• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.15-21
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• 2019

Let X be a reduced closed subscheme in ${\mathbb{P}}^n$ and $${\pi}_q:X{\rightarrow}Y={\pi}_q(X){\subset}{\mathbb{P}}^{n-1}$$ be an isomorphic projection from the center $q{\in}{\mathbb{P}}^n{\backslash}X$. Suppose that the minimal free presentation of $I_X$ is of the following form $$R(-3)^{{\beta}2,1}{\oplus}R(-4){\rightarrow}R(-2)^{{\beta}1,1}{\rightarrow}I_X{\rightarrow}0$$. In this paper, we prove that $H^1(I_X(k))=H^1(I_Y(k))$ for all $k{\geq}3$. This implies that Y is k-normal if and only if X is k-normal for $k{\geq}3$. Moreover, we also prove that reg(Y) ${\leq}$ max{reg(X), 4} and that $I_Y$ is generated by homogeneous polynomials of degree ${\leq}4$.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.181-188
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• 2021

Let X be a nondegenerate reduced closed subscheme in ℙⁿ. Assume that π_q : X → Y = π_q(X) ⊂ ℙ^n-1 is a generic projection from the center q ∈ Sec(X) \ X where Sec(X) = ℙⁿ. Let Z be the singular locus of the projection π_q(X) ⊂ ℙ^n-1. Suppose that I_X has the almost minimal presentation, which is of the form R(-3)^β_2,1 ⊕ R(-4) → R(-2)^β_1,1 → I_X → 0. In this paper, we prove the followings: (a) Z is either a linear space or a quadric hypersurface in a linear subspace; (b) $H^1({\mathcal{I}_X(k)})=H^1({\mathcal{I}_Y(k)})$ for all k ∈ ℤ; (c) reg(Y) ≤ max{reg(X), 4}; (d) Y is cut out by at most quartic hypersurfaces.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.895-903
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• 2023

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring R is 2-strongly Gorenstein hereditary if and only if every ideal of R is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.57-66
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• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

• Fire Science and Engineering
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• v.26 no.2
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• pp.75-83
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• 2012

An experimental study was conducted to investigate the effects of change in heat release rate on unsteady fire characteristics of under-ventilated fire in a semi-closed compartment. A standard doorway width of the full-scale ISO 9705 room was modified to 0.1 m and the flow rate of heptane fuel was increased linearly with time using a spray nozzle located at the center of enclosure. Temperature, heat flux, species concentrations and heat release rate were continuously measured and then global equivalence ratio (GER) concept was adopted to represent the unsteady thermal and chemical characteristics inside the compartment. It was observed that there was a significant difference in unsteady behavior between global and local combustion efficiency, and the GERs predicted by ideal and measured heat release rate were also shown different results in time. The unsteady behaviors of temperature, heat flux and species concentrations were represented well using the GER concept. It was important to note that CO concentration was gradually decreased with the increase in GER after reaching its maximum value in the range of 2.0~3.0 of global equivalence ratio. In addition, the experimental data on unsteady thermal and chemical behaviors obtained in a semi-closed compartment will be usefully used to validate a realistic fire simulation.

• Fire Science and Engineering
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• v.26 no.3
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• pp.21-28
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• 2012

The objective of this study is to evaluate the prediction accuracy of FDS(Fire Dynamic Simulator) for the thermal and chemical characteristics of under-ventilated fire with unsteady fire growth in a semi-closed compartment. To this end, a standard doorway width of the full-scale ISO 9705 room was modified to 0.1 m and the flow rate of heptane fuel was increased linearly with time (until maximum 2.0 MW based on ideal heat release rate) using a spray nozzle located at the center of enclosure. To verify the capability of FDS, the predicted results were compared with a previous experimental data under the identical fire conditions. It was observed that with an appropriate grid system, the numerically predicted temperature and heat flux inside the compartment showed reasonable agreement with the experimental data. On the other hand, there were considerable limitations to predict accurately the unsteady behaviors of CO and $CO_2$ concentration under the condition of continuous fire growth. These results leaded to a discrepancy between the present evaluation of FDS and the previous evaluation conducted for steady-state under-ventilated fires. It was important to note that the prediction of transient CO production characteristics using FDS was approached carefully for the under-ventilated fire in a semi-closed compartment.

• Journal of the Korean Society of Costume
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• v.57 no.1 s.110
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• pp.105-117
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• 2007

The purpose of this study is to help the understanding the characteristics in the costumes of men and women throughout the overall acceptance process of 'Naewaebub' in the late 'Chosun Dynasty' in which the notion of 'Naewae' is more prosperous than any other period in Korean history. Originally the distinction between man and woman was not intended to display the high and the low but to show the mutual respect according to each duty. As time goes on, that ideal became gradually changed to heighten the man and lower the women especially in 'Han' period of China. There was the ideal of distinction in the ancient times in Korea. Until 'Koryo Dinasty' the community has the system of blood-tied that put together maternal and paternal. 'Karye' was introduced in the late 'Koryo Dynasty' and accepted to the stereotype of morale in the 'Chosun Dynasty' and there seemed to be 'Samgang' and 'Oryun' at once. Many restrictions was imposed to behavior in women like rules of prohibition in attending the temple and concealment of woman's face and was recognized to rule of distinction between man and woman. Confucian life custom has been settled to Korean society throughout the late 16th century and 17th century and there were some appearances in the housing construction which divide the residences of man and woman. The characteristics in the costume from the avoidance of opposite sexes are clear in the structure of clothes changed from similar style to different style. The examples of those characteristics are as fellows. The costume in man was developed to advanced 'Pyoun-bokkwan' and 'Pyounbokpo' as social action of man prospered. Meanwhile the trousers which had been the same in the man and woman were separated to different trousers between man and woman. The costume life style of woman was changed to using the a hair whirl, hiding the face in the street and overlapping the innerwear under the skirt which was extension of woman's closed life style in late 'Chosun Dynasty'.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.787-811
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• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.

• Journal of radiological science and technology
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• v.44 no.6
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• pp.599-605
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• 2021

The International Electrotechnical Commission (IEC) 62494-1 has defined the exposure index (EI) that have a proportional relationship with the dose incident on the image receptor, and target exposure index (EI_T), deviation index (DI). In this study, an appropriate EI_T for skull radiography was established through the diagnostic reference level (DRL) and changes in DI were confirmed. Entrance surface dose (ESD) and EI were obtained using the computed radiography system displayed the EI as per IEC on console and skull phantom by experiment based on the national average exposure conditions announced in 2012 and 2019. And appropriate EI_T was established by applying the DRL in 2012 and 2019. As a results, the EI_T is changed according to the change in the DRL, and the exposure condition that becomes the ideal DI according to the change in the EI_T also has a difference of about 1.41 times. DRL is recommended to optimize the patient dose, however it is difficult to measure in real time at medical institutions whereas EI and DI are displayed on the console at the same time as exposure. When the EI_T is set based on the DRL and the DI is closed to an ideal value, it is useful as a patient dose management tool. Therefore, when the EI_T is periodically managed along with the revision of the DRLs, the patient dose can be optimized through the EI, EI_T and DI.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.1974-1987
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• 2023

The load-following operation of small modular reactors (SMRs) requires accurate prediction of transient behaviors that can occur in the balance of plants (BOP) and the nuclear steam supply system (NSSS). However, 1-D thermal-hydraulics analysis codes developed for safety and performance analysis have conventionally excluded the BOP from the simulation by assuming ideal boundary conditions for the main steam and feed water (MS/FW) systems, i.e., an open loop. In this study, we introduced a lumped model of BOP fluid system and coupled it with NSSS without any ideal boundary conditions, i.e., in a closed loop. Various methods for coupling boundary conditions at MS/FW were tested to validate their combination in terms of minimizing numerical instability, which mainly arises from the coupled boundaries. The method exhibiting the best performance was selected and applied to a transient simulation of an integrated NSSS and BOP system of a SMART. For a transient event with core power change of 100-20-100%, the simulation exhibited numerical stability throughout the system without any significant perturbation of thermal-hydraulic parameters. Thus, the introduced boundary-condition coupling method and BOP fluid system model can expectedly be employed for the transient simulation and performance analysis of SMRs requiring daily load-following operations.