The Experts below are selected from a list of 3081 Experts worldwide ranked by ideXlab platform
Yoshitsugu Takei - One of the best experts on this subject based on the ideXlab platform.
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exact wkb analysis of a schrodinger Equation with a merging triplet of two simple poles and one simple turning point ii its relevance to the Mathieu Equation and the legendre Equation
Advances in Mathematics, 2014Co-Authors: Shingo Kamimoto, Takahiro Kawai, Yoshitsugu TakeiAbstract:Abstract We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrodinger Equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu Equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre Equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu Equation and the Legendre Equation.
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microlocal analysis of fixed singularities of wkb solutions of a schrodinger Equation with a merging triplet of two simple poles and a simple turning point
2012Co-Authors: Shingo Kamimoto, Takahiro Kawai, Yoshitsugu TakeiAbstract:We first show that the WKB-theoretic canonical form of an M2P1T (merging two poles and one turning point) Schrodinger Equation is given by the algebraic Mathieu Equation. We further show that, in analyzing the structure of WKB solutions of a Mathieu Equation near fixed singular points relevant to simple poles of the Equation, we can focus our attention on the pole part of the Equation so that we may reduce it to the Legendre Equation. The Borel transformation of WKB-theoretic transformations thus obtained gives rise to microdifferential relations, which lead to the microlocal analysis of the Borel transformed WKB solutions of an M2P1T Equation near their fixed singular points. The fully detailed account of the results will be given in Kamimoto et al. (Exact WKB analysis of a Schrodinger Equation with a merging triplet of two simple poles and one simple turning point—its relevance to the Mathieu Equation and the Legendre Equation, 2011).
Shaopu Yang - One of the best experts on this subject based on the ideXlab platform.
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dynamical analysis of Mathieu Equation with two kinds of van der pol fractional order terms
International Journal of Non-linear Mechanics, 2016Co-Authors: Shaofang Wen, Yongjun Shen, Shaopu YangAbstract:Abstract In this paper the dynamics of Mathieu Equation with two kinds of van der Pol (VDP) fractional-order terms is investigated. The approximately analytical solution is obtained by the averaging method. The steady-state solution, existence conditions and stability condition for the steady-state solution are presented, and it is found that the two kinds of VDP fractional coefficients and fractional orders remarkably affect the steady-state solution, which is characterized by the additional damping coefficient (ADC) and additional stiffness coefficient (ASC). The comparisons between the analytical and numerical solutions verify the correctness and satisfactory precision of the approximately analytical solution. The presented typical amplitude–frequency curves illustrate the important effects of two kinds of VDP fractional-order terms on system dynamics. The application of two VDP fractional-order terms in vibration control is discussed. At last, the detailed results are summarized and the conclusions are made.
Shingo Kamimoto - One of the best experts on this subject based on the ideXlab platform.
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exact wkb analysis of a schrodinger Equation with a merging triplet of two simple poles and one simple turning point ii its relevance to the Mathieu Equation and the legendre Equation
Advances in Mathematics, 2014Co-Authors: Shingo Kamimoto, Takahiro Kawai, Yoshitsugu TakeiAbstract:Abstract We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrodinger Equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu Equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre Equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu Equation and the Legendre Equation.
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microlocal analysis of fixed singularities of wkb solutions of a schrodinger Equation with a merging triplet of two simple poles and a simple turning point
2012Co-Authors: Shingo Kamimoto, Takahiro Kawai, Yoshitsugu TakeiAbstract:We first show that the WKB-theoretic canonical form of an M2P1T (merging two poles and one turning point) Schrodinger Equation is given by the algebraic Mathieu Equation. We further show that, in analyzing the structure of WKB solutions of a Mathieu Equation near fixed singular points relevant to simple poles of the Equation, we can focus our attention on the pole part of the Equation so that we may reduce it to the Legendre Equation. The Borel transformation of WKB-theoretic transformations thus obtained gives rise to microdifferential relations, which lead to the microlocal analysis of the Borel transformed WKB solutions of an M2P1T Equation near their fixed singular points. The fully detailed account of the results will be given in Kamimoto et al. (Exact WKB analysis of a Schrodinger Equation with a merging triplet of two simple poles and one simple turning point—its relevance to the Mathieu Equation and the Legendre Equation, 2011).
Raymond E. March - One of the best experts on this subject based on the ideXlab platform.
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An Introduction to Quadrupole Ion Trap Mass Spectrometry
Journal of Mass Spectrometry, 1997Co-Authors: Raymond E. MarchAbstract:A concise introduction is presented to the theory and application of quadrupole ion trap mass spectrometry. The presentation of the theoretical treatment is based on a demonstration of the equivalence of the force acting on an ion in a quadrupole field and the force derived from the Mathieu Equation; this equivalence permits the application of the solutions of Mathieu’s Equation to the confinement of gaseous ions. Resonant excitation, collision-induced dissociation, mass spectrometry, tandem mass spectrometry and chemical ionization are discussed in the context of analytical applications. Sample calculations of the trapping parametersqzand βz, the axial secular frequency, mass range, mass range extension and the magnitude of the potential well depth are given. © 1997 by John Wiley & Sons, Ltd.
S Kumashiro - One of the best experts on this subject based on the ideXlab platform.
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ion motion in the rectangular wave quadrupole field and digital operation mode of a quadrupole ion trap mass spectrometer
Rapid Communications in Mass Spectrometry, 2006Co-Authors: L Ding, S KumashiroAbstract:A quadrupolar electric field driven by a rectangular wave voltage can be used for mass-selective storage and analysis. The ion motion in such an electric field is derived, and the stability of ions is presented in the a-q diagram that is commonly used for sinusoidal wave quadrupole mass spectrometry in association with the solution of the Mathieu Equation. The pseudo-potential well is discussed in an approximation that leads to the relation of secular frequency to operating parameters. A scheme for a digital ion trap mass spectrometer is described, based on this theory. An ion optics simulation was performed to check the theory of resonant ejection, and to prove the feasibility of the mass scan method for a practical ion trap of such geometry. Copyright © 2005 John Wiley & Sons, Ltd.