?
A counterexample on tropical linear spaces
Linear Algebra and its Applications. 2016. Vol. 511. P. 19-21.
Shitov Y.
Let K be a field with non-Archimedean valuation v, and assume A is a matrix of size m×n and rank k over K. Richter- Gebert, Sturmfels, and Theobald proved that the rows of A are a tropical basis of the corresponding linear space whenever m = k and any submatrix formed by k columns of v(A) has tropical rank k. We show that this result is no longer true without assumption m = k, refuting the conjecture proposed by Yu and Yuster in 2007.
M. : Higher School of Economics Publishing House, 2012
Toric geometry exhibited a profound relation between algebra and topology on one side and combinatorics and convex geometry on the other side. In the last decades, the interplay between algebraic and convex geometry has been explored and used successfully in a much more general setting: first, for varieties with an algebraic group action (such as ...
Added: November 17, 2012
Providence : American Mathematical Society, 2014
This volume contains the proceedings of the International Workshop on Tropical and Idempotent Mathematics, held at the Independent University of Moscow, Russia, from August 26-31, 2012. The main purpose of the conference was to bring together and unite researchers and specialists in various areas of tropical and idempotent mathematics and applications. This volume contains articles ...
Added: February 1, 2015
Esterov A. I., / Cornell University. Series math "arxiv.org". 2015. No. arXiv:1305.3234v6.
An enumerative problem on a variety V is usually solved by reduction to intersection theory in the cohomology of a compactification of V. However, if the problem is invariant under a "nice" group action on V (so that V is spherical), then many authors suggested a better home for intersection theory: the direct limit of ...
Added: February 28, 2015
Alexander Esterov, / Cornell University. Series math "arxiv.org". 2013.
We introduce tropical characteristic classes of very affine algebraic varities, and use this tool to deduce the tropical double point formula, i. e. to tropicalize the variety of double tangents to a smooth toric variety. ...
Added: May 15, 2013
Feigin E., Makhlin I., Fourier G. et al., / Cornell University. Series math "arxiv.org". 2017. No. 1711.00751.
We study algebraic, combinatorial and geometric aspects of weighted PBW-type degenerations of (partial) flag varieties in type A. These degenerations are labeled by degree functions lying in an explicitly defined polyhedral cone, which can be identified with a maximal cone in the tropical flag variety. Varying the degree function in the cone, we recover, for ...
Added: November 3, 2017
Kalinin N., Journal of Combinatorial Theory, Series A 2016 No. 137 P. 226-256
Let a planar algebraic curve C be defined over a valuation field by an equation F (x, y) = 0. Valuations of the coefficients of F define a subdivision of the Newton polygon Δ of the curve C. If a given point p is of multiplicity m on C, then the coefficients of F are subject to ...
Added: March 2, 2017
Shkolnikov M., Kalinin N., Comptes Rendus Mathematique 2016 Vol. 354 No. 2 P. 125-130
We study a sandpile model on the set of the lattice points in a large lattice polygon. A small perturbation ψ of the maximal stable state μ ≡ 3 is obtained by adding extra grains at several points. It appears that the result ψ◦ of the relaxation of ψ coincides with μ almost everywhere; the ...
Added: March 2, 2017
Shkolnikov M., Kalinin N., European Journal of Mathematics 2019 Vol. 5 No. 3 P. 909-928
√√
Abstract Let f(a,b,c,d) = a2+b2 + c2+d2 − (a+c)2+(b+d)2, let
(a,b,c,d) stand for a,b,c,d ∈ Z0 such that ad − bc = 1. Defines
In other words, we consider the sum of the powers of the triangle inequality defects for the lattice parallelograms (in the first quadrant) of area one.
We prove that F(s) converges when s > 1 and diverges at s = 1/2. We also prove that
1=1,(a,b,c,d) (a+c)2(b+d)2(a+b+c+d)2 3 ...
Added: August 15, 2019
СПб. : ВВМ, 2014
Тропическая (идемпотентная) математика представляет собой быстро развивающуюся область прикладной математики, которая связана с изучением полумодулей над полукольцами с идемпотентным сложением и имеет много приложений, включая задачи экономики и управления. Использование языка тропической математики позволяет некоторые нелинейные в обычном смысле задачи превращать в линейные, что в ряде случаев упрощает процедуру решения этих задач, а ткже облегчает ...
Added: December 29, 2014
Kalinin N., Discrete and Computational Geometry 2017 Vol. 58 No. 1 P. 158-179
Suppose that there exists a hypersurface with the Newton polytope Δ, which passes through a given set of subvarieties. Using tropical geometry, we associate a subset of Δ to each of these subvarieties. We prove that a weighted sum of the volumes of these subsets estimates the volume of Δ from below. As a particular ...
Added: May 16, 2017
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
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
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
Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240
We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019
ООО Фирма "Элист", 2014
В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...
Added: October 17, 2014
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
Added: February 2, 2017
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
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
Zinder Y., Lazarev A. A., Musatova E. G., Автоматика и телемеханика 2020 Т. 5 С. 91-104
Представлен полиномиальный алгоритм корректировки расписания движения поездов для случая, когда один из путей двухпутной железной дороги становится недоступным, оставшийся путь содержит разъезд, а все поезда делятся на две категории: приоритетные поезда, например пассажирские, и обычные поезда, к которым относятся большинство грузовых поездов. Представленный алгоритм минимизирует негативное влияние, оказываемое блокировкой пути, сначала для приоритетных поездов, а ...
Added: September 2, 2020