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INVERSE SPECTRAL PROBLEMS AND MATHEMATICAL MODELS OF CONTINUUM MECHANICS
Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software. 2019. Vol. 12. No. 2. P. 5–24.
Zakirova G.
The article contains results in the field of spectral problems for mathematical models with discrete semi-bounded operator. The theory is based on linear formulas for calculating the eigenvalues of a discrete operator. The main idea is to reduce spectral problem to the Fredholm integral equation of the first kind. A computationally efficient numerical method for solving inverse spectral problems is developed. The method is based on the Galerkin method for discrete semi-bounded operators. This method allows to reconstruct the coefficient functions of boundary value problems with a high accuracy. The results obtained in the article are applicable to the study of problems for differential operators of any order. The results of a numerical solution of the inverse spectral problem for a fourth-order perturbed differential operator are presented. We study some mathematical models of continuum mechanics based on spectral problems for a discrete semi-bounded operator.
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f is bounded from below by the Motzkin density.
We generalize the bound to polynomials in several variables and almost periodic functions.
We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...
Added: September 7, 2026
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Madera A. G., International Journal of Accounting and Economics Studies 2016 Vol. 4 No. 1 P. 76–80
The article elaborates a method for estimating the probabilities of occurrence of prognosticated events in future. On the basis of the data from the previous periods about prognosticating the relevant events, as well as the data about the trends observed at present, two matrices are formed, the product of which is the matrix for the ...
Added: August 19, 2016
Kravchenko N., Mukhin S., В кн.: II Всероссийская объединённая научная конференция "Проблемы СВЧ-электроники" МИЭМ НИУ ВШЭ – "Инновационные решения" Keysight Technologies. Сборник трудов конференции.: М.: ИД Медиа Паблишер, 2015. С. 33–36.
Предметом рассмотрения данного доклада является разработка алгоритма и программы расчета дисперси- онных характеристик резонаторных замедляющих систем с использованием результатов их трехмерного мо- делирования в HFSS. Трехмерное моделирование замедляющих систем не позволяет вычислить их дисперсион- ные характеристики, оно лишь предоставляет некоторые исходные данные, которые требуют дальнейшее обработки, которую и осуществляет рассматриваемая программа. Для расчета необходимо получить ...
Added: November 16, 2015
Chelkak D., Matveenko S., / Series 1312.3621v1 "1312.3621v1". 2013.
This paper starts a series devoted to the vector-valued Sturm-Liouville problem $-\psi''+V(x)\psi=\lambda\psi$, $\psi\in L^2([0,1];\C^N)$, with separated boundary conditions. The overall goal of the series is to give a complete characterization of classes of spectral data corresponding to potentials $V=V^*\in L^p([0,1];\C^{N\times N})$ for a fixed $1\le p <+\infty$ and separated boundary conditions having the most general ...
Added: October 15, 2015
Shitov Y., Linear and Multilinear Algebra 2015 Vol. 63 No. 2 P. 221–221
We show that a rank-three symmetric matrix with exactly one negative eigenvalue can have arbitrarily large nonnegative rank. ...
Added: January 27, 2014
Madera A. G., Менеджмент в России и за рубежом 2013 № 6 С. 21–29
A new method to predict the probabilities of future events that are consequences of the subject, are presented. The method is based on combining the two types of forecasts – forecasted events using statistical data predictions for previous periods, as well as subjective, using expert estimates, using new information. Shows that an objective forecast is ...
Added: September 2, 2013
Samovol V., Доклады Академии наук 2010 Vol. 81 No. 3 P. 351–353
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations for which one eigenvalue of the matrix of the linear part is zero and the remaining eigenvalues do not belong to the imaginary axis. We study the reducibility of such systems to normal form. We prove that the problem of ...
Added: January 12, 2013
Bruning J., Grushin V. V., Dobrokhotov S. Y., Russian Journal of Mathematical Physics 2012 Vol. 19 No. 3 P. 261–272
In the paper, using relatively simple formulas derived in the abstract perturbation theory of selfadjoint operators, we obtain explicit asymptotic formulas for a family of elliptic operators of Laplace type that arise in linear problems with rapidly oscillating coefficients. ...
Added: December 24, 2012
Андреев К. К., Busjatskaja I., М.: МИЭМ, 2007.
На конкретных примерах излагаются способы решения задач домашней контрольной работы по теме «Линейные операторы». Приводится ряд дополнительных сведений из теории линейных операторов, некоторые из которых доказываются, а некоторые предоставляются для доказательства студентам. ...
Added: June 28, 2012