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From the Fibonacci Icosagrid to E8 (Part II): The Composite Mapping of the Cores
CrystalsThis paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its relation to the E8 root lattice. The FIG was originally constructed to represent the intersection points of an icosahedrally symmetric collection of planar ...
Richard Clawson, Fang Fang, Klee Irwin
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Boundary Value Problems, 2019 In this paper we study a new class of functions, which we call (ω,c)$(\omega ,c)$-pseudo periodic functions. This collection includes pseudo periodic, pseudo anti-periodic, pseudo Bloch-periodic, and unbounded functions.
E. Alvarez, S. Castillo, M. Pinto
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From the Fibonacci Icosagrid to E8 (Part I): The Fibonacci Icosagrid, an H3 Quasicrystal
CrystalsThis paper introduces a new kind of quasicrystal by Fibonacci-spacing a multigrid of a certain symmetry, like H2, H3, T3, etc. Multigrids of a certain symmetry can be used to generate quasicrystals, but multigrid vertices are not a quasicrystal due to ...
Fang Fang, Klee Irwin
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On positive periodic solutions of second order singular equations
Boundary Value Problems, 2018 Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations {x¨+a(t)x=f(x),x(0)=x(T),x˙(0)=x˙(T). $$\begin{aligned} \textstyle\begin{cases} \ddot{x}+a(t) x=f(x),\\ x(0)=
Yunhai Wang, Yuanfang Ru
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Abstract and Applied Analysis, 2012 In this paper, two classes of first-order neutral functional differential equations with periodic delays are considered. Some results on the existence of positive periodic solutions for the equations are obtained by using the Krasnoselskii fixed point ...
Zeqing Liu +3 more
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Trajectory analysis of high-order-harmonic generation from periodic crystals [PDF]
, 2016 We theoretically study high-order-harmonic generation (HHG) from solids driven by intense laser pulses using a one-dimensional model periodic crystal.
Takuya Ikemachi +5 more
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Self-consistent second-order Green's function perturbation theory for periodic systems. [PDF]
Journal of Chemical Physics, 2015 Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and at least ...
A. Rusakov, D. Zgid
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Periodic solutions of third order differential equations
Journal of Innovative Applied Mathematics and Computational SciencesIn this paper, we study the existence of periodic solutions for the following piecewise third-order differential equation: $$ \dddot{x}+\dot{x}-\varepsilon\sum\limits_{i=1}^{2}c_i|x|^i=0, $$ with $\varepsilon$ a real parameter sufficiently small, $c_1$
Nabil Rezaiki, Amel Boulfoul
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Periodic perturbations of reducible scalar second order functional differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2023 Using a topological approach we investigate the structure of the set of forced oscillations of a class of reducible second order functional retarded differential equations subject to periodic forcing.
Alessandro Calamai +2 more
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Periodic Quasiregular Mappings of Finite Order
Revista Matemática Iberoamericana, 2003 The authors construct a periodic quasiregular function of any finite order \rho , 1\leq\rho < \infty . This completes earlier work of O. Martio and U. Srebro.
Drasin, David, Sastry, Swati
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