• 대한수학회보
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• 제58권4호
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.223-236
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• 2023

In the present paper, we investigate the subordination and superordination implications for a class of certain nonlinear integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Further, we extend some results given earlier as special cases of the main results presented here.

• 대한산업공학회지
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• 제32권2호
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• pp.74-81
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• 2006

In this paper, we deal with the separation of data by concurrently determined, piecewise nonlinear discriminant functions. Toward the end, we develop a new $l_1$-distance norm error metric and cast the problem as a mixed 0-1 integer and linear programming (MILP) model. Given a finite number of discriminant functions as an input, the proposed model considers the synergy as well as the individual role of the functions involved and implements a simplest nonlinear decision surface that best separates the data on hand. Hence, exploiting powerful MILP solvers, the model efficiently analyzes any given data set for its piecewise nonlinear separability. The classification of four sets of artificial data demonstrates the aforementioned strength of the proposed model. Classification results on five machine learning benchmark databases prove that the data separation via the proposed MILP model is an effective supervised learning methodology that compares quite favorably to well-established learning methodologies.

• 제어로봇시스템학회논문지
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• 제8권11호
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• pp.941-947
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• 2002

Two methods of constructing T-S fuzzy model which is equivalent to a given nonlinear system are presented. The first method is to obtain an equivalent T-S fuzzy model by using the sum of linearly independent scalar functions with constant real matrix coefficients. The sum of products of linearly independent scalar functions is used in the second method. The former method is to formulate the procedures of T-S fuzzy modeling dealt in many examples of previous publications; the latter is a new method. By comparing the number of linearly independent functions used in the two methods, we can easily find out which method makes fewer rules than the other. The nonlinear dynamics of an inverted Pendulum on a cart is used as an equivalent T-5 fuzzy modeling example.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.1017-1020
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• 2000

In this paper, a CNN using 1-dimensional chaos circuits with controllable nonlinear functions is proposed. The proposed CNN consists of $\p{times}q$ chaos circuits which are called cell circuits. The nonlinear functions of the cell circuits can be controlled by employing fuzzy scheme. Thanks to the controllability of the nonlinear functions, the proposed circuit can adjust transition behavior of the CNN electronically. Furthermore, the chaotic behavior of the cell circuit which is a portion of the proposed CNN is simple since the cell circuit is a 1-dimensional chaos circuit. To confirm the validity of the circuit design, SPICE simulations were performed concerning the proposed CNN.

• Earthquakes and Structures
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• 제5권4호
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• pp.439-459
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• 2013

Main objective of the present study is to determine the statistical properties and suitable probability distribution functions of spectral displacements from nonlinear static and nonlinear dynamic analysis within the frame work of Monte Carlo simulation for typical low rise and high rise RC framed buildings located in zone III and zone V and designed as per Indian seismic codes. Probabilistic analysis of spectral displacement is useful for strength assessment and loss estimation. To the author's knowledge, no study is reported in literature on comparison of spectral displacement including the uncertainties in capacity and demand in Indian context. In the present study, uncertainties in capacity of the building is modeled by choosing cross sectional dimensions of beams and columns, density and compressive strength of concrete, yield strength and elastic modulus of steel and, live load as random variables. Uncertainty in demand is modeled by choosing peak ground acceleration (PGA) as a random variable. Nonlinear static analysis (NSA) and nonlinear dynamic analysis (NDA) are carried out for typical low rise and high rise reinforced concrete framed buildings using IDARC 2D computer program with the random sample input parameters. Statistical properties are obtained for spectral displacements corresponding to performance point from NSA and maximum absolute roof displacement from NDA and suitable probability distribution functions viz., normal, Weibull, lognormal are examined for goodness-of-fit. From the hypothesis test for goodness-of-fit, lognormal function is found to be suitable to represent the statistical variation of spectral displacement obtained from NSA and NDA.

• International Journal of Naval Architecture and Ocean Engineering
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• 제11권1호
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• pp.211-224
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• 2019

This paper deals with a nonlinear controller based on saturation functions with variable parameters for set-point regulation and trajectory tracking control of an Autonomous Underwater Vehicle (AUV). In many cases, saturation functions with constant parameters are used to limit the input signals generated by a classical PD (Proportional-Derivative) controller to avoid damaging the actuators; however this abrupt bounded harms the performance of the controller. We, therefore, propose to replace the conventional saturation function, with constant parameters, by a saturation function with variable parameters to limit the signals of a PD controller, which is the base of the nonlinear PD with gravitational/buoyancy compensation and the nonlinear PD + controllers that we propose in this paper. Consequently, the mathematical model is obtained, considering the featuring operation of the underwater vehicle LIRMIA 2, to do the stability analysis of the closed-loop system with the proposed nonlinear controllers using the Lyapunov arguments. The experimental results show the performance of an AUV (LIRMIA 2) for the depth control problems in the case of set-point regulation and trajectory tracking control.

• Structural Engineering and Mechanics
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• 제30권6호
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• pp.763-785
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• 2008

In this study, a flexibility-based finite element method considering geometric and material nonlinearities is developed for analyzing steel-concrete frame structures. The stability functions obtained from the exact buckling solution of the beam-column subjected to end moments are used to accurately capture the second-order effects. The proposed method uses the force interpolation functions, including a moment magnification due to the axial force and lateral displacement. Thus, only one element per a physical member can account for the interaction between the bending moment and the axial force in a rational way. The proposed method applies the Newton method based on the load control and uses the secant stiffness method, which is computationally both efficient and stable. According to the evaluation result of this study, the proposed method consistently well predicts the nonlinear inelastic behavior of steel-concrete composite frames and gives good efficiency.

• 한국정밀공학회지
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• 제22권4호
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• pp.128-135
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• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• Transactions on Control, Automation and Systems Engineering
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• 제2권3호
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• pp.169-174
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• 2000

In this paper, Haar wavelet-based neural network is described for the identification and control of discrete-time nonlinear dynamical systems. Wavelets are suited to depict functions with local nonlinearities and fast variations because of their intrinsic properties of finite support and self-similarity. Due to the orthonormal properties of Haar wavelet functions, wavelet neural networks result in a greatly simplified training problem. This wavelet-based scheme performs adaptively both the identification of nonlinear functions and the control of the overall system, while the multilayer neural network is applied to the control system just after its sufficient learning of the unknown functions. Simulation shows that the wavelet network can be a good alternative to a multilayer neural network with backpropagation.