• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1810-1815
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• 2003

Sliding mode control with nonlinear interpolation in the boundary layer is proposed. A modified sigmoid function is used for nonlinear interpolation in the boundary layer and its parameter is tuned by a fuzzy logic controller. The fuzzy logic controller that takes the distance between the system state and the sliding surface as its input guides the choice of parameter of the modified sigmoid function and the parameter is on-line tuned. Owing to the decreased thickness, the proposed method has better tracking performance than the conventional linear interpolation method. To demonstrate its performance, the proposed control algorithm is applied to a simple nonlinear system model.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.523-529
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• 2004

Sliding mode control with nonlinear interpolation in the boundary layer is proposed. A modified sigmoid function is used for nonlinear interpolation in the boundary layer and its parameter is tuned by a fuzzy controller. The fuzzy controller that takes both the sliding variable and a measure of chattering as its inputs tunes the parameter of the modified sigmoid function. Owing to the decreased thickness of the boundary layer and the tuned parameter, the proposed method has superior tracking performance than the conventional linear interpolation method.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.69-93
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• 2023

Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

• Imaging Science in Dentistry
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• v.31 no.3
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• pp.145-151
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• 2001

Purpose : To investigate the hypothesis that the morphology of the articular eminence of the temporomandibular joint is a predisposing factor for disc displacement. Materials and Methods: MR images of 126 temporomandibular joints in 94 patients were analyzed to assess for morphology of the articular eminence and disc displacement. The displaced disc was further categorized as disc displacement with reduction (DDWR) and disc displacement without reduction (DDWOR). The morphology of the articular eminence was classified into four types; box, sigmoid, flattened, and deformed. The relationship between the four types of shape of the articular eminence and the two types of disc position was assessed. Results: In the DDWR and DDWOR groups, the morphology of articular eminence were a box type in 40.5%, a sigmoid type in 30.2%, a flattened type in 24.6%, and a deformed type in 4.7%. The box type of the articular eminence were 34.3% in the DDWR group and 42.9% in the DDWOR group. The sigmoid type of the articular eminence were 34.3% in the DDWR group and 28.6% in the DDWOR group. The flattened type of the articular eminence were 28.6% in the DDWR group and 23.1 % in the DDWOR group. The deformed type of articular eminence were 2.9% in the DDWR group and 5.5% in the DDWOR group. Conclusion: Disc displacement is more likely to be found in the temporomandibular joints with a box-shaped articular eminence. It can be considered that shape of the articular eminence is related to the development of disc displacement.

• Textile Coloration and Finishing
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• v.24 no.4
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• pp.239-246
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• 2012

The binding isotherms of ionic dyes with Poly(vinylpyrrolidone) in aqueous solution were determined by the dynamic dialysis technique. The shape of the isotherms of cationic dye, C. I. Basic Red 18 with poly(vinlypyrrolidone) showed a partition type. It suggests that the binding involves a non-cooperative mode. Isotherms of an anion dye, a synthesized dye by coupling of diazotized m-trifluoromethylaniline with 2-naphthol-6-sulfonic acid, were sigmoid type and showed multimode interaction. The results were interpreted by the McGhee von Hippel theory. The thermodynamic parameters for the complex formation of the dyes-polymer were calculated from their temperature dependences of the intrinsic binding constant.

• Structural Engineering and Mechanics
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• v.74 no.1
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• pp.83-90
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• 2020

Several classical and higher order plate theories were used to study the buckling of functionally graded material (FGM) plates. In the great majority of research, a power function is used to represent metal and ceramic material transverse distribution (P-FGM). Therefore, the effect of having other transverse variation of material properties on the buckling behavior of thick rectangular FGM plates was not properly addressed. In the present work, this effect is investigated using the Third order Shear Deformable Theory (TSDT) for the case of simply supported FGM plate. Both a sigmoid function and an exponential functions are used to represent the transverse gradual property variation. The plate governing equations are combined with a Navier type expanded solution of the unknown displacements to derive the buckling equation in terms of the pre-buckling in-plane loads. Finally, the critical in-plane load is calculated for the different buckling modes. The model is verified by a comparison of the calculated buckling loads with available published results of Al-SiC P-FGM plates. The conducted parametric study shows that manufacturing FGM plates with sigmoid variation of properties in the thickness direction increases the buckling load considerably. This improvement is found to be more significant for the case of thick plates than that of thin plates. Results also show that this stiffening-like effect of the sigmoid function profile is more evident for cases where the in-plane loads are applied along the shorter edge of the plate.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.2
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• pp.56-64
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• 1998

Multi-layered perceptrons that are a nonlinear neural network model, have been widely used for various applications mainly thanks to good function approximation capability for nonlinear fuctions. However, for digital hardware implementation of the multi-layere perceptrons, the quantization scheme using "look-up tables (LUTs)" is commonly employed to handle nonlinear signmoid activation functions in the neworks, and thus requires large amount of storage to prevent unacceptable quantization errors. This paper is concerned with a new effective methodology for digital hardware implementation of multi-layered perceptrons, and proposes a "piecewise affine approximation" method in which input domain is divided into (small number of) sub-intervals and nonlinear sigmoid function is linearly approximated within each sub-interval. Using the proposed method, we develop an expression and an error backpropagation type learning algorithm for a multi-layered perceptron, and compare the performance with the quantization method through Monte Carlo simulations on XOR problems. Simulation results show that, in terms of learning convergece, the proposed method with a small number of sub-intervals significantly outperforms the quantization method with a very large storage requirement. We expect from these results that the proposed method can be utilized in digital system implementation to significantly reduce the storage requirement, quantization error, and learning time of the quantization method.quantization method.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.26 no.2
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• pp.7-17
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• 1996

This study was performed to determine the postitional relationships of two lobes of parenchyma and to analysis the anatomical feature and its variations of duct on the panoramic views of the normal parotid glands in adults. Materials included 66 panoramic views and anterioposterior views of sialograms of selected persons and the radiograms of the gland experimentally reproduced on dry skull with lead foil and the reference images of computed tomograms of normal persons. Results were as follows : 1. On panoramic view of sialogram, the superficial lobe was revealed with totally being superimposed with the mandibular ramus and condyle and its tail portion superimposed with mandibular angle area, the deep lobe was revealed between the posterior border of the ramus and the mastoid process, and the isthmus was begin from the marked furcation off main duct and superimposed partially with the medial part of the deep lobe. 2, The mean length and the lateral extension of parenchyma was 63.18±8.05mm and 21.78±4.87mm respectively on panoramic view and showed no statistical relationship between them. 3. The main duct was generally perpendicular to the posterior border of ramus at middle portion and its configurations revealed 57,58％ of curvilinear type, 21.21％ sigmoid type, 15.15％ reverse sigmoid type. 4, The interlobular ducts of the deep lobe showed relatively well defined features between the mandibular ramus and the mastoid process.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.197-210
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• 2014

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.