• 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.

• 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.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.161-164
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• 2002

This study was performed to find out the regression function to calculate the modulus of elasticity of concrete mixed by river coarse aggregate. The distribution of the group of core strength made a normal curve and the effect factor in the modulus of elasticity was 0.97 at the concrete compounded by river coarse aggregate.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.173-178
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• 2000

New prediction model is investigated estimating splitting tensile strength and modulus of elasticity with curing temperature and aging. New prediction model is based on the model which was proposed to predict compressive strength, and splitting tensile strength and modulus of elasticity calculated by this model are compared with experimental values. New prediction model well estimated splittinge tensile strength and elastic modulus as well as compressive strength.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.100-114
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• 2021

In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.235-244
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• 2024

In this paper, we establish relations between the sets of strongly Cesàro summable sequences of complex numbers for modulus functions f and g satisfying various conditions. Furthermore, for some special modulus functions, we obtain relations between the sets of strongly Cesàro summable and statistically convergent sequences of complex numbers.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.91-97
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• 2001

Case records comprising the results of down-hole seismic surveys collected at nine sites worldwide, together with comparative results of laboratory bender element tests on reconstituted clay samples, were examined in an attempt to quantify the shear modulus of normally consolidated clays at very small strain of the order of 0.001%. The shear modulus G$_{max}$ under the current state of stresses is given in a formula which includes a newly proposed void ratio function. An empirical expression incorporating the new void ratio function is also proposed for practical use in estimating G$_{max}$ profiles with depth in natural soil deposits from routinely available borehole data.ata.

• International Journal of Highway Engineering
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• v.16 no.3
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• pp.43-50
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• 2014

PURPOSES : The dynamic modulus can be determined by applying the various theories from the Impact Resonance Testing(IRT) Method. The objective of this paper is to determine the best theory to produce the dynamic modulus that has the lowest error as the dynamic modulus data obtained from these theories(Complex Wave equation Resonance Method related to either the transmissibility loss or not, Dynamic Stiffness Resonance Method) compared to the results for dynamic modulus determined by using the Universal Testing Machine. The ultimate object is to develop the predictive model for the dynamic modulus of a Linear Visco-Elastic specimen by using the Complex Wave equation Resonance Method(CWRM) came up for an existing study(S. O. Oyadiji; 1985) and the Optimization. METHODS : At the destructive test which uses the Universal Testing Machine, the dynamic modulus results along with the frequency can be used for determining the sigmoidal master curve function related to the reduced frequency by applying Time-Temperature Superposition Principle. RESULTS : The constant to be solved from Eq. (11) is a value of 14.13. The reduced dynamic modulus obtained from the IRT considering the loss factor related to the impact transmissibility has RMSE of 367.7MPa, MPE of 3.7%. When the predictive dynamic modulus model was applied to determine the master curve, the predictive model has RMSE of 583.5MPa, MPE of 3.5% compared to the destructive test results for the dynamic modulus. CONCLUSIONS : Because we considered that the results obtained from the destructive test had the most highest source credibility in this study, the dynamic modulus data obtained respectively from DSRM, CWRM were compared to the results obtained from the destructive test by using th IRT. At the result, the reduced dynamic modulus derived from DSRM has the most lowest error.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.865-874
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• 1998

A modulus of continuity on the increments of a two-parameter Gaussian process is obtained via estimating large deviation probability inequalities on the suprema of the Gaussian process.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.8
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• pp.88-95
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• 2008

Young's modulus of electroplated nickel thin film is systematically investigated using the resonance method of atomic force microscope. Thin layers of nickel to be measured are electroplated onto the surface of an AFM silicon cantilever and Young's modulus of plated nickel film is investigated as a function of process conditions such as the plating temperature and applied current density. It is found that Young's modulus of plated nickel thin film is as high as that of bulk nickel at low plating temperature or low current density, but decreases with increasing plating temperature or current density. The results imply that the plating rate increases as increasing the plating temperature or current density, therefore, slow plating rate produces a dense plating material due to the sufficient time fur nickel ions to form a dense coating.