• 대한수학회지
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• 제36권3호
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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.

• 제어로봇시스템학회논문지
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• 제15권8호
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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.

• 대한수학회논문집
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• 제15권4호
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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.

• 대한수학회지
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• 제59권3호
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• pp.449-468
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• 2022

In this paper we determine explicitly the kernels 𝕜_α,β associated with new Bergman spaces A²_α,β(𝔻) considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when α ∈ ℕ where the zeros are given by the zeros of a real polynomial Q_α,β. Some numerical results are given throughout the paper.

• 대한수학회논문집
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• 제19권3호
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• pp.453-459
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• 2004

In this paper, we provide an example of "worst cases" of bad pairs of polynomial zeros, namely sums of two polynomials with all pairs of zeros bad and all their zeros real.

• International journal of advanced smart convergence
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• 제6권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권2호
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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.

• 대한수학회논문집
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• 제24권2호
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• pp.239-245
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• 2009

We estimate the positive real zeros of certain trinomial equations and then deduce zeros bounds of some lacunary polynomials.

• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.409-425
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• 2024

Logistic regression models are commonly used to explain binary health outcome variable using independent variables such as patient characteristics in medical science and public health research. Although there is no distributional assumption required for independent variables in logistic regression, variables with severely right-skewed distribution such as lab values are often log-transformed to achieve symmetry or approximate normality. However, lab values often have zeros due to limit of detection which makes it impossible to apply log-transformation. Therefore, preprocessing to handle zeros in the observation before log-transformation is necessary. In this study, five methods that remove zeros (shift by 1, shift by half of the smallest nonzero, shift by square root of the smallest nonzero, replace zeros with half of the smallest nonzero, replace zeros with the square root of the smallest nonzero) are investigated in logistic regression setting. To evaluate performances of these methods, we performed a simulation study based on randomly generated data from log-normal distribution and logistic regression model. Shift by 1 method has the worst performance, and overall shift by half of the smallest nonzero method, replace zeros with half of the smallest nonzero method, and replace zeros with the square root of the smallest nonzero method showed comparable and stable performances.

• 대한수학회보
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• 제41권4호
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• pp.641-646
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• 2004

A convex combination of two products with same degree of finitely many finite geometric series with each having even degree does not always have all its zeros on the unit circle. However, in this paper, we show that a polynomial obtained by just adding a finite geometric series multiplied by a large constant to such a convex combination has all its zeros on the unit circle.