• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.487-494
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• 2021

In this paper, we study rings with Noetherian spectrum, rings with locally Noetherian spectrum and rings with t-locally Noetherian spectrum in terms of the polynomial ring, the Serre's conjecture ring, the Nagata ring and the t-Nagata ring. In fact, we show that a commutative ring R with identity has Noetherian spectrum if and only if the Serre's conjecture ring R[X]_U has Noetherian spectrum, if and only if the Nagata ring R[X]_N has Noetherian spectrum. We also prove that an integral domain D has locally Noetherian spectrum if and only if the Nagata ring D[X]_N has locally Noetherian spectrum. Finally, we show that an integral domain D has t-locally Noetherian spectrum if and only if the polynomial ring D[X] has t-locally Noetherian spectrum, if and only if the t-Nagata ring $D[X]_{N_v}$ has (t-)locally Noetherian spectrum.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.60-63
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• 1990

This note presents a direct adaptive pole assignment control for general discrete, linear, time-invariant, nonmimum phase system.Controller parameters are estimated from the recursive least-squares algorithm, and some additional auxiliary parameters are obtained from aset of recursive equations based on a certain polynomial identity which is derived from the pole assignment equation and the Bezout identity. This scheme increase the numerical stability of the auxiliary parameters, and guarantees local convergence without any extra conditions for the external input. The effectiveness of the proposed scheme is demonstrated by the computer simulation.

• Acta Via Serica
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• v.6 no.1
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• pp.141-164
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• 2021

The Khitans were a Turco-Mongol clan who dominated China north of the Yangtze River during the early mediaeval period. They adopted and then adapted many of the cultural traditions of their powerful neighbours to the south, the Song Chinese. However, before their absorption into the Mongol Empire in the late 13^th century they proved pivotal, firstly in the eastward expansion of the armies of Chinggis Khan, secondly, in the survival of the Persian heartlands after the Mongol invasions of the 1220s and thirdly, in the revival and integration of the polity of Iran into the Chinggisid Empire. Da Liao, the Khitans, the Qara Khitai, names which have served this clan well, strengthened and invigorated the hosts which harboured them. The Liao willingly assimilated into the Chinggisid Empire of whose formation they had been an integral agent and in doing so they also surrendered their identity but not their history. Recent scholarship is now unearthing and recognising their proud legacy and distinct identity. Michal Biran placed the Khitans irrevocably and centrally in mediaeval Asian history and this study emphasises their role in the establishment of the Mongol Empire.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.11-21
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• 1998

A vorticity-based method for the numerical solution of the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations for vorticity, velocity and pressure variables are expressed in an integro-differential form. The global coupling between the vorticity and the pressure boundary conditions is fully considered in an iterative procedure when numerical schemes are employed. The finite volume method of the second order TVD scheme is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition. The velocity field is obtained by using the Biot-Savart integral. The Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well established for potential flow analysis. The present formulation is validated by comparison with data from the literature for the two-dimensional cavity flow driven by shear in a square cavity. We take two types of the cavity now: (ⅰ) driven by non-uniform shear on top lid and body forces for which the exact solution exists, and (ⅱ) driven only by uniform shear (of the classical type).

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.655-660
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• 1999

Let R be an integral domain with identity. In this paper we will show that if R is integrally closed or if t-dim $R{\leq}1$, then R[{$X_{\alpha}$}] satisfies the principal ideal theorem for each family {$X_{\alpha}$} of algebraically independent indeterminates if and only if R is an S-domain and it satisfies the principal ideal theorem.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.71-77
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• 2024

Let A be a commutative integral domain with identity element and S a multiplicatively closed subset of A. In this paper, we introduce the concept of S-valuation domains as follows. The ring A is said to be an S-valuation domain if for every two ideals I and J of A, there exists s ∈ S such that either sI ⊆ J or sJ ⊆ I. We investigate some basic properties of S-valuation domains. Many examples and counterexamples are provided.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.349-364
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• 2024

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of Hölder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.

• Journal of the Korean Institute of Landscape Architecture
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• v.13 no.1
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• pp.109-121
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• 1985

A study on the image identification of urban streetscape is valuable for illuminating identity that is not yet fully approached in the field of environmental design. This analysis of urban streetscape for image identification allows us to make a more detailed exploration of an important approaching methods in dealing with the structural characteristics of identity. As a matter of fact, the earlier indirect studies on this image identification were made by environmental designers, such as architectural and urban designer in the field of environmental perception and came to its environmental cognition & environmental pattern research with assistances by such researchers as K. Lynch A. Rapoport & Christopher Alexander. Through its environmental perception research, we can see its structural characteristics that is aesthetic & visual structural contents of physical environmental elements. And we can see its cognitive characteristics through the environmental cognitive research, that is continuity, territoriality, identity of place, uniqueness or individuality, meaning & symbolism. Through its environmental pattern research, we can see its physical, socio - economic, cultural and symbolic pattern identification contents, that is physical form of the city, style of the street, pattern of streetscape, socio- economic & geographical locality, arid life cycle, life style, common style of the behavior, cultural pattern of the activity, socio - cultural expression of the symbol. In these process, we can set up a set of the environmental design criterias from those three integral studies for identity. And for an environmental research, Tongsung-Ro around the CBD (central business district) in Taegu City was selected for a case study, because this streetscape is suitable for that approaching methods in this study.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.65-72
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• 1992

All rings are commutative, Noetherian with identity and of prime characteristic p, unless otherwise specified. First, we describe the definition of tight closure of an ideal and the properties about the tight closure used frequently. The technique used here for the tight closure was introduced by M. Hochster and C. Huneke [4,5, or 6]. Using the concepts of the tight closure and its properties, we will prove that if R is a complete local domain and F-rational, then R is Cohen-Macaulay. Next, we study the properties of R$^{+}$, the integral closure of a domain in an algebraic closure of its field of fractions. In fact, if R is a complete local domain of characteristic p>0, then R$^{+}$ is Cohen-Macaulay [8]. But we do not know this fact is true or not if the characteristic of R is zero. For the special case we can show that if R is a non-Cohen-Macaulay normal domain containing the rationals Q, then R$^{+}$ is not Cohen-Macaulay. Finally we will prove that if R is an excellent local domain of characteristic p and F-ratiional, then R is Cohen-Macaulay.aulay.