• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Restorative Dentistry and Endodontics
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• v.38 no.3
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• pp.146-153
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• 2013

Objectives: Aluminum step wedge (ASW) equivalent radiodensity (eRD) has been used to quantify restorative material's radiodensity. The aim of this study was to evaluate the effects of image acquisition control (IAC) of a digital X-ray system on the radiodensity quantification under different exposure time settings. Materials and Methods: Three 1-mm thick restorative material samples with various opacities were prepared. Samples were radiographed alongside an ASW using one of three digital radiographic modes (linear mapping (L), nonlinear mapping (N), and nonlinear mapping and automatic exposure control activated (E)) under 3 exposure time settings (underexposure, normal-exposure, and overexposure). The ASW eRD of restorative materials, attenuation coefficients and contrasts of ASW, and the correlation coefficient of linear relationship between logarithms of gray-scale value and thicknesses of ASW were compared under 9 conditions. Results: The ASW eRD measurements of restorative materials by three digital radiographic modes were statistically different (p = 0.049) but clinically similar. The relationship between logarithms of background corrected grey scale value and thickness of ASW was highly linear but attenuation coefficients and contrasts varied significantly among 3 radiographic modes. Varying exposure times did not affect ASW eRD significantly. Conclusions: Even though different digital radiographic modes induced large variation on attenuation of coefficient and contrast of ASW, E mode improved diagnostic quality of the image significantly under the underexposure condition by improving contrasts, while maintaining ASW eRDs of restorative materials similar. Under the condition of this study, underexposure time may be acceptable clinically with digital X-ray system using automatic gain control that reduces radiation exposure for patient.

• Computational Structural Engineering
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• v.10 no.3
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• pp.241-250
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• 1997

The strain localization of concrete is a phenomenon such that the deformation of concrete is localized in finite region along with softening behavior. The objective of this paper is to develop a plasticity and damage algorithm for the finite element analysis of the strain-localization in concrete. In this paper, concrete member under strain localization is modeled with localized zone and non-localized zone. For modeling of the localized zone in concrete under strain localization, a general Drucker-Prager failure criterion by which the nonlinear strain softening behavior of concrete after peak-stress can be considered is introduced in a thermodynamic formulation of the classical plasticity model. The return-mapping algorithm is used for the integration of the elasto-plastic rate equation and the consistent tangent modulus is also derived. For the modeling of non-localized zone in concrete under strain localization, a consistent nonlinear elastic-damage algorithm is developed by modifying the free energy in thermodynamics. Using finite element program implemented with the developed algorithm, strain localization behaviors for concrete specimens under compression are simulated.

• Journal of KIISE:Software and Applications
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• v.31 no.3
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• pp.361-368
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• 2004

The purpose of this study is to propose a new on-line nonlinear PCA(OL-NPCA) method for a nonlinear feature extraction from the incremental data. Kernel PCA(KPCA) is widely used for nonlinear feature extraction, however, it has been pointed out that KPCA has the following problems. First, applying KPCA to N patterns requires storing and finding the eigenvectors of a N${\times}$N kernel matrix, which is infeasible for a large number of data N. Second problem is that in order to update the eigenvectors with an another data, the whole eigenspace should be recomputed. OL-NPCA overcomes these problems by incremental eigenspace update method with a feature mapping function. According to the experimental results, which comes from applying OL-NPCA to a toy and a large data problem, OL-NPCA shows following advantages. First, OL-NPCA is more efficient in memory requirement than KPCA. Second advantage is that OL-NPCA is comparable in performance to KPCA. Furthermore, performance of OL-NPCA can be easily improved by re-learning the data.

• Journal of KSNVE
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• v.9 no.1
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• pp.196-205
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• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• ETRI Journal
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• v.42 no.4
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• pp.619-632
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• 2020

Highly dispersive S-boxes are desirable in cryptosystems as nonlinear confusion sublayers for resisting modern attacks. For a near optimal cryptosystem resistant to modern cryptanalysis, a highly nonlinear and low differential probability (DP) value is required. We propose a method based on a piecewise linear chaotic map (PWLCM) with optimization conditions. Thus, the linear propagation of information in a cryptosystem appearing as a high DP during differential cryptanalysis of an S-box is minimized. While mapping from the chaotic trajectory to integer domain, a randomness test is performed that justifies the nonlinear behavior of the highly dispersive and nonlinear chaotic S-box. The proposed scheme is vetted using well-established cryptographic performance criteria. The proposed S-box meets the cryptographic performance criteria and further minimizes the differential propagation justified by the low DP value. The suitability of the proposed S-box is also tested using an image encryption algorithm. Results show that the proposed S-box as a confusion component entails a high level of security and improves resistance against all known attacks.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2209-2211
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• 2004

Unlike the wavelet neural network, since a mother wavelet layer of the self-recurrent wavelet neural network (SRWNN) is composed of self-feedback neurons, it has the ability to store past information of the wavelet. Therefore we propose the prediction method for the nonlinear chaotic time series model using a SRWNN. The SRWNN model is learned for the modeling of a function such that the inputs arc known values of the time series and the output is the value in the future. The parameters of the network are tuned to minimize the difference between the nonlinear mapping of the chaotic time series and the output of SRWNN using the gradient-descent method for the adaptive backpropagation algorithm. Through the computer simulations, we demonstrate the feasibility and the effectiveness of our method for the prediction of the logistic map and the Mackey-Glass delay-differential equation as a nonlinear chaotic time series.

• Steel and Composite Structures
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• v.34 no.2
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• pp.227-239
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• 2020

The aim of this study is to obtain the nonlinear and post-buckling responses of relatively thick functionally graded plates with oblique elliptical cutouts using a new semi-analytical approach. To model the oblique elliptical hole in a FGM plate, six plate-elements are used and the connection between these elements is provided by the well-known Penalty method. Therefore, the semi-analytical technique used in this paper is known as the plate assembly technique. In order to take into account for functionality of the material in a perforated plate, the volume fraction of the material constituents follows a simple power law distribution. Since the FGM perforated plates are relatively thick in this research, the structural model is assumed to be the first order shear deformation theory and Von-Karman's assumptions are used to incorporate geometric nonlinearity. The equilibrium equations for FGM plates containing elliptical holes are obtained by the principle of minimum of total potential energy. The obtained nonlinear equilibrium equations are solved numerically using the quadratic extrapolation technique. Various sets of boundary conditions for FGM plates and different cutout sizes and orientations are assumed here and their effects on nonlinear response of plates under compressive loads are examined.

• Journal of Power Electronics
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• v.19 no.3
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• pp.655-664
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• 2019

In order to analyze the nonlinear phenomena of the bifurcation and chaos caused by the switching of nonlinear switching devices in inductively coupled power transfer (ICPT) systems, a Jacobian matrix model, based on discrete mapping numerical modeling, is established to judge the system stability of the periodic closed orbit and to study the nonlinear behavior of Hopf bifurcation in a system under full resonance. The general flow of the parameter design, based on the stability principle for ICPT systems, is proposed to avoid the chaos and bifurcation phenomena caused by unreasonable parameter selection. Firstly, based on the state equation of SS-type compensation, a three-dimensional bifurcation diagram with the coupling coefficient as the bifurcation parameter is established with a numerical simulation to observe the nonlinear phenomena in the system. Then Filippov's method based on a Jacobian matrix model is adopted to deduce the boundary of stable operation and to judge the type of the bifurcation in the system. Then the general flow of the parameter design based on the stability principle for ICPT systems is proposed through the above analysis to realize stable operation under the conditions of weak coupling. Finally, an experimental platform is built to confirm the correctness of the numerical simulation and modeling.

• The Transactions of the Korean Institute of Power Electronics
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• v.4 no.4
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• pp.368-376
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• 1999

This paper studies the operational characteristics of thyristor controlled shunt compensator in a simple power t transmission system. With Fourier series representation of the thyristor switching action and the system parameters, t the thyristor current equations are derived, which transmit the required real power of the simple power transmission s system. Bisection algorithm is used to solve the thyristor current equations, which informs the thyristor firing an밍e, t the thyristor conduction an밍e, the power flows and the harmonic characteristics. The stability analysis is performed w with the theory of Poincare mapping for the nonlinear discrete periodic dynamic system. EMTP simulations at the v various operating points show the transient characteristics of the thyristor controlled shunt compensator and C correspond to the results calculated with Fourier series representation and the stability analysis.