Г. Л. Литвинов, В. П. Маслов, Г. Б. Шпиз, “Идемпотентный функциональный анализ. Алгебраический подход”, Матем. заметки, 69:5 (2001), 758–797; Math. Notes, 69:5 (2001), 696

Математические заметки

RUS ENG

ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	Общая информация
	Последний выпуск
	Скоро в журнале
	Архив
	Импакт-фактор
	Подписка
	Правила для авторов
	Лицензионный договор
	Загрузить рукопись

	Поиск публикаций
	Поиск ссылок

	RSS
	Последний выпуск
	Текущие выпуски
	Архивные выпуски
	Что такое RSS

Матем. заметки:
Год:
Том:
Выпуск:
Страница:
	Найти

Персональный вход:
Логин:
Пароль:
	Запомнить пароль
	Войти
	Забыли пароль?
	Регистрация

Матем. заметки, 2001, том 69, выпуск 5, страницы 758–797 (Mi mz539)

Эта публикация цитируется в 107 научных статьях (всего в 107 статьях)

Математические обзоры

Идемпотентный функциональный анализ. Алгебраический подход

Г. Л. Литвинов^a, В. П. Маслов^b, Г. Б. Шпиз^a

^a Международный центр "Софус Ли"
^b Московский государственный университет им. М. В. Ломоносова, физический факультет

Аннотация: Статья посвящена идемпотентному функциональному анализу, который является “абстрактной” версией идемпотентного анализа, разработанного В. П. Масловым и его сотрудниками. Дан обзор основных идей идемпотентного анализа. Обсуждается соответствие между концепциями и теоремами традиционного функционального анализа и его идемпотентной версии в духе принципа соответствия Н. Бора в квантовой теории. Представлен алгебраический подход к идемпотентному функциональному анализу. Основные понятия и результаты сформулированы в алгебраических терминах; при этом существенно, что операция идемпотентного сложения может быть определена для бесконечного множества слагаемых. Исследованы идемпотентные аналоги основных принципов линейного анализа и результатов об общем виде линейного функционала и о скалярных произведениях на идемпотентных пространствах.
Библиография: 81 название.

DOI: https://doi.org/10.4213/mzm539

Полный текст: PDF файл (428 kB)

Список литературы: PDF файл HTML файл

Англоязычная версия:
Mathematical Notes, 2001, 69:5, 696–729

Реферативные базы данных:

УДК: 519
Поступило: 17.05.2000

Образец цитирования: Г. Л. Литвинов, В. П. Маслов, Г. Б. Шпиз, “Идемпотентный функциональный анализ. Алгебраический подход”, Матем. заметки, 69:5 (2001), 758–797; Math. Notes, 69:5 (2001), 696–729

Цитирование в формате AMSBIB

\RBibitem{LitMasShp01}

\by Г.~Л.~Литвинов, В.~П.~Маслов, Г.~Б.~Шпиз

\paper Идемпотентный функциональный анализ. Алгебраический подход

\jour Матем. заметки

\yr 2001

\vol 69

\issue 5

\pages 758--797

\mathnet{http://mi.mathnet.ru/mz539}

\crossref{https://doi.org/10.4213/mzm539}

\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1846814}

\zmath{https://zbmath.org/?q=an:1017.46034}

\elib{https://elibrary.ru/item.asp?id=13682001}

\transl

\jour Math. Notes

\yr 2001

\vol 69

\issue 5

\pages 696--729

\crossref{https://doi.org/10.1023/A:1010266012029}

\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169913100012}

Образцы ссылок на эту страницу:

http://mi.mathnet.ru/mz539

https://doi.org/10.4213/mzm539

http://mi.mathnet.ru/rus/mz/v69/i5/p758

ОТПРАВИТЬ:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

Эта публикация цитируется в следующих статьяx:

Shu Q.-yu., Wang X.-p., Qiao L., “Extension of Free Sets Over Commutative Semirings”, Linear Multilinear Algebra
Litvinov, GL, “Nuclear semimodules and kernel theorems in idempotent analysis: An algebraic approach”, Doklady Mathematics, 66:2 (2002), 197
Litvinov G., Maslov V., Shpiz G., “Idempotent (Asymptotic) Mathematics and the Representation Theory”, Asymptotic Combinatorics with Applications to Mathematical Physics, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 77, eds. Malyshev V., Vershik A., Springer, 2002, 267–278
С. Н. Сергеев, “Алгоритмическая сложность одной задачи идемпотентно выпуклой геометрии”, Матем. заметки, 74:6 (2003), 896–901 ; S. N. Sergeev, “Algorithmic Complexity of a Problem of Idempotent Convex Geometry”, Math. Notes, 74:6 (2003), 848–852
McEneaney, WM, “Max-plus eigenvector methods for nonlinear H-infinity problems: Error analysis”, SIAM Journal on Control and Optimization, 43:2 (2004), 379
Katsov, Y, “On flat semimodules over semirings”, Algebra Universalis, 51:2–3 (2004), 287
Gaubert, S, “Rational semimodules over the max-plus semiring and geometric approach to discrete event systems”, Kybernetika, 40:2 (2004), 153
Cohen, G, “Duality and separation theorems in idempotent semimodules”, Linear Algebra and Its Applications, 379 (2004), 395
Kim, KH, “Inclines and incline matrices: a survey”, Linear Algebra and Its Applications, 379 (2004), 457
McEneaney W., “Combining Legendre/Fenchel Transformed Operators on Max-Plus Spaces for Nonlinear Control Solution”, 2004 43rd IEEE Conference on Decision and Control (CDC), Vols 1-5, IEEE Conference on Decision and Control - Proceedings, IEEE, 2004, 1152–1157
Г. Л. Литвинов, “Деквантование Маслова, идемпотентная и тропическая математика: краткое введение”, Теория представлений, динамические системы, комбинаторные и алгоритмические методы. XIII, Зап. научн. сем. ПОМИ, 326, ПОМИ, СПб., 2005, 145–182 ; G. L. Litvinov, “The Maslov dequantization, idempotent and tropical mathematics: a brief introduction”, J. Math. Sci. (N. Y.), 140:3 (2007), 426–444
McEneaney W.M., “Curse-of-Dimensionality Free Method for Bellman PDEs with Hamiltonian Written as Maximum of Quadratic Forms”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, IEEE Conference on Decision and Control - Proceedings, IEEE, 2005, 42–47
Akian M., Gaubert S., Lakhoua A., “The Max-Plus Finite Element Method for Optimal Control Problems: Further Approximation Results”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, IEEE Conference on Decision and Control - Proceedings, IEEE, 2005, 4505–4510
Akian M., Gaubert S., Kolokoltsov V., “Solutions of Max-Plus Linear Equations and Large Deviations”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, IEEE Conference on Decision and Control - Proceedings, IEEE, 2005, 7787–7792
Litvinov G., “The Maslov Dequantization, Idempotent and Tropical Mathematics: a Very Brief Introduction”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, 377, ed. Litvinov G. Maslov V., Amer Mathematical Soc, 2005, 1–17
Akian M., Gaubert S., Walsh C., “Discrete Max-Plus Spectral Theory”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, 377, eds. Litvinov G., Maslov V., Amer Mathematical Soc, 2005, 53–77
Cohen G., Gaubert S., Quadrat J., Singer I., “Max-Plus Convex Sets and Functions”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics Series, 377, eds. Litvinov G., Maslov V., Amer Mathematical Soc, 2005, 105–129
Litvinov G., Shpiz G., “The Dequantization Transform and Generalized Newton Polytopes”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics Series, 377, eds. Litvinov G., Maslov V., Amer Mathematical Soc, 2005, 181–186
Г. Л. Литвинов, Г. Б. Шпиз, “Теоремы о ядре и ядерность в идемпотентной математике. Алгебраический подход”, Теория представлений, динамические системы, комбинаторные и алгоритмические методы. XIV, Зап. научн. сем. ПОМИ, 331, ПОМИ, СПб., 2006, 60–83 ; G. L. Litvinov, G. B. Shpiz, “Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach”, J. Math. Sci. (N. Y.), 141:4 (2007), 1417–1428
Gaubert, S, “Max-plus convex geometry”, Relations and Kleene Algebra in Computer Science, Proceedings, 4136 (2006), 192
McEneaney W.M., “Curse-of-Dimensionality Free Method for Bellman PDEs with Semiconvex Hamiltonians”, Proceedings of the 45th IEEE Conference on Decision and Control, Vols 1-14, IEEE Conference on Decision and Control, IEEE, 2006, 967–972
С. Гобер, С. Н. Сергеев, “Циклические проекторы и теоремы отделимости в идемпотентных полумодулях”, Фундамент. и прикл. матем., 13:4 (2007), 31–52 ; S. Gaubert, S. N. Sergeev, “Cyclic projectors and separation theorems in idempotent convex geometry”, J. Math. Sci., 155:6 (2008), 815–829
Г. Б. Шпиз, “Теорема о существовании собственного вектора в идемпотентном анализе”, Матем. заметки, 82:3 (2007), 459–468 ; G. B. Shpiz, “An Eigenvector Existence Theorem in Idempotent Analysis”, Math. Notes, 82:3 (2007), 410–417
McEneaney W. M., “A curse-of-dimensionality-free numerical method for solution of certain HJB PDEs”, SIAM J. Control Optim., 46:4 (2007), 1239–1276
McEneaney, WM, “Max-plus summation of Fenchel-transformed semigroups for solution of nonlinear Bellman equations”, Systems & Control Letters, 56:4 (2007), 255
Sergeev, S, “Max-plus definite matrix closures and their eigenspaces”, Linear Algebra and Its Applications, 421:2–3 (2007), 182
Gaubert, S, “The Minkowski theorem for max-plus convex sets”, Linear Algebra and Its Applications, 421:2–3 (2007), 356
Nitica, V, “Max-plus convex sets and max-plus semispaces. I”, Optimization, 56:1–2 (2007), 171
McEneaney W.M., “Using Semiconvex Duality and Max-Plus Analysis to Obtain a New Fundamental Solution for the Differential Riccati Equation”, Proceedings of the 46th IEEE Conference on Decision and Control, Vols 1-14, IEEE Conference on Decision and Control - Proceedings, IEEE, 2007, 3032–3037
Л. Е. Базилевич, “Гиперпространство max-плюс выпуклых компактных множеств”, Матем. заметки, 84:5 (2008), 658–666 ; L. E. Bazilevich, “Hyperspace of Max-Plus Convex Compact Sets”, Math. Notes, 84:5 (2008), 615–622
Briec, W, “Halfspaces and Hahn-Banach like properties in B-convexity and Max-Plus convexity”, Pacific Journal of Optimization, 4:2 (2008), 293
Hubal, O, “Idempotent probability measures on ultrametric spaces”, Journal of Mathematical Analysis and Applications, 343:2 (2008), 1052
McEneaney, WM, “A new fundamental solution for differential Riccati equations arising in control”, Automatica, 44:4 (2008), 920
Akian, M, “The max-plus finite element method for solving deterministic optimal control problems: Basic properties and convergence analysis”, SIAM Journal on Control and Optimization, 47:2 (2008), 817
Briec, W, “Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and B-convexity”, Journal of Mathematical Analysis and Applications, 341:1 (2008), 188
Akian M., Gaubert S., Lakhoua A., “Convergence Analysis of the Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems”, 47th IEEE Conference on Decision and Control, 2008 (CDC 2008), IEEE Conference on Decision and Control, IEEE, 2008, 927–934
Allamigeon X., Gaubert S., Goubault E., “Inferring Min and Max Invariants Using Max-Plus Polyhedra”, Static Analysis, Lecture Notes in Computer Science, 5079, eds. Alpuente M., Vidal G., Springer-Verlag Berlin, 2008, 189–204
McEneaney W.M., Deshpande A., Gaubert S., “Curse-of-Complexity Attenuation in the Curse-of-Dimensionality-Free Method for Hjb PDEs”, 2008 American Control Conference, Vols 1-12, Proceedings of the American Control Conference, IEEE, 2008, 4684–4690
McEneaney W. M., “Convergence Rate for a Curse-of-dimensionality-Free Method for Hamilton–Jacobi–Bellman PDEs Represented as Maxima of Quadratic Forms”, SIAM J. Control Optim., 48:4 (2009), 2651–2685
Akian, M, “THE MAX-PLUS MARTIN BOUNDARY”, Documenta Mathematica, 14 (2009), 195
Gaubert, S, “The tropical analogue of polar cones”, Linear Algebra and Its Applications, 431:5–7 (2009), 608
Gaubert S., “Max-Plus Algebraic Tools for Discrete Event Systems, Static Analysis, and Zero-Sum Games”, Formal Modeling and Analysis of Timed Systems, Proceedings, Lecture Notes in Computer Science, 5813, eds. Ouaknine J., Vaandrager F., Springer-Verlag Berlin, 2009, 7–11
Fan B., Zhang H., Dou W., “A Max-Plus Network Calculus”, Proceedings of the 8th IEEE/Acis International Conference on Computer and Information Science, eds. Miao H., Hu G., IEEE Computer Soc, 2009, 149–154
Mceneaney W.M., Kluberg L.J., “Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of Hjb PDEs”, SIAM J. Control Optim., 48:5 (2009), 3052–3079
Akian M., Gaubert S., Guterman A., “Linear Independence Over Tropical Semirings and Beyond”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 1–38
Akian M., Gaubert S., Kolokoltsov V., “The Optimal Assignment Problem for a Countable State Space”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 39–60
Joswig M., “Tropical Convex Hull Computations”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 193–212
McEneaney W.M., “Complexity Reduction, Cornices and Pruning”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 293–303
Sergeev S., “Multiorder, Kleene Stars and Cyclic Projectors in the Geometry of Max Cones”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 317–342
Shpiz G.B. Litvinov G.L., “A Tropical Version of the Schauder Fixed Point Theorem”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, ed. Litvinov G. Sergeev S., Amer Mathematical Soc, 2009, 343–350
Fan Baohua, Zhang Heying, Dou Wenhua, “A Matrix Interpretation of Network Calculus”, 2009 First International Conference on Future Information Networks, eds. Zhang H., Coyle E., Kuo S., Zukerman M., IEEE, 2009, 45–49
Gaubert S., Meunier F., “Carath,odory, Helly and the Others in the Max-Plus World”, Discrete & Computational Geometry, 43:3 (2010), 648–662
М. М. Заричный, “Пространства и отображения идемпотентных мер”, Изв. РАН. Сер. матем., 74:3 (2010), 45–64 ; M. M. Zarichnyi, “Spaces and maps of idempotent measures”, Izv. Math., 74:3 (2010), 481–499
Nitica V., Sergeev S., “ON HYPERPLANES AND SEMISPACES IN MAX-MIN CONVEX GEOMETRY”, Kybernetika (Prague), 46:3 (2010), 548–557
Singer I., “Elementary Topical Functions on B-Complete Semimodules Over B-Complete Idempotent Semifields”, Linear Alg. Appl., 433:11-12 (2010), 2139–2146
Ruuge A.E., van Oystaeyen F., “Q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant”, J. Phys. A-Math. Theor., 43:34 (2010), 345203
Di Loreto M., Gaubert S., Katz R.D., Loiseau J.-J., “Duality Between Invariant Spaces for Max-Plus Linear Discrete Event Systems”, SIAM J. Control Optim., 48:8 (2010), 5606–5628
Gaubert S., McEneaney W., Qu Zh., “Curse of Dimensionality Reduction in Max-Plus Based Approximation Methods: Theoretical Estimates and Improved Pruning Algorithms”, 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-Ecc), IEEE, 2011, 1054–1061
Akian M., Gaubert S., Nitica V., Singer I., “Best Approximation in Max-Plus Semimodules”, Linear Alg. Appl., 435:12 (2011), 3261–3296
Allamigeon X., Gaubert S., Katz R.D., “Tropical Polar Cones, Hypergraph Transversals, and Mean Payoff Games”, Linear Alg. Appl., 435:7, SI (2011), 1549–1574
Nitica V., Sergeev S., “An Interval Version of Separation by Semispaces in Max-Min Convexity”, Linear Alg. Appl., 435:7, SI (2011), 1637–1648
Peperko A., “On the Continuity of the Generalized Spectral Radius in Max Algebra”, Linear Alg. Appl., 435:4 (2011), 902–907
Gaubert S., Katz R.D., “Minimal Half-Spaces and External Representation of Tropical Polyhedra”, J. Algebr. Comb., 33:3 (2011), 325–348
Litvinov G.L., “Tropical Mathematics, Idempotent Analysis, Classical Mechanics and Geometry”, Spectral Theory and Geometric Analysis, Contemporary Mathematics, 535, ed. Braverman M. Friedlander L. Kappeler T. Kuchment P. Topalov P. Weitsman J., Amer Mathematical Soc, 2011, 159–186
Allamigeon X., Gaubert S., Katz R.D., “The Number of Extreme Points of Tropical Polyhedra”, J. Comb. Theory Ser. A, 118:1 (2011), 162–189
Singer I., Nitica V., “Topical Functions on Semimodules and Generalizations”, Linear Alg. Appl., 437:10 (2012), 2471–2488
Bazylevych L., Repovs D., Zarichnyi M., “Hyperspaces of Max-Plus Convex Subsets of Powers of the Real Line”, J. Math. Anal. Appl., 394:2 (2012), 481–487
Gaubert S., McEneaney W.M., “Min-Max Spaces and Complexity Reduction in Min-Max Expansions”, Appl. Math. Optim., 65:3 (2012), 315–348
Butkovic P., Schneider H., Sergeev S., “Z-Matrix Equations in Max-Algebra, Nonnegative Linear Algebra and Other Semirings”, Linear Multilinear Algebra, 60:10 (2012), 1191–1210
Maslov V.P., “New Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts”, Russ. J. Math. Phys., 19:1 (2012), 63–100
Akian M., Gaubert S., Guterman A., “Tropical Polyhedra Are Equivalent to Mean Payoff Games”, Int. J. Algebr. Comput., 22:1 (2012), 1250001
Allamigeon X., Gaubert S., Goubault E., “Computing the Vertices of Tropical Polyhedra Using Directed Hypergraphs”, Discret. Comput. Geom., 49:2 (2013), 247–279
Litvinov G.L., Rodionov A.Ya., Sergeev S.N., Sobolevski A.N., “Universal Algorithms for Solving the Matrix Bellman Equations Over Semirings”, Soft Comput., 17:10 (2013), 1767–1785
Shpiz G.B., Litvinov G.L., Sergeev S.N., “On Common Eigenvectors for Semigroups of Matrices in Tropical and Traditional Linear Algebra”, Linear Alg. Appl., 439:6 (2013), 1651–1656
Litvinov G.L., “Idempotent and Tropical Mathematics; Complexity of Algorithms and Interval Analysis”, Comput. Math. Appl., 65:10 (2013), 1483–1496
Cencelj M., Repovs D., Zarichnyi M., “Max-Min Measures on Ultrametric Spaces”, Topology Appl., 160:5 (2013), 673–681
McEneaney W.M., Deshpande A.S., “Payoff Suboptimality and Errors in Value Induced by Approximation of the Hamiltonian”, SIAM J. Control Optim., 51:5 (2013), 3993–4015
Katz R.D., Nitica V., Sergeev S., “Characterization of Tropical Hemispaces by (P, R)-Decompositions”, Linear Alg. Appl., 440 (2014), 131–163
Fitzpatrick B.G., Holmbeck-Cannell K., Laffin M., Wang Yu., “Optimal Perimeter Patrol Via Max-Plus Probability”, 2014 American Control Conference, Proceedings of the American Control Conference, IEEE, 2014, 5248–5253
Allamigeon X., Benchimol P., Gaubert S., Joswig M., “Combinatorial Simplex Algorithms Can Solve Mean Payoff Games”, SIAM J. Optim., 24:4 (2014), 2096–2117
Allamigeon X., Fahrenberg U., Gaubert S., Katz R.D., Legay A., “Tropical Fourier-Motzkin Elimination, With An Application To Real-Time Verification”, Int. J. Algebr. Comput., 24:5 (2014), 569–607
Singer I., Nitica V., “Extended-Valued Topical and Anti-Topical Functions on Semimodules”, Linear Alg. Appl., 446 (2014), 25–70
Allamigeon X., Benchimol P., Gaubert S., Joswig M., “Tropicalizing the Simplex Algorithm”, SIAM Discret. Math., 29:2 (2015), 751–795
Dower P.M., Zhang H., “a New Fundamental Solution For Differential Riccati Equations Arising in l-2-Gain Analysis”, 2015 5Th Australian Control Conference (Aucc), IEEE, 2015, 65–68
Joswig M., Loho G., “Weighted digraphs and tropical cones”, Linear Alg. Appl., 501 (2016), 304–343
Bhuniya A.K., Jana K., “Semigroup of k-bi-Ideals of a Semiring with Semilattice Additive Reduct”, Demonstr. Math., 49:2 (2016), 119–128
Akian M., Bapat R., Gaubert S., “Non-archimedean valuations of eigenvalues of matrix polynomials”, Linear Alg. Appl., 498:SI (2016), 592–627
Ludkowski S.V., “Skew Continuous Morphisms of Ordered Lattice Ringoids”, 4, no. 1, 2016
McEneaney W.M., Pandey A., “An idempotent algorithm for a class of network-disruption games”, Kybernetika, 52:5 (2016), 666–695
Barsam H., Mohebi H., “Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions”, Numer. Funct. Anal. Optim., 37:11 (2016), 1354–1377
Hassani S., Mohebi H., “Characterizations of minimal elements of topical functions on semimodules with applications”, Linear Alg. Appl., 520 (2017), 104–124
Maragos P., “Dynamical Systems on Weighted Lattices: General Theory”, Math. Control Signal Syst., 29:4 (2017), 1
Muller V., Peperko A., “On the Bonsall Cone Spectral Radius and the Approximate Point Spectrum”, Discret. Contin. Dyn. Syst., 37:10 (2017), 5337–5354
Dower P.M., Zhang H., “A Max-Plus Primal Space Fundamental Solution For a Class of Differential Riccati Equations”, Math. Control Signal Syst., 29:3 (2017), 15
Shitov Ya., “Which Semifields Are Exact?”, J. Algebra, 492 (2017), 393–401
Allamigeon X., Katz R.D., “Tropicalization of Facets of Polytopes”, Linear Alg. Appl., 523 (2017), 79–101
Fijavz M.K., Peperko A., Sikolya E., “Semigroups of Max-Plus Linear Operators”, Semigr. Forum, 94:2 (2017), 463–476
Avendano M., Kogan R., Nisse M., Rojas J.M., “Metric Estimates and Membership Complexity For Archimedean Amoebae and Tropical Hypersurfaces”, J. Complex., 46 (2018), 45–65
Bhuniya A.K., Jana K., “Representation of Normal Bands as Semigroups of K-Bi-Ideals of a Semiring”, Algebr. Universalis, 79:1 (2018), UNSP 6
Legaz-Aparicio A.-G., Verdu-Monedero R., Angulo J., “Adaptive Morphological Filters Based on a Multiple Orientation Vector Field Dependent on Image Local Features”, J. Comput. Appl. Math., 330 (2018), 965–981
Komenda J., Lahaye S., Boimond J.-L., van den Boom T., “Max-Plus Algebra in the History of Discrete Event Systems”, Annu. Rev. Control, 45 (2018), 240–249
Muller V., Peperko A., “Lower Spectral Radius and Spectral Mapping Theorem For Suprema Preserving Mappings”, Discret. Contin. Dyn. Syst., 38:8 (2018), 4117–4132
Gasik M., Zuhlke A., Haaparanta A.-M., Muhonen V., Laine K., Bilotsky Y., Kellomaki M., Kiviranta I., “The Importance of Controlled Mismatch of Biomechanical Compliances of Implantable Scaffolds and Native Tissue For Articular Cartilage Regeneration”, Front. Bioeng. Biotechnol., 6 (2018), 187
Tsiamis A., Maragos P., “Sparsity in Max-Plus Algebra and Systems”, Discret. Event Dyn. Syst.-Theory Appl., 29:2 (2019), 163–189
Park S., “B-Spaces Are Kkm Spaces”, J. Nonlinear Convex Anal., 20:4 (2019), 739–746
Maragos P., “Tropical Geometry, Mathematical Morphology and Weighted Lattices”, Mathematical Morphology and Its Applications to Signal and Image Processing, Ismm 2019, Lecture Notes in Computer Science, 11564, eds. Burgeth B., Kleefeld A., Naegel B., Passat N., Perret B., Springer International Publishing Ag, 2019, 3–15
Bai R., Yang Y., “Structure and Representation of Semimodules Over Inclines”, Ann. Pure Appl. Log., 171:10 (2020), 102844

Просмотров:
Эта страница:	1365
Полный текст:	519
Литература:	85
Первая стр.:	6

Что такое QR-код?

Обратная связь:

Пользовательское соглашение

Регистрация посетителей портала

Логотипы