• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.757-771
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• 2022

In this paper, we present some fixed point theorems for rational type contractive conditions in the setting of a complete metric space via a cyclic (𝛼, 𝛽)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.

• 대한수학회보
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• 제61권1호
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• 대한수학회지
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• 제58권6호
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.285-288
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• 1998

A least-squares identification method is studied that estimates a finite number of coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions, We will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. We show that the Laplace transform of the expansion for some sets$\Psi_{\kappa}(Z)$ is equivalent to a series expansion . Techniques based on this result are presented for obtaining the coefficients $c_{n}$ as those of a series. One of their important properties is that, if chosen properly, they can substantially increase the speed of convergence of the series expansion. This leads to accurate approximate models with only a few coefficients to be estimated. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained.

• 대한수학회보
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• 제41권3호
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• pp.451-456
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• 2004

Given a function on a scheme over a finite field, we can count the number of rational points of the scheme having the same values. We show that if the function, viewed as a morphism to the affine line, is proper and its higher direct image sheaves are tamely ramified at the infinity then the values are uniformly distributed up to some degree.

• Transactions on Control, Automation and Systems Engineering
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• 제1권1호
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• pp.50-53
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• 1999

It has been pointed out in the literature that the Routh approximation method for order reduction has limitations in treating transfer functions with the denominator-numerator order difference not equal to one. The purpose of this paper is to present a new algorithm based on the Routh approximation method that can be applied to general rational transfer functions, yield ing reduced models with arbitrary order.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권2호
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• pp.141-155
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• 2011

We compute zeta functions of 1-solenoids. When our 1-solenoid is nonorientable, we compute Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid and its orientable double cover explicitly in terms of adjacency matrices and branch points. And we show that Artin-Mazur zeta function of orientable double cover is a rational function and a quotient of Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid.

• 드라이브 ㆍ 컨트롤
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• 제15권4호
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• pp.67-73
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• 2018

The paper deals with an approach to time domain simulation for closed end at the downstream of pipe, hydraulic lines terminating into a tank and series lines with change of cross sectional area. Time domain simulation of a fluid power systems containing hydraulic lines is very complex and difficult if the transfer functions consist of hyperbolic Bessel functions which is the case for the distributed parameter dissipative model. In this paper, the magnitudes and phases of the complex transfer functions of hydraulic lines are calculated, and the MATLAB Toolbox is used to formulate a rational polynomial approximation for these transfer functions in the frequency domain. The approximated transfer functions are accurate over a designated frequency range, and used to analyze the time domain response. This approach is usefully to simulate fluid power systems with hydraulic lines without to approximate the frequency dependent viscous friction.

• 호남수학학술지
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• 제43권2호
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• 대한수학회보
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• 제53권3호
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• pp.821-831
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• 2016

A case study is added to our recent work on Quillen phenomenon. Pointwise positivity of polynomials on generalized lemniscates of the complex plane is related to sums of hermitian squares of rational functions, and via operator quantization, to essential subnormality.