
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are
reduced to discrete-time random dynamical systems generated by time-one maps, so that
the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using
irreducible representations of the Karasev–Novikova algebra with quadratic commutation
relations. We find the asymptotics of a series of eigenvalues and the corresponding
asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1174–1178
Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...
Added: September 30, 2026
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 8 С. 110–123
Для многокритериальных задач принятия решений по аналогии с качественной вероятностью введены понятия полной и частичной качественной важности как бинарных отношений, обладающих постулируемыми
свойствами. Предложено новое определение отношения нестрогого предпочтения на множестве вариантов решений, порождаемое качественной
важностью. Исследованы его свойства. Указаны аналитические правила,
позволяющие попарно сравнивать варианты по предпочтительности. Проведено сравнение новых отношений предпочтения с разработанными ранее для задач, ...
Added: September 9, 2026
Nelyubin A. P., Podinovskiy V. V., Computational Mathematics and Mathematical Physics 2025 Vol. 65 No. 4 P. 689–697
This paper continues the development of a new approach to estimating approximation
parameters in which the distance of the approximating function from a given finite set of points is estimated
by a vector criterion whose components are the moduli of the residuals at all points. Using this
vector criterion, a preference relation in terms of distance is defined, ...
Added: July 1, 2025
Нелюбин А. П., Podinovskiy V. V., Журнал вычислительной математики и математической физики 2025 Т. 65 № 4 С. 426–433
Статья продолжает развитие нового подхода к оцениванию параметров аппроксимации, при котором удаленность аппроксимирующей функции от заданного конечного множества точек оценивается векторным критерием, компонентами которого являются модули невязок во всех точках. При помощи этого векторного критерия задается отношение предпочтения в удаленности и лучшей считается аппроксимирующая функция, недоминируемая по такому отношению. В отличие от первой статьи авторов ...
Added: July 1, 2025
Nelyubin A. P., Podinovskiy V. V., Control Sciences 2024 No. 1 P. 13–17
A new approach to defining mean values based on the ideas of multicriteria optimiza-tion was proposed and developed previously; see the papers [4] and [5]. The distances between the current point and the sample points were treated as components of a vector estimate. The con-ventional approach to defining mean values involves the scalarization of vector ...
Added: March 30, 2024
Нелюбин А. П., Podinovskiy V. V., Проблемы управления 2024 № 1 С. 17–22
В статьях авторов («Проблемы управления» 2020, № 5 и 2001, № 2) предложен и развит новый подход к определению средних величин, исследованы свойства введенных средних предложены методы их построения. В данной статье, которая является непосредственным их продолжением, представлен точный численный метод построения множества одного из видов таких средних Он проиллюстрирован расчетным примером. ...
Added: March 13, 2024
Nelyubin A. P., Podinovskiy V. V., Журнал вычислительной математики и математической физики 2023 Т. 63 № 5 С. 717–730
Развит новый подход к оцениванию параметров аппроксимации, при котором удаленность аппроксимирующей функции от заданного конечного множества точек оценивается векторным критерием, компонентами которого являются модули невязок во всех точках. При помощи этого критерия задается отношение предпочтения в удаленности и лучшей считается аппроксимирующая функция, недоминируемая по такому отношению. Изучена аппроксимация для нескольких отношений предпочтения, в том числе ...
Added: July 3, 2023
A. P. Nelyubin, V. V. Podinovski, Computational Mathematics and Mathematical Physics 2023 Vol. 63 No. 5 P. 730–742
A new approach to estimating approximation parameters is developed. In this approach, the
distance of the approximating function from a given finite set of points is estimated by a vector criterion
the components of which are the absolute values of residuals at all points. Using this criterion, the
remoteness preference relation is defined, and the nondominated function with ...
Added: June 9, 2023
В. В. Подиновский, М.: Юрайт, 2022.
Курс посвящен теории и методам анализа многокритериальных задач, т. е. математическим методам поддержки принятия решений при многих критериях. Изложение методов сопровождается анализом их достоинств и недостатков, возможностей и ограничений и иллюстрируется примерами.
Курс состоит из трех разделов. В разделе I рассматриваются вопросы моделирования ситуации принятия решения и формирования решений требуемого типа. В разделе II излагаются методы анализа ...
Added: September 27, 2022