• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.191-202
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• 2022

In this paper, we obtain the quantitative weighted bounds of oscillatory singular integral with rough kernel. Moreover, the quantitative weighted bounds of maximally truncated oscillatory singular integral with rough kernel are also obtained.

• Magazine of the Korean Society of Agricultural Engineers
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• v.26 no.2
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• pp.59-68
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• 1984

The Purpose of this study was to investigate the effect of the change in misture content on some physical properties of grains, and some relations amont the properties. Materials included ere rough rice, brown rice, barley and wheat with the range of moisture content of 6~26 percent, 7~25 percent, 10~24 percent and 6~22 percent, respectively. Kernel dimension, sphericity, kernel weight, and volume were included as the physical properties of the grains. The results obtained are summarized as follows; 1. The ratio of grain length to the thickness was in the range of 3.59~4.16 for rough rice(Indica type), 2.98~3.27 for rough rice(Japonica type), 3.25 for brown rice (I.T.), 2.14~2.38 for brown rice(J.T.), 2.92~3.13 for barley and 2.10~2.21 for wheat, respectively. 2. The sphericity was found to be 42 percent for rough rice(I.T.), 48 percent for rough rice(J.T.), 52 percent for brown rice(I.T.), 62 percent for brown rice(J.T.), 45 percent for barley and 61 percent for wheat, respectively. 3. The kernel weight of grains was linealy increased with the increase of moisture content. At a specified moisture centent of 14 percent, the kernel weight was shown to be in the range of 4.72${\times}10^{-5}$~3.58${\times}10^{-5}$kg for wheat, 3.60${\times}10^{-5}$~3.12${\times}10^{-5}$kg for barley, 2.80${\times}10^{-5}$~2.35${\times}10^{-5}$kg for rough rice, and 2.24${\times}10^{-5}$~1.82${\times}10^{-5}$kg for brown rice, respectively. 4. The kernel volume was linearly increased with increase of moisture content. The rate of increase was significantly low for rough rice in comparison with the remaining grains. The kernel volume, at a specified moisture content of 14 percent, was in the range of 3.51${\times}10^{-8}$~2.76${\times}10^{-8}m^3$ for wheat, 2.84${\times}10^{-8}$~2.43${\times}10^{-8}m^3$ for barley, 2.93${\times}10^{-8}$~1.97${\times}10^{-8}m^3$ for rough rice, and 1.61${\times}10^{-8}$~1.29${\times}10^{-8}m^3$ for brown rice, respectively. 5. The kernel volume of grains was found to be related to the length, width, thickness and kernel weight as a exponential function. The kernel volume was shown to have correlation coefficient to the length factor rough rice and barley which were of low sphericity, while the width factor was predominant for brown rice and wheat which was of high sphericity.

• Journal of Biosystems Engineering
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• v.15 no.3
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• pp.219-229
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• 1990

The compression creep behavior of grains when loaded depends not only on load but also on duration of load application. The most common methods of studying the load-time characteristics of agricultural products is by employing rheological models such as Burger's model. However it is sometimes not sufficient to describe the viscoelastic behavior of grains to be Burger's model. For this reason, this study was conducted to develop the rheological model which represented the creep compliance response of the rough rice kernel and was a function of initial stress applied and time. The effects of the initial stress applied and the moisture content on the compression creep behavior of the rough rice kernel were analyzed. The results were obtained from the study as follows: 1. Since the viscoelastic behavior of the rough rice kernel was nonlinear, the transient and steady state creep compliance was satisfactorily modelled as follows: $$J({\sigma},t)=A{\sigma}^B[C+Dt-exp(-Ft)]$$ But, for the every stress applied, the compression creep behavior of the samples tested can be well described by Burger's model respectively. 2. The creep compliance, the instantaneous elastic strain, the retarded elastic strain and the viscous strain of the sample tested generally increased in magnitude with increasing the applied initial stress and the moisture content used in the tests. At low moisture content, the creep compliance for the Japonica-type rough rice kernel Was a little higher than those for Indica-type and at high moisture content, vice versa at high moisture content. 3. The retardation times of the samples had not an uniform tendency by the initial stress and the moisture content. The retardation times ranged from 0.66 to 6.76 seconds, and the creep progressed from transient to steady state at a relatively high rate. 4. The less viscous strain than the instantaneous elastic strain for the samples tested indicated that rough rice kernel behaved as a viscoelastic body characterized by elasticity than viscosity.

• Journal of Biosystems Engineering
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• v.15 no.2
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• pp.99-109
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• 1990

Rough rice is subjected to a series of static and dynamic forces during mechanical harvesting, handling and processing operations. The mechanical properties such as bioyield point, compressive strength, and deformations at the bioyield point and rupture point are important engineering data needed to develop processing machines and to determine reasonable operating conditions for these machines. The objectives of this study were to determine the mechanical properties of the rough rice kernel at loading rate of 0.664 mm/min and 1.673 mm/min and at various moisture contents, and to examine the effect of the moisture content and the loading rate on these mechanical properties. The follwing results were obtained from the study. 1. Bioyield point, rupture point, bioyield strength and ultimate strength of the rough rice kernel generally decreased in magnitude with an increase in moisture content. A little larger values of these mechanical properties were obtained at the higher loading rate. The rough rice variety and the loading rate affected significantly these mechanical properties at low moisture content, but not at the higher moisture levels. 2. Bioyield point of the sample grains varied from 20 to 80 N, and rupture point varied from 45 to 130N. Bioyield point for Japonica-type rough rice was a little higher than that for Indica-type rough rice, but there were little differnces in rupture point between two types of rough rice. 3. Bioyield strength and ultimate strength of the Japonica-type rough rice varied from 10 MPa. to 39 MPa., and from 13 MPa. to 45 MPa. respectively. Those of the Indica-type rough rice varied from 12 MPa. to 42 MPa., and from 15 MPa. to 53 MPa. respectively. 4. Deformations at bioyield point and rupture point ranged from 0.18 mm/min to 0.26 mm, and from 0.28 mm to 0.53 mm respectively. These deformations decreased with an increase in moisture content up to moisture content of approximately 17% (w.b.) and increased again thereafter. 5. Regression equations were developed to predict these mechanical properties for the rough rice kernel as a function of moisture content.

• Journal of Biosystems Engineering
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• v.15 no.3
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• pp.207-218
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• 1990

Grains display characteristics of both elastic bodies and viscous fluids when they are subjected to mechanical treatments in harvesting, handling, and processing. This viscoelastic behavior of grains when mechanically stressed must be fully understood to establish maximum machine efficiency and have a minimum degree of grain damage and the highest quality of the final product. The studies were conducted to examine the effect of the moisture content, the loading rate and the initial deformation on the stress relaxation behavior of whole kernel of rough rice, and develop the rheological model to represent its stress relaxation behavior. The following results were obtained from the study. 1. Moisture content had the greatest influence on the initial portion of the relaxation curve. With elapsing time the lower moisture content resulted in the lower residual stress for the Japonica-type rough rice and vice versa for the Indica-type rough rice. But within the ranges of moisture content tested, the degree of stress relaxation per unit strain on the Indica-type rough rice was a little higher than those on the Japonica-type rough rice. 2. The slower loading rate resulted in less initial stress. The decreasing trend of residual stress for all the samples tested with increasing loading rate was shown. 3. The higher initial deformation for all the samples resulted in less initial stress. The increasing of amount of stress relaxation per unit strain with increase of initial stress indicated that viscoelastic properties of rough rice depended not only upon duration of load applied but also initial stress applied. This means that rough rice is nonlinear viscoelastic material. 4. The compression stress relaxation properties of rough rice kernel can be described by a generalized Maxwell model representing by the Maxwell elements.

• Journal of Biosystems Engineering
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• v.25 no.1
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• pp.33-38
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• 2000

This study was performed to investigate airtight storage characteristics of rough rice using airtight flexible pve container. A storage test of rough rice of 4 tonnes was carried out to determine the changes of gas composition of air in the container, grain moisture content, air temperature and relative humidity , the presence of insects ,germination rate, crack ratio , fat acidity , 1000-kernel weight, and brown rice recovery over storage period of 5 months in Suwon. Concentration of oxygen was decreased from 20% to 16% and carbon dioxide was increased of from 0.03% to 1.6%. The grain moisture content was decreased from 14.4%(w.b) to 14.1%(w.b) for 5 months storage period . Insect population levels were low but these increased after 5 months storage. Most of insects were dead, Fat acidity increased from 7.5(mg KOH/100g) to 10.2(mg KOH/100g). Other storage factors such as germination rate, brown rice recovery and 1000-kernel , and 1000-kernel weight slightly decreased and crack ratio was slightly increased. Qualities of rough rice during 5 months storage period under hemetic air conditions were maintained fairly good considering the above changes of quality factors during storage.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.703-725
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• 2011

In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.733-745
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• 2007

We prove the $L^p(1 boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega{\in}L(log^+L)^{1/2}(S^{n-1})$. The result is an improvement and extension of some known results.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.69-90
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• 2021

In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ △γ(ℝ+) and Ω ∈ ����β(Sn-1) for some γ > 1 and β > 1. Here Ω ∈ ����β(Sn-1) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.

• Journal of Biosystems Engineering
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• v.16 no.3
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• pp.263-271
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• 1991

When grains is subjected to oscillating load, the dynamic viscoelastic behavior of the material will be describe the complex modulus of the material. The complex modulus and therefore the storage modulus, the loss modulus, and the phase angle for the sample should be obtainable with a given static viscoelastic property of the material under static load. The complex relaxation moduli of the rough rice kernel were computed from the Burger's model describing creep behavior of the material which were obtained in the previous study. Also, the effects of cyclic load and moisture content of grain on the dynamic viscoelastic behavior of the samples were analized. The storage modulus of the rough rice kernel slightly increased with the frequency applied but at above the frequency of 0.1 Hz it was nearly constant with the frequency, and the loss modulus of the sample very rapidly decreased with increase in the frequency on those frequency ranges. It was shown that the storage modulus and the loss modulus of the sample increased with decrease in grain moisture content. Effect of grain moisture content on the storage modulus of the sample was highly significant than effect of the frequency applied, but effect of the frequency on the loss modulus of the sample was more significant than effect of grain moisture content.