Zobrazeno 1 - 10
of 451
pro vyhledávání: '"Shapiro, Boris"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G2, Pp 445-451 (2023)
The Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutive Wronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation
Externí odkaz:
https://doaj.org/article/9919d9b02e2d4acca3fc06ac3d9057f6
We study plasmonic time crystals, which constitute an extension of the dielectric-based photonic time crystals to plasmonic media. A salient feature of plasmonic time crystals is their ability to support amplification of both longitudinal and transve
Externí odkaz:
http://arxiv.org/abs/2407.19958
Zonotopal algebras (external, central, and internal) of an undirected graph G introduced by Postnikov-Shapiro and Holtz-Ron, are finite-dimensional commutative graded algebras whose Hilbert series contain a wealth of combinatorial information about G
Externí odkaz:
http://arxiv.org/abs/2407.19431
Publikováno v:
Phys. Rev. B 110, L100306 (2024)
Lorentzian-type media support optical phonons that oscillate with longitudinal polarization parallel to the wave direction, at a wave vector-independent frequency at which the permittivity becomes zero. Here, we study the interactions between the lon
Externí odkaz:
http://arxiv.org/abs/2407.04502
A linear differential operator $T=Q(z)\frac{d}{dz}+P(z)$ with polynomial coefficients defines a continuous family of Hutchinson operators when acting on the space of positive powers of linear forms. In this context, $T$ has a unique minimal Hutchinso
Externí odkaz:
http://arxiv.org/abs/2406.10963
Given a linear ordinary differential operator T with polynomial coefficients, we study the class of closed subsets of the complex plane such that T sends any polynomial (resp. any polynomial of degree exceeding a given positive integer) with all root
Externí odkaz:
http://arxiv.org/abs/2404.14365
In this paper, we prove a number of results providing either necessary or sufficient conditions guaranteeing that the number of real roots of real polynomials of a given degree is either less or greater than a given number. We also provide counterexa
Externí odkaz:
http://arxiv.org/abs/2403.12200
Below we study a linear differential equation $\MM (v(z,\eta))=\eta^M{v(z,\eta)}$, where $\eta>0$ is a large spectral parameter and $\MM=\sum_{k=1}^{M}\rho_{k}(z)\frac{d^k}{dz^k},\; M\ge 2$ is a differential operator with polynomial coefficients such
Externí odkaz:
http://arxiv.org/abs/2402.19087
Autor:
Kurnosov, Arkady, Fernández-Alcázar, Lucas J., Ramos, Alba Y., Shapiro, Boris, Kottos, Tsampikos
Recent experimental developments in multimode nonlinear photonic circuits (MMNPC), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a non-equilibrium t
Externí odkaz:
http://arxiv.org/abs/2310.16784
Publikováno v:
Phys. Rev. Lett. 130, 093803 (2023)
Time metamaterials exhibit a great potential for wave manipulation, drawing increasing attention in recent years. Here, we explore the exotic wave dynamics in an anisotropic photonic time crystal (APTC), formed by an anisotropic medium whose optical
Externí odkaz:
http://arxiv.org/abs/2209.10964