Stability analysis by maclaurin series expansion of system function and its applications

1986 ◽  
Vol 17 (3) ◽  
pp. 1-10
Author(s):  
Shinji Hayashi ◽  
Nozomu Hamada
Keyword(s):  
Stability Analysis ◽  
Series Expansion ◽  
System Function ◽  
Maclaurin Series

Behavior of Coefficients of Inverses of α-Spiral Functions

1986 ◽  
Vol 38 (6) ◽  
pp. 1329-1337 ◽  
Author(s):  
Richard J. Libera ◽  
Eligiusz J. Złotkiewicz
Keyword(s):  
Unit Disk ◽  
Series Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Maclaurin Series ◽  
Koebe Function ◽  
One To One ◽  
Image Position

If f(z) is univalent (regular and one-to-one) in the open unit disk Δ, Δ = {z ∊ C:│z│ < 1}, and has a Maclaurin series expansion of the form(1.1)then, as de Branges has shown, │ak│ = k, for k = 2, 3, … and the Koebe function.(1.1)serves to show that these bounds are the best ones possible (see [3]). The functions defined above are generally said to constitute the class .

scholarly journals Series expansion of the Gamma function and its reciprocal

2021 ◽  
Vol 27 (4) ◽  
pp. 104-115
Author(s):  
Ioana Petkova ◽  
Keyword(s):  
Differential Operator ◽  
Explicit Form ◽  
Series Expansion ◽  
Exponential Function ◽  
Gamma Function ◽  
Linear Functional ◽  
Maclaurin Series

In this paper we give representations for the coefficients of the Maclaurin series for \Gamma(z+1) and its reciprocal (where \Gamma is Euler’s Gamma function) with the help of a differential operator \mathfrak{D}, the exponential function and a linear functional ^{*} (in Theorem 3.1). As a result we obtain the following representations for \Gamma (in Theorem 3.2): \begin{align*} \Gamma(z+1) & = \big(e^{-u(x)}e^{-z\mathfrak{D}}[e^{u(x)}]\big)^{*}, \\ \big(\Gamma(z+1)\big)^{-1} & = \big(e^{u(x)}e^{-z\mathfrak{D}}[e^{-u(x)}]\big)^{*}. \end{align*} Theorem 3.1 and Theorem 3.2 are our main results. With the help of the first theorem we give our approach for finding the coefficients of Maclaurin series for \Gamma(z+1) and its reciprocal in an explicit form.

scholarly journals A Maclaurin-series expansion approach to multiple paired queues

2014 ◽  
Vol 42 (3) ◽  
pp. 203-207 ◽  
Author(s):  
Eline De Cuypere ◽  
Koen De Turck ◽  
Dieter Fiems
Keyword(s):  
Series Expansion ◽  
Maclaurin Series

scholarly journals Relationship between the 2-body Energy of the Biswas-Hamann and the Murrell-Mottram Potential Functions

2004 ◽  
Vol 59 (3) ◽  
pp. 116-118 ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Bond Length ◽  
Potential Function ◽  
Series Expansion ◽  
Potential Functions ◽  
Scaling Functions ◽  
Maclaurin Series ◽  
Scaling Factors ◽  
Equilibrium Bond Length ◽  
Exponential Term ◽  
Body Energy

The two-body interactions in the Biswas-Hamann (BH) and Murrell-Mottram (MM) potential functions are analytically related in this paper by equating the zeroth to second differentials at equilibrium bond length. By invoking the Maclaurin series expansion for the exponential term, the MM potential function could be expressed in a manner that enables comparison of repulsive and attractive terms. Approximate and refined sets of scaling factors were obtained upon comparing the indices and coefficients, respectively. Finally, the suitability for each set of scaling functions is discussed in terms of the “softness” of the bonds.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions

1995 ◽  
Author(s):  
Jeffrey A. Morgan ◽  
Christophe Pierre ◽  
Gregory M. Hulbert
Keyword(s):  
Frequency Response ◽  
Series Expansion ◽  
Dynamic Models ◽  
Component Mode Synthesis ◽  
Residual Effects ◽  
Response Functions ◽  
Maclaurin Series ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response

Abstract This paper shows how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method and the use of a Maclaurin series expansion to represent the residual effects of the omitted modes. It was developed as a base-band method for structures exhibiting normal modes of vibration determined from free boundary vibration tests. Of particular importance is the procedure developed for the estimation of the Maclaurin series expansion coefficients and for the recovery of the Craig-Bampton matrices from the residual flexibility formulation. This allows accurate dynamic models to be determined for measured systems that can be used to predict the effects of structural modifications and in substructure coupling analyses. The performance of the new method is demonstrated by comparison of experiment and analysis for two simple beams.

A Generally Optimized FDTD Model for Simulating Arbitrary Dispersion Based on the Maclaurin Series Expansion

2010 ◽  
Vol 28 (19) ◽  
pp. 2843-2850 ◽  
Author(s):  
Zhili Lin ◽  
Chunxi Zhang ◽  
Pan Ou ◽  
Yudong Jia ◽  
Lishuang Feng
Keyword(s):  
Series Expansion ◽  
Maclaurin Series
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