• International Journal of Control, Automation, and Systems
• /
• v.5 no.1
• /
• pp.1-7
• /
• 2007

In this paper, the necessary and sufficient conditions for strict positive realness of the rational transfer functions directly from basic definitions in the frequency domain are studied. A new frequency domain approach is used to check if a rational transfer function is a strictly positive real or not. This approach is based on the Taylor expansion and the Maximum Modulus Principle which are the fundamental tools in the complex functions analysis. Four related common statements in the strict positive realness literature which is appeared in the control theory are discussed. The drawback of these common statements is analyzed through some counter examples. Moreover a new necessary condition for strict positive realness is obtained from high frequency behavior of the Nyquist diagram of the transfer function. Finally a more simplified and completed conditions for strict positive realness of single-input single-output linear time-invariant systems are presented based on the complex functions analysis approach.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.17 no.3
• /
• pp.87-92
• /
• 2017

This paper compares the equalization algorithm of CR-MMA (Constellation Reduction-Multi Modulus Algorithm) and RMMA (Region based Multi Modulus Algorithm) for the compensation of channel's distortion in nonconstant modulus signal. In order to obtain the error signal for adaptive equalization, every signal points are reduced to the constant modulus signal in CR-MMA and every signal points are separated into the 4 regions, then the reductions are performed based on this region in RMMA. These two algorithm based on the reduction principle such as in order to updating the tap coefficient in the adaptive equalization, it has different equalization performance. The computer simulation was performed in order to compare the each equalization performance in this paper. As a result of computer simulation, RMMA has more good performance in the residual isi, maximum distortion and SER performance than CR-MMA, but not in convergence speed.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.16 no.5
• /
• pp.91-97
• /
• 2016

This paper evaluates the equalization algorithm of FC-MMA (Fast Convergence-Multi Modulus Algorithm) and RMMA (Region based Multi Modulus Algorithm) for the compensation of intersymbol interference which is due to the distortion of communication channel. In order to obtain the error signal for adaptive equalization, the FC-MMA use the modified dispersion constant considering the number of signal symbol, the RMMA separates the 4 region which every symbol points are located, then reduce the symbol point based on this region into constant modulus symbol point. By applying the different principle in order to get the error signal for the updating the tap coefficient of adaptive equalizer, it has the different equalization performance by these error signal. The computer simulation was performed in order to compare the different equalization performance in this paper. The performance index includes the output signal constellation, the residual isi and maximum distortion that is for the convergence characteristics, the SER. As a result of computer simulation, RMMA has more good performance in the residual isi, maximum distortion after in steady state and SER performance than FC-MMA, but not in convergence speed to reach the steady state.

• Korean Journal of Mathematics
• /
• v.30 no.2
• /
• pp.231-238
• /
• 2022

In this paper we prove some results by using a simple but elegant techniques to improve and strengthen some generalizations and refinements of two widely known polynomial inequalities and thereby deduce some useful corollaries.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.943-956
• /
• 2023

Let p(z) be a polynomial of degree n and for any complex number 𝛽, let D_𝛽p(z) = np(z) + (𝛽 - z)p'(z) denote the polar derivative of the polynomial with respect to 𝛽. In this paper, we consider the class of polynomial $$p(z)=(z-z_0)^s \left(a_0+\sum\limits_{{\nu}=0}^{n-s}a_{\nu}z^{\nu}\right)$$ of degree n having a zero of order s at z₀, |z₀| < 1 and the remaining n - s zeros are outside |z| < k, k ≥ 1 and establish upper bound estimates for the maximum of |D_𝛽p(z)| as well as |p(Rz) - p(rz)|, R ≥ r ≥ 1 on the unit disk.

• International Journal of Highway Engineering
• /
• v.14 no.5
• /
• pp.75-83
• /
• 2012

PURPOSES: Suggestion of asphalt binder constitutive model based on time-temperature superposition principle and overstress concept in order to describe behavior of asphalt binders. METHODS: A series of temperature sweep tests and multiple stress creep and recovery(MSCR) tests are performed to verify the applicability of time-temperature superposition principle(t-Ts) and to develop viscoelastoplastic constitutive equation based on overstress concept. For the tests, temperature sweep tests at various high temperature and various frequency and MSCR test at $58^{\circ}C$, $64^{\circ}C$ $70^{\circ}C$, $76^{\circ}C$, and $82^{\circ}C$ are performed. From the temperature sweep tests, dynamic shear modulus mastercurve and time-temperature shift function are built and the shift function and MSCR at $58^{\circ}C$ are utilized to determine model coefficients of VBO model. RESULTS: It is observed that the time-temperature shift function built at low strain level of 0.1% is applicable not only to 1.0% strain level temperature sweep test but also maximum 500,00% strain level of MSCR test. As well, the modified VBO model shows perfect prediction on MSCR measured strain at the other temperatures. CONCLUSIONS: The Time-temperature superposition principle stands hold from very low strain level to very high strain level and that the modified VBO model can be applicable for various range of strain and temperature region to predict elastic, viscoelastic, and viscoplastic strain of asphalt binders.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.63 no.6
• /
• pp.17-26
• /
• 2021

Greenhouses have been damaged due to the uplift pressure from strong wind, for which rebar piles are often installed near the greenhouse to resist the pressure. For the effective design of rebar piles, it is necessary to access the shear strength of soil on which the greenhouse is constructed. This study experimentally evaluates the shear strength of the soil beneath the greenhouse. Four soil samples were collected from four agricultural sites, and prepared for testing with 75, 80, 85, and 90% compaction rates. One-dimensional unconfined compression test (UC), consolidated-undrained triaxial test (CU), and resonant column test (RC) were performed for the evaluation of shear strength and shear modulus. Generally, the higher shear strength and modulus were observed with the higher compaction rates. In particular, the UC shear strength increases with the increase of #200 sieve passing rate. Resulting from the CU test, the sample with the most of coarse soil had the highest friction angle, but the variation is small among samples. Resulting from the CU and RC tests, the ratio of maximum shear modulus with the major principle stress at failure was the higher at the finer soil. The ratio was two to three times greater than the ratio from the standard sand. This indicates that the shear strength is lower for the fine soil than the coarse soil at the same shear modulus. The results of this study will be a useful resource for the estimation of the pull-out strength of the rebar pile against the uplift pressure.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.127-145
• /
• 2009

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.41-49
• /
• 2009

Let $\zeta$ be a fixed complex number. In this paper, we study the quantity $S(\zeta,\;n):=mas_{f{\in}{\Lambda}_n}\;|f(\zeta)|$, where ${\Lambda}_n$ is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given ${\zeta}\;{\in}\;{\mathbb{C}}$ and $n\;{\in}\;{\mathbb{N}}$, the quantity S($\zeta$, n) can be calculated. Then we compute the limit $lim_{n{\rightarrow}{\infty}}\;S(\zeta,\;n)/n$ for every ${\zeta}\;{\in}\;{\mathbb{C}}$ of modulus 1. It is equal to 1/$\pi$ if $\zeta$ is not a root of unity. If $\zeta\;=\;\exp(2{\pi}ik/d)$, where $d\;{\in}\;{\mathbb{N}}$ and k $\in$ [1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin($\pi$/d)) and 1/(2d sin($\pi$/2d)) for d = 1, d even and d > 1 odd, respectively.

• Structural Engineering and Mechanics
• /
• v.91 no.4
• /
• pp.417-426
• /
• 2024

Nanotechnology has emerged as a promising avenue for enhancing musical structures. In this study, we analyze the static behavior of laser harp (i.e., electronic musical instrument) reinforced with Zinc Oxide (ZnO) nanoparticles. Leveraging the piezoelectric properties of ZnO nanoparticles, the structure is subjected to an electric field for intelligent control. The electronic musical structure is situated in a foundation with vertical springs and shear modulus constants. We employ the exponential Shear Deformation Beam Theory (ESDBT) to mathematically model the structure. A micro-electro-mechanical model is employed to determine the equivalent properties of the system. By utilizing nonlinear stress-strain relations, energy methods, and Hamilton's principle, we derive the motion equations. The buckling load of the electronic musical beam is calculated using the Difference Quadrature Method (DQM). The primary objective of this study is to present a mathematical model for electronic musical beams and determining the buckling load of the structure and to investigate the influence of nanotechnology and electric fields on its buckling behavior. The buckling is the case when the structure becomes deforms and unstable. Our findings reveal that the application of negative external voltage to the electronic musical structure increases both the stiffness and the buckling load of the musical system. Furthermore, reinforcing the electronic musical structure with ZnO nanoparticles results in an increased buckling load. Notably, the maximum enhancement in the 28-day compressive and tensile strengths of samples containing zinc oxide nanoparticles compared to the control sample resulting in increases of 18.70% and 3.77%, respectively.