• Title, Summary, Keyword: zeros

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ON THE EXTREME ZEROS OF ORTHOGONAL POLYNOMIALS

  • Kwon, K.H.;Lee, D.W.
    • Journal of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.489-507
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    • 1999
  • We investigate the asymptotic behavior of the extreme zeros of orthogonal polynomials with respect to a positive measure d$\alpha$(x) in terms of the three term recurrence coefficients. We then show that the asymptotic behavior of extreme zeros of orthogonal polynomials with respect to g(x)d$\alpha$(x) is the same as that of extreme zeros of orthogonal polynomials with respect to d$\alpha$(x) when g(x) is a polynomial with all zeros in a certain interval determined by d$\alpha$(x). several illustrating examples are also given.

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Complex Quadruplet Zero Locations from the Perturbed Values of Cross-Coupled Lumped Element

  • Um, Kee-Hong
    • International journal of advanced smart convergence
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    • v.6 no.4
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    • pp.33-40
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    • 2017
  • In this paper, complex quadruplet zeros of microwave filter systems are investigated. For the cascaded systems the chain matrices are most conveniently used to derive the voltage transfer function of Laplace transform with cascaded two-port subsystems. The convenient relations of transfer function and chain matrix are used in order to find the transmission zeros. Starting from a ladder network, we introduced a crossed-coupled lumped element, in order to show the improved response of bandpass filter. By solving the transmission zero characteristic equation derived from the cascaded subsystems, we found the zeros of filter system with externally cross-coupled lumped elements. With the cross-coupled elements of capacitors, the numerator polynomial of system transfer function is used to locate the quadruplet zeros in complex plane. When the two pairs of double are on the zeros -axis, with the perturbed values of element, we learned that the transition band of lowpass filter is improved. By solving the characteristic equation of cascaded transfer function, we can obtain the zeros of the cross-coupled filter system, as a result of perturbed values on lumped element.

BD PAIRS OF POLYNOMIAL ZEROS

  • Kim, Seon-Hong
    • Communications of the Korean Mathematical Society
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    • v.15 no.4
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    • pp.697-706
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    • 2000
  • If an arithmetic progression F of length 2n and the number k with 2k$\leq$n are give, can we find two monic polynomials with the same degrees whose set of all zeros form F such that both the number of bad pairs and the number of nonreal zeros are 2k? We will consider the case that both the number of bad pairs and the number of nonreal zeros are two. Moreover, we will see the fundamental relation between the number of bad pairs and the number of nonreal zeros, and we will show that the polynomial in x where the coefficient of x(sup)k is the number of sequences having 2k bad pairs has all zeros real and negative.

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Zeros and Step Response αlaracteristics in LTI SISO Systems (선형시불변 단일입출력 시스템의 영점과 계단응답 특성)

  • Lee, Sang-Yong
    • Journal of Institute of Control, Robotics and Systems
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    • v.15 no.8
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    • pp.804-811
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    • 2009
  • This paper deals with the relationship between zeros and step response of the second and third order LTI(Linear Time Invariant) SISO(Single-Input and Single-Output) systems. As well known, if a system has a single unstable zero, it shows the step response with undershoot and, on the other hand, a stable zero slower than the dominant pole causes the system to have the step response with overshoot. Generally, in the case of a system with two unstable real zeros, it is known to have B type undershoot[7]. But there are many complex cases of the step response extrema corresponding to zeros location in third order systems. This paper investigates the whole cases depending on DC gains of the additive equivalence systems and they are to be classified by the region of zeros which are related to the shape of the step response. Moreover, monotone nondecreasing conditions are proposed in the case of complex conjugate zeros as well as the case of two stable zeros.

Estimating the Partition Function Zeros by Using the Wang-Landau Monte Carlo Algorithm

  • Kim, Seung-Yeon
    • Journal of the Korean Physical Society
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    • v.70 no.6
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    • pp.561-566
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    • 2017
  • The concept of the partition function zeros is one of the most efficient methods for investigating the phase transitions and the critical phenomena in various physical systems. Estimating the partition function zeros requires information on the density of states ${\Omega}(E)$ as a function of the energy E. Currently, the Wang-Landau Monte Carlo algorithm is one of the best methods for calculating ${\Omega}(E)$. The partition function zeros in the complex temperature plane of the Ising model on an $L{\times}L$ square lattice (L = 10 ~ 80) with a periodic boundary condition have been estimated by using the Wang-Landau Monte Carlo algorithm. The efficiency of the Wang-Landau Monte Carlo algorithm and the accuracies of the partition function zeros have been evaluated for three different, 5%, 10%, and 20%, flatness criteria for the histogram H(E).

ON ZERO DISTRIBUTIONS OF SOME SELF-RECIPROCAL POLYNOMIALS WITH REAL COEFFICIENTS

  • Han, Seungwoo;Kim, Seon-Hong;Park, Jeonghun
    • The Pure and Applied Mathematics
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    • v.24 no.2
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    • pp.69-77
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    • 2017
  • If q(z) is a polynomial of degree n with all zeros in the unit circle, then the self-reciprocal polynomial $q(z)+x^nq(1/z)$ has all its zeros on the unit circle. One might naturally ask: where are the zeros of $q(z)+x^nq(1/z)$ located if q(z) has different zero distribution from the unit circle? In this paper, we study this question when $q(z)=(z-1)^{n-k}(z-1-c_1){\cdots}(z-1-c_k)+(z+1)^{n-k}(z+1+c_1){\cdots}(z+1+c_k)$, where $c_j$ > 0 for each j, and q(z) is a 'zeros dragged' polynomial from $(z-1)^n+(z+1)^n$ whose all zeros lie on the imaginary axis.

On the zeros of a multivariable discrete-time control system with approximate fractional order hold

  • Han, Seong-Ho;Yoshihiro, Takita
    • 제어로봇시스템학회:학술대회논문집
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    • pp.47.2-47
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    • 2001
  • This paper is concerned with the limiting zeros, as the sampling period tends to zero, of a multivariable discrete-time system composed of an approximate fractional-order hold (AFROH), a continuous-time plant and a sampler in cascade. An approximate fractional-order hold is proposed to implement fractional-order hold (FROH) and is applied to instead of the zero-order hold (ZOH). The implementing problem of the fractional-order hold is overcome. The properties of the limiting zeros are studied and the location problem of them is solved. In addition, a stability condition of the zeros for sufficiently small sampling period is derived ...

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THE ZEROS DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN AN ANGULAR DOMAIN

  • Huang, Zhibo;Chen, Zongxuan
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.443-454
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    • 2010
  • In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation $f^{(n)}+A_{n-2}(z)f^{(n-2)}+{\cdots}+A_1(z)f'+A_0(z)f=0(n{\geq}2)$ in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.