• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.385-395
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• 2006

We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.

• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.79-96
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• 2013

Exponential distribution plays a key role in engineering reliability and its applications. The exponential failure model has been studied for years. This article introduces two new preliminary test estimators for the reliability function (R(t)) in complete and censored samples from the exponential model with the use of a prior estimation (${\theta}_0$) of the mean (${\theta}$). The proposed preliminary test estimators are studied and compared numerically with the existing estimators. Computer-intensive calculations for bias and relative efficiency show that for, different values of levels of significance and for varying constants involved in the proposed estimators, the proposed estimators are far better than classical and existing estimators.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 2009

With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.5
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• pp.761-773
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• 2023

This paper proposes a method to increase the power-analysis resistance of the neural network model's feedforward process by replacing the exponential-based activation function, used in the deep-learning field, with an approximated function especially at the multi-layer perceptron model. Due to its nature, the feedforward process of neural networks calculates secret weight and bias, which already trained, so it has risk of exposure of internal information by side-channel attacks. However, various functions are used as the activation function in neural network, so it's difficult to apply conventional side-channel countermeasure techniques, such as masking, to activation function(especially, to exponential-based activation functions). Therefore, this paper shows that even if an exponential-based activation function is replaced with approximated function of simple form, there is no fatal performance degradation of the model, and than suggests a power-analysis resistant feedforward neural network with exponential-based activation function, by masking approximated function and whole network.

• Journal of the Semiconductor & Display Technology
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• v.19 no.1
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• pp.61-66
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• 2020

Threshold voltage shift occurring during operation is implemented in a SPICE simulation tool. Among the shift models the stretched-exponential function model, which is frequently observed from both single-crystal silicon and thin-film transistors regardless of the nature of causes, is selected, adapted to transient simulation, and added to BSIM4 developed by BSIM Research Group at the University of California, Berkeley. The adaptation method used in this research is to select degradation and recovery models based on the comparison between the gate and threshold voltages. The threshold voltage shift is extracted from SPICE transient simulation and shows the stretched-exponential time dependence for both degradation and recovery situations. The implementation method developed in this research is not limited to the stretched-exponential function model and BSIM model. The proposed method enables to perform transient simulation with threshold voltage shift in situ and will help to verify the reliability of a circuit.

• Korean Journal of Mathematics
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• v.9 no.1
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• pp.67-73
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• 2001

For some equation related with exponential function, we seek roots and find the properties of the roots. By using the relation of the roots and attractors, we find a region in the basin of attraction of the attractor at infinity for Newton's method for solving given equation.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.53-61
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• 2010

In this article, we discuss the reflective function which can be represented by three exponential matrixes and apply the results to studying the existence of periodic solutions of these systems. The obtained conclusions extend and improve the foregoing results.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.193-198
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• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.163-178
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• 2023

We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function p defined on the unit disc so that the function p is subordinate to the function e^z. These results are applied to find sufficient conditions for the normalised analytic functions f defined on the unit disc to satisfy the subordination zf'(z)/f(z) ≺ e^z.