• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.413-420
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• 2020

Considering inverse cotangential shear strain function, the present paper studies nonlinear stability of nonlocal higher-order refined beams made of metal foams based on Chebyshev-Ritz method. Based on inverse cotangential beam model, it is feasible to incorporate shear deformations needless of shear correction factor. Metal foam is supposed to contain different distributions of pores across the beam thickness. Also, presented Chebyshev-Ritz method can provide a unified solution for considering various boundary conditions based on simply-supported and clamped edges. Nonlinear effects have been included based upon von-karman's assumption and nonlinear elastic foundation. The buckling curves are shown to be affected by pore distribution, geometric imperfection of the beam, nonlocal scale factor, foundation and geometrical factors.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.337-347
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• 2024

Kernel density estimation is a prevalent technique employed for nonparametric density estimation, enabling direct estimation from the data itself. This estimation involves two crucial elements: selection of the kernel function and the determination of the appropriate bandwidth. The selection of the bandwidth plays an important role in kernel density estimation, which has been developed over the past decade. A range of methods is available for selecting the bandwidth, including the plug-in bandwidth. In this article, the proposed plug-in bandwidth is introduced, which leverages shifted Chebyshev series-based approximation to determine the optimal bandwidth. Through a simulation study, the performance of the suggested bandwidth is analyzed to reveal its favorable performance across a wide range of distributions and sample sizes compared to alternative bandwidths. The proposed bandwidth is also applied for kernel density estimation on real dataset. The outcomes obtained from the proposed bandwidth indicate a favorable selection. Hence, this article serves as motivation to explore additional plug-in bandwidths that rely on function approximations utilizing alternative series expansions.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.527-543
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• 2024

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.11 s.102
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• pp.1155-1163
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• 2005

In this paper, we suggest the new method to considerably enlarge stopband without increment of filter sire and loss. The proposed low pass filter looks like outward configuration with the published Modified Generalized Chebyshev (MGC) low pass filter, but the element values completely differ from each other. The published MGC fille, had been considered only the second attenuation pole to reject(or suppress) the harmonic, whereas the stopband of the proposed filter is superior to the published MGC filter because not only the second attenuation pole but also the third harmonic of the first attenuation pole is made use of profitably. We fabricate a low pass filter according to the proposed theory. From the measurement of the fabricated filter, we can confirm that the stopband of the proposed filter is reached above 4 times wider than the conventional Generalized Chebyshev(GC) filter and above 1.7 times wider than the published MGC filter.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.1
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• pp.11-18
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• 2024

This paper presents a procedure to optimize the design of 70GHz band array antenna for automotive short range radar sensor applications using Chebyshev polynomials. SRR(: Short Range Radar) systems require a wide angle width and low Side lobe level to detect targets within close proximity while ensuring a high Field of View(FoV). The optimized antenna operates in the 76 to 81GHz frequency range, and to reduce the antenna size, we arranged 12 patches in series, achieving an SLL of 10dB, angle with of 112.5o, gain of 15.4dB and an input return loss of less than -10dB at 78GHz. In this paper, we proceed with antenna design for SRR using Chebyshev polynomials, and present an optimal design for antenna structures to be used in MRR(: Medium-Range Radar) and LRR(: Long Range Radar) applications based on this paper

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.439-451
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• 2000

To compute derivatives using matrix vector multiplication method, new algorithms were introduced in [1.2]n By these algorithms, we reduced roundoff error in computing derivative using Chebyshev collocation methods (CCM). In this paper, some applications of these algorithms ar presented.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.3
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• pp.44-49
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• 2002

A study of free vibration of axisymmetric circular plates based on Mindlin theory using a pseudospectral method is presented. The analysis is based on Chebyshev polynomials that are widely used in the fluid mechanics research community. Clamped, simply supported and flee boundary conditions are considered, and numerical results are presented for various thickness-to-radius ratios.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.223-236
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• 2000

In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.47-54
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• 2000

This article is concerned with the algorithm for the Chebyshev estimation with/without linear equality and/or inequality constraints. The algorithm employs a linear scaling transformation scheme to reduce the computational burden which is induced when the data set is quite large. The convergence of the proposed algorithm is proved. And the updating and orthogonal decomposition techniques are considered to improve the computational efficiency and numerical stability.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.37-42
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• 1983

The elliptic functions have transmission zeros on the imaginary axis and exhibit equal ripples in the stopband as well as in the passband. As a consequence they can be made optimal in the sense that the transition band is minimal. However the time domain behaviors turned out to be inferior to those of Chebyshev and Butterworth responses. This paper investigates the unit step responses and impulse responses in order to analyze the effects of various parameters such as passband attenuation, stopband frequencies M. etc., The following are the prominent features. Step responses of elliptic filters rise faster and produce larger overshoots and undershoots with higher natural frequencies. In the case of even functions, the initial values are non-zero which decreases as $\omega$s increases. Unlike Butter-worth or Chebyshev cases the impulse responses start with nonzero valses which also decrease as $\omega$s or order of the function increases. Eight figures are included to illustrate above analysis.