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Найдено 5 656 публикаций
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Статья
Kudryashov Y., Goncharuk N. B. Bulletin of the Brazilian Mathematical Society. 2017. No. 1.
Добавлено: 15 апреля 2016
Статья
Kanovich M., Ban Kirigin T., Nigam V. et al. Information and Computation. 2014. No. 238. P. 233-261.
Добавлено: 23 марта 2015
Статья
Kanovich M., Ban Kirigin T., Nigam V. et al. Computer Languages, Systems & Structures. 2014. No. 40. P. 137-154.
Добавлено: 23 марта 2015
Статья
Birkar C., Loginov K. Journal fuer die reine und angewandte Mathematik. 2021.
Добавлено: 3 сентября 2021
Статья
Balkanova O., Frolenkov D. Journal of London Mathematical Society. 2019. Vol. 99. No. 2. P. 249-272.
Добавлено: 25 августа 2019
Статья
Przyjalkowski V., Shramov K. Communications in Number Theory and Physics. 2020. Vol. 14. No. 3. P. 511-553.
Добавлено: 13 октября 2020
Статья
Maslov V. P. Mathematical notes. 2017. Vol. 102. No. 4. P. 583-586.
Добавлено: 17 ноября 2018
Статья
Maslov V. P., Maslova T. V. Russian Journal of Mathematical Physics. 2014. Vol. 21. No. 3. P. 373-378.
Добавлено: 30 ноября 2014
Статья
Gurevich D., Saponov P. A. Advances in Applied Mathematics. 2013. Vol. 51. P. 228-253.

We introduce the notion of a braided algebra and study some examples of these. In particular, R-symmetric and R-skew-symmetric algebras of a linear space V equipped with a skew-invertible Hecke symmetry R are braided algebras. We prove the “mountain property” for the numerators and denominators of their Poincaré–Hilbert series (which are always rational functions). Also, we further develop a differential calculus on modified Reflection Equation algebras. Thus, we exhibit a new form of the Leibniz rule for partial derivatives on such algebras related to involutive symmetries R. In particular, we present this rule for the algebra U(gl(m)). The case of the algebra U(gl(2)) and its compact form U(u(2)) (which can be treated as a deformation of the Minkowski space algebra) is considered in detail. On the algebra U(u(2)) we introduce the notion of the quantum radius, which is a deformation of the usual radius, and compute the action of rotationally invariant operators and in particular of the Laplace operator. This enables us to define analogs of the Laplace–Beltrami operators corresponding to certain Schwarzschild-type metrics and to compute their actions on the algebra U(u(2)) and its central extension. Some “physical” consequences of our considerations are presented.

Добавлено: 15 мая 2013
Статья
Pyatov P. N., Gurevich D., Saponov P. A. Journal of Geometry and Physics. 2012. Vol. 62. No. 5. P. 1175-1188.

On any reflection equation algebra corresponding to a skew-invertible Hecke symmetry (i.e., a special type solution of the Quantum Yang-Baxter equation) we define analogs of the partial derivatives. Together with elements of the initial reflection equation algebra they generate a "braided analog" of the Weyl algebra. When q→1, the braided Weyl algebra corresponding to the Quantum Group U q(sl(2)) goes to the Weyl algebra defined on the algebra Sym(u(2)) or U(u(2)) depending on the way of passing to the limit. Thus, we define partial derivatives on the algebra U(u(2)), find their "eigenfunctions", and introduce an analog of the Laplace operator on this algebra. Also, we define the "radial part" of this operator, express it in terms of "quantum eigenvalues", and sketch an analog of the de Rham complex on the algebra U(u(2)). Eventual applications of our approach are discussed.

Добавлено: 7 февраля 2013
Статья
Saponov P. A., Gurevich D. Journal of Geometry and Physics. 2019. Vol. 138. P. 124-143.
Добавлено: 12 января 2017
Статья
Brav C. I., Thomas H. Mathematische Annalen. 2011. Vol. 351. No. 4. P. 1005-1017.
Добавлено: 29 сентября 2014
Статья
Esterov A. I., Lang L. Geometry and Topology. 2021.
Добавлено: 27 октября 2020
Статья
Feigin B. L., Jimbo M., Miwa T. et al. Advances in Mathematics. 2016. Vol. 300. P. 229-274.

We construct an analog of the subalgebra Ugl(n)⊗Ugl(m)⊂Ugl(m+n) in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.

 

 

Добавлено: 2 декабря 2016
Статья
Roman Avdeev, Petukhov A. Algebras and Representation Theory. 2020. Vol. 23. No. 3. P. 541-581.
Добавлено: 11 февраля 2019
Статья
Kolesnikov A., Milman E. Journal of Geometric Analysis. 2017. Vol. 27. No. 2. P. 1680-1702.

It is known that by dualizing the Bochner–Lichnerowicz–Weitzenböck formula, one obtains Poincaré-type inequalities on Riemannian manifolds equipped with a density, which satisfy the Bakry–Émery Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature and an upper bound on its generalized dimension). When the manifold has a boundary, an appropriate generalization of the Reilly formula may be used instead. By systematically dualizing this formula for various combinations of boundary conditions of the domain (convex, mean-convex) and the function (Neumann, Dirichlet), we obtain new Brascamp–Lieb-type inequalities on the manifold. All previously known inequalities of Lichnerowicz, Brascamp–Lieb, Bobkov–Ledoux, and Veysseire are recovered, extended to the Riemannian setting and generalized into a single unified formulation, and their appropriate versions in the presence of a boundary are obtained. Our framework allows to encompass the entire class of Borell’s convex measures, including heavy-tailed measures, and extends the latter class to weighted-manifolds having negative generalized dimension.

Добавлено: 11 ноября 2016
Статья
Zykin A. I. Moscow Mathematical Journal. 2005. Vol. 5. No. 4. P. 961-968.

Классическая теорема Брауэра-Зигеля утверждает, что если $k$ пробегает последовательность числовых полей, нормальных над $\mathbb{Q},$ таких что $n_k/\log|D_k|\to 0,$ то $\log h_k R_k/\log \sqrt{|D_k|}\to 1.$ В этой статье мы получаем обобщение теорем Брауэра-Зигеля и Цфасмана-Влэдуца на случай почти нормальных числовых полей. Кроме того, используя подход Хаджира и Мэра, мы строим некоторые примеры асимптотически хороших башен числовых полей, для которых значения отношения Брауэра-Зигеля меньше, чем в примерах, найденных Цфасманом и Влэдуцем.  

Добавлено: 15 сентября 2009
Статья
Katzarkov L., Dimitrov G. Advances in Mathematics. 2016. Vol. 288. P. 825-886.
Добавлено: 23 октября 2017
Статья
Manita A. Communications in Statistics-Theory and Method. 2011. Vol. 40. No. 19-20. P. 3440-3451.
Добавлено: 19 марта 2015
Статья
Omelchenko A., Краско Е. С. Electronic Journal of Combinatorics. 2015. Vol. 22. No. 1. P. 1-17.

We present new functional equations connecting the counting series of plane and planar (in the sense of Harary and Palmer) dissections. Simple rigorous expressions for counting symmetric rr-dissections of polygons and planar SS-dissections are obtained.

Добавлено: 29 августа 2018
Статья
Tikhomirov A. S., Markushevich D., Trautmann G. Central European Journal of Mathematics. 2012. Vol. 19. No. 4. P. 1331-1355.
Добавлено: 21 октября 2014