• 대한수학회지
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• 제50권6호
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• pp.1183-1198
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• 2013

We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.

• 대한수학회보
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• 제59권2호
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• pp.419-429
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• 2022

An integral domain R is an RTP domain (or has the radical trace property) (resp. an LTP domain) if I(R : I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R : I)R_P = PR_P for each minimal prime P of I(R : I)). Clearly each RTP domain is an LTP domain, but whether the two are equivalent is open except in certain special cases. In this paper, we study the descent of these notions from particular overrings of R to R itself.

• 한국수학교육학회지시리즈A:수학교육
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• 제56권4호
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• pp.387-405
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• 2017

The purpose of this study is to investigate the change of students 'perception and expression about the motion of object following distance function $={x \atop 3}$ and distance function $y=\frac{x^3}{3}+3$ according to the necessity of research on students' perception and expression about integral constant. In this paper, we present the recognition and the expression of the difference of the constant in the relationship between the distance function and the speed function of the students, while examining the process of constructing the speed function and the inverse process of the distance function. This provides implications for the relationship between the derivative and the indefinite integral corresponding to the inverse process. In particular, in a teaching experiment, a constructive activity was performed to analyze the motion of two distance functions, where the student had a difference of the constant term. At this time, the students used the expression 'starting point' for the constants in the distance function, and the motion was interpreted by using the meaning. This can be seen as a unique 'students' mathematics' in the process of analyzing the motion of objects. These scenes, in introducing the notion of the relation between differential and indefinite integral, it is beyond the comprehension of the integral constant as a computational procedure, so that the learner can understand the meaning of the integral constant in relation to the motion of the object. It is expected that it will be a meaningful basic research on the relationship between differential and integral.

• Wind and Structures
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• 제14권1호
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• pp.35-53
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• 2011

Spherical object in wind is a common scenario in daily life and engineering practice. The main challenge in understanding the aerodynamics in turbulent wind lies in the multi-aspect of turbulence. This paper presents a wind tunnel study, which focuses on the role of turbulence integral length scale ${\Lambda}$ on the drag of a sphere. Particular turbulent flow conditions were achieved via the proper combination of wind speed, orifice perforated plate, sphere diameter (D) and distance downstream from the plate. The drag was measured in turbulent flow with $2.2{\times}10^4{\leq}Re{\leq}8{\times}10^4$, $0.043{\leq}{\Lambda}/D{\leq}3.24$, and turbulence intensity Tu up to 6.3%. Our results confirmed the general trends of decreasing drag coefficient and critical Reynolds number with increasing turbulence intensity. More interestingly, the unique role of the relative integral length scale has been revealed. Over the range of conditions studied, an integral length of approximately 65% the sphere diameter is most effective in reducing the drag.

• Nuclear Engineering and Technology
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• 제45권3호
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• pp.347-360
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• 2013

This paper presents an experimental investigation of the small-break loss-of-coolant accident (SBLOCA) and the loss-of-feedwater accident (LOFW) in a scaled integral test facility of REX-10. REX-10 is a small integral-type PWR in which the coolant flow is driven by natural circulation, and the RCS is pressurized by the steam-gas pressurizer. The postulated accidents of REX-10 include the system depressurization initiated by the break of a nitrogen injection line connected to the steam-gas pressurizer and the complete loss of normal feedwater flow by the malfunction of control systems. The integral effect tests on SBLOCA and LOFW are conducted at the REX-10 Test Facility (RTF), a full-height full-pressure facility with reduced power by 1/50. The SBLOCA experiment is initiated by opening a flow passage out of the pressurizer vessel, and the LOFW experiment begins with the termination of the feedwater supply into the helical-coil steam generator. The experimental results reveal that the RTF can assure sufficient cooldown capability with the simulated PRHRS flow during these DBAs. In particular, the RTF exhibits faster pressurization during the LOFW test when employing the steam-gas pressurizer than the steam pressurizer. This experimental study can provide unique data to validate the thermal-hydraulic analysis code for REX-10.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.153-159
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• 2005

In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.181-206
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• 2014

Let $R={\bigoplus}_{\alpha{\in}\Gamma}R_{\alpha}$ be a graded integral domain graded by an arbitrary grading torsionless monoid ${\Gamma}$, and ⋆ be a semistar operation on R. In this paper we define and study the graded integral domain analogue of ⋆-Nagata and Kronecker function rings of R with respect to ⋆. We say that R is a graded Pr$\ddot{u}$fer ⋆-multiplication domain if each nonzero finitely generated homogeneous ideal of R is ⋆$_f$-invertible. Using ⋆-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr$\ddot{u}$fer ⋆-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a $P{\upsilon}MD$.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2007년도 춘계학술대회 학술발표 논문집 제17권 제1호
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• pp.209-212
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• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}_1,\;{\mu}_2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• 대한수학회지
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• 제43권5호
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• pp.911-929
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• 2006

A refinement of $Gr\ddot{u}ss$ type inequality for the Bochner integral of vector-valued functions in real or complex Hilbert spaces is given. Related results are obtained. Application for finite Fourier transforms of vector-valued functions and some particular inequalities are provided.

• Structural Engineering and Mechanics
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• 제27권5호
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• pp.609-623
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• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.