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1.
P. Zinn-Justin 《Theoretical and Mathematical Physics》2015,185(3):1741-1758
We show how equivariant volumes of tensor product quiver varieties of type A are given by matrix elements of vertex operators of centrally extended doubles of Yangians and how these elements satisfy the rational level-one quantum Knizhnik–Zamolodchikov equation in some cases. 相似文献
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Lucio Simone Cirio João Faria Martins 《Differential Geometry and its Applications》2012,30(3):238-261
In the context of higher gauge theory, we construct a flat and fake flat 2-connection, in the configuration space of n particles in the complex plane, categorifying the Knizhnik–Zamolodchikov connection. To this end, we define the differential crossed module of horizontal 2-chord diagrams, categorifying the Lie algebra of horizontal chord diagrams in a set of n parallel copies of the interval. This therefore yields a categorification of the 4-term relation. We carefully discuss the representation theory of differential crossed modules in chain-complexes of vector spaces, which makes it possible to formulate the notion of an infinitesimal 2-R matrix in a differential crossed module. 相似文献
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For an oriented 2-dimensional manifold Σ of genus g with n boundary components, the space carries the Goldman–Turaev Lie bialgebra structure defined in terms of intersections and self-intersections of curves. Its associated graded Lie bialgebra (under the natural filtration) is described by cyclic words in and carries the structure of a necklace Schedler Lie bialgebra. The isomorphism between these two structures in genus zero has been established in [13] using Kontsevich integrals and in [2] using solutions of the Kashiwara–Vergne problem.In this note, we give an elementary proof of this isomorphism over . It uses the Knizhnik–Zamolodchikov connection on . We show that the isomorphism naturally depends on the complex structure on the surface. The proof of the isomorphism for Lie brackets is a version of the classical result by Hitchin [9]. Surprisingly, it turns out that a similar proof applies to cobrackets.Furthermore, we show that the formality isomorphism constructed in this note coincides with the one defined in [2] if one uses the solution of the Kashiwara–Vergne problem corresponding to the Knizhnik–Zamolodchikov associator. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(2):377-382
A new general theorem, which does not require the existence of Lagrangians, allows to compute conservation laws for an arbitrary differential equation. This theorem is based on the concept of self-adjoint equations for nonlinear equations. In this paper we show that the Zakharov–Kuznetsov equation is self-adjoint and nonlinearly self-adjoint. This property is used to compute conservation laws corresponding to the symmetries of the equation. In particular the property of the Zakharov–Kuznetsov equation to be self-adjoint and nonlinearly self-adjoint allows us to get more conservation laws. 相似文献
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The Fokker–Planck–Kolmogorov parabolic second-order differential operator is considered, for which its fundamental solution is derived in explicit form. Such operators arise in numerous applications, including signal filtering, portfolio control in financial mathematics, plasma physics, and problems involving linear-quadratic regulators. 相似文献
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We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa–Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several facts for the dispersionless Camassa–Holm equation. In particular, we show that initial conditions with integrable momentum asymptotically split into a sum of peakons as conjectured by McKean. 相似文献
9.
Panagiotis Rizomiliotis 《Designs, Codes and Cryptography》2010,57(3):283-292
In the past few years, algebraic attacks against stream ciphers with linear feedback function have been significantly improved.
As a response to the new attacks, the notion of algebraic immunity of a Boolean function f was introduced, defined as the minimum degree of the annihilators of f and f + 1. An annihilator of f is a nonzero Boolean function g, such that fg = 0. There is an increasing interest in construction of Boolean functions that possess optimal algebraic immunity, combined
with other characteristics, like balancedness, high nonlinearity, and high algebraic degree. In this paper, we investigate
a recently proposed infinite class of balanced Boolean functions with optimal algebraic immunity, optimum algebraic degree
and much better nonlinearity than all the previously introduced classes of Boolean functions with maximal algebraic immunity.
More precisely, we study the resistance of the functions against one of the new algebraic attacks, namely the fast algebraic
attacks (FAAs). Using the special characteristics of the family members, we introduce an efficient method for the evaluation
of their behavior against these attacks. The new algorithm is based on the well studied Berlekamp–Massey algorithm. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(1):49-52
Many real nonlinear evolution equations exhibiting soliton properties display a special superposition principle, where an infinite array of equally spaced, identical solitons constitutes an exact periodic solution. This arrangement is studied for the modified Korteweg–de Vries equation with positive cubic nonlinearity, which possesses algebraic solitons with nonvanishing far field conditions. An infinite sum of equally spaced, identical algebraic pulses is evaluated in closed form, and leads to a complex valued solution of the nonlinear evolution equation. 相似文献
12.
Andrei Yu. Khrennikov 《Applicable analysis》2020,99(8):1425-1435
ABSTRACTWe prove the local solvability of the p-adic analog of the Navier–Stokes equation. This equation describes, within the p-adic model of porous medium, the flow of a fluid in capillaries. 相似文献
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This paper is concerned with the Cauchy problem for the Dullin–Gottwald–Holm equation. First, the local well-posedness for this system in Besov spaces is established. Second, the blow-up criterion for solutions to the equation is derived. Then, the existence and uniqueness of global solutions to the equation are investigated. Finally, the sharp estimate from below and lower semicontinuity for the existence time of solutions to this equation are presented. 相似文献
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A. Rozanova-Pierrat 《Applicable analysis》2013,92(3):391-408
Recalling the proprieties of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, we prove the controllability of moments result for the linear part of the KZK equation and its non-linear perturbation. 相似文献
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H. Péics 《Journal of Difference Equations and Applications》2013,19(3):257-273
In this paper we study the asymptotic behaviour of solutions of the pantograph-type differnce equation, and obtain aymptotic estimates, which can imply asymptotic stability or stability of solutions 相似文献
18.
Eliza Jabłońska 《Aequationes Mathematicae》2014,87(1-2):125-133
We characterize solutions ${f, g : \mathbb{R} \to \mathbb{R}}$ of the functional equation f(x + g(x)y) = f(x)f(y) under the assumption that f is locally bounded above at each point ${x \in \mathbb{R}}$ . Our result refers to Go?a?b and Schinzel (Publ Math Debr 6:113–125, 1959) and Wo?od?ko (Aequationes Math 2:12–29, 1968). 相似文献
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Y. M. aleksentsev 《Mathematical Notes》1999,66(4):395-403
By means of the method of the Laurent interpolation determinant, it is proved that, if ζ is an algebraic number, the real
numbersd andL satisfy the inequalitiesd≥degζ,L≥L(ζ), andL≥3, and the numberd is sufficiently large, then the inequality
holds. The constant 21.4708 in the above estimate for the measure of transcendence of the number π is the best among the
known values.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 483–493, October, 1999. 相似文献