• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.939-962
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• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.

• Nuclear Engineering and Technology
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• v.10 no.2
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• pp.73-78
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• 1978

The effect of temperature and strain rate on the deformation behavior of $\alpha$-uranium was investigated in the temperature ranged 300$^{\circ}$ to 55$0^{\circ}C$ by strain, rate change test. Strain rate sensitivity, activation volume, strain rate sensitivity exponent and dislocation velocity exponent were determined. The strain rate sensitivity exponent and dislocation velocity exponent were determined. The strain rate sensitivity exponent increases with strain below 40$0^{\circ}C$, while the exponent decreases with strain above 50$0^{\circ}C$. It is believed that the increase of strain rate sensitivity exponent with strain below 40$0^{\circ}C$ can be attributed to an increase in internal stress as a result of work hardening while decrease of the exponent with strain above 50$0^{\circ}C$ is due to predominance of thermal softening over work hardening because more slip, system are active in deformation above about 50$0^{\circ}C$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

• Industrial Engineering and Management Systems
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• v.10 no.3
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• pp.185-190
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• 2011

A driver interacts directly with the car seat at all times. There are ergonomic characteristics that have to be followed to produce comfortable seats. However, most of previous researches focused on either static or dynamic condition only. In addition, research on car seat development is critically lacking although Malaysia herself manufactures its own car. Hence, this paper integrates objective measurements and subjective evaluation to predict seat discomfort. The objective measurements consider both static and dynamic conditions. Steven's psychophysics power law has been used in which after expansion; ${\psi}\;=\;a+b{\varphi}_s^{\alpha}+c{\varphi}_v^{\beta}$ where ${\psi}$ is discomfort sensation, ${\varphi}_s^{\alpha}$ is static modality with exponent ${\alpha}$ and ${\varphi}_v^{\beta}$ is dynamic modality with exponent ${\beta}$. The subjects in this study were local and the cars used were Malaysian made compact car. Static objective measurement was the seat pressure distribution measurement. The experiment was carried out on the driver's seat in a real car with the engine turned off. Meanwhile, the dynamic objective measurement was carried out in a moving car on real roads. During pressure distribution and vibration transmissibility experiments, subjects were requested to evaluate their discomfort levels using vehicle seat discomfort survey questionnaire together with body map diagram. From subjective evaluations, seat pressure and vibration dose values exponent for static modality ${\alpha}$ = 1.51 and exponent for dynamic modality ${\beta}$ = 1.24 were produced. The curves produced from the $E_{q.s}$ showed better $R_{-sq}$ values (99%) when both static and dynamic modalities were considered together as compared to Eq. with single modality only (static or dynamic only R-Sq = 95%). In conclusion, car seat discomfort prediction gives better result when seat development considered both static and dynamic modalities; and using ergonomic approach.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.259-275
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• 2019

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

• Science of Emotion and Sensibility
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• v.18 no.3
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• pp.63-70
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• 2015

This study identified heart response of participants while listening to sounds which have 1/f fluctuations with exponent ${\alpha}$ gradient. The participants were engaged in emotional stress work. Prior studies related to 1/f fluctuation sound have reported that sound source can alleviate psychological and physiological state of users. Subjects of this study were exposed to sound with three levels of ${\alpha}$ gradient. Heart response of subjects were measured with Photoplethysmography(PPG) sensor simultaneously. The dependent variables of this study were beat per minute(BPM), very low frequency percent of pulse rate variability (VLF percent), the standard deviation of all normal RR intervals (SDNN), and high frequency power(HF power). Subject showed arousal response when exposed to sound with exponent ${\alpha}$ gradient of 3 whereas the sound with exponent ${\alpha}$ gradient of 1 and 2 resulted in relax effect. The characteristic of 1/f fluctuation sounds can be applied to alleviate stress for employers under emotional labor.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.1
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• pp.269-286
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• 2018

Signal detection in symmetric alpha-stable ($S{\alpha}S$) distributed noise is a challenging problem. This paper proposes a detector based on a decreasing exponential function (DEF). The DEF detector can effectively suppress the impulsive noise and achieve good performance in the presence of $S{\alpha}S$ noise. The analytical expressions of the detection and false alarm probabilities of the DEF detector are derived, and the parameter optimization for the detector is discussed. A performance analysis shows that the DEF detector has much lower computational complexity than the Gaussian kernelized energy detector (GKED), and it performs better than the latter in $S{\alpha}S$ noise with small characteristic exponent values. In addition, the DEF detector outperforms the fractional lower order moment (FLOM)-based detector in $S{\alpha}S$ noise for most characteristic exponent values with the same order of magnitude of computational complexity.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.921-936
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• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• Convergence Security Journal
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• v.18 no.1
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• pp.13-18
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• 2018

Efficiency is one of the most important factors in cryptographic systems. Cheon et al. proposed a new exponent form for speeding up the exponentiation operation in discrete logarithm based cryptosystems. It is called split exponent with the form $e_1+{\alpha}e_2$ for a fixed element ${\alpha}$ and two elements $e_1$, $e_2$ with low Hamming weight representations. They chose $e_1$, $e_2$ in two unbalanced subsets $S_1$, $S_2$ of $Z_p$, respectively. We achieve efficiency improvement making $S_1$, $S_2$ balanced subsets of $Z_p$. As a result, speedup for exponentiations on binary fields is 9.1% and speedup for scalar multiplications on Koblitz Curves is 12.1%.

• Journal of the Korean Solar Energy Society
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• v.32 no.2
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• pp.87-94
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• 2012

In this study, we found a relationship between wind shear exponent, ${\alpha}$, and a few factors such as the wind speed, $V$, ruggedness index($RIX$), and the Weibull shape parameter, $k$ of sites in complex terrain in Korea. Wind shear exponents in main wind directions were calculated using wind speed data measured for one year from various heights of eleven meteorological masts in Gangwon province. It was found from the analysis that the reciprocal of the wind shear exponent can be expressed by an exponentially decaying function with respect to a multiple of $V$, $RIX$ and $k$. This result is considered useful to be used to characterize wind characteristics of specific sites in complex terrain in Korea with limited information.