• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Computers and Concrete
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• v.2 no.3
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• pp.239-248
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• 2005

The article presents the results of examination of the fractal dimension D of concrete specimen fracture surfaces obtained in fracture toughness tests. The concretes were made from three different types of coarse aggregate: gravel, dolomite and basalt aggregate. Ordinary concretes (C40) and high-performance concretes (HPC) were subjected to testing after 7, 14, 28 and 90 days of curing, respectively. In fracture toughness and compressive tests, different behaviours of concretes were found, depending on the type of aggregate and class of concrete (C40, HPC). A significant increase in the strength parameters tested occurred also after a period of 28 days (up to the $90^{th}$ day of curing) and was particularly large for concretes C40. Fractal examinations performed on fracture replicas showed that the fractal dimension D was diverse, depending on the coarse aggregate type and concrete class being, however, statistically constant after 7 and 14 days for respective concretes during curing. The fractal dimension D was the greater, the worse strength properties were possessed by the concrete. A cross-grain crack propagation occurred in that case, due to weak cohesion forces at the coarse aggregate/mortar interface. A similar effect was observed for C40 and HPC made from the same aggregate. A greater dimension D was exhibited by concretes C40, in which case the fracture was easier to form compared with high-performance concretes, where, as a result of high aggregate/mortar cohesion forces, the crack propagation was of inter-granular type, and the resulted fracture was flatter.

• Journal of the Korea Fashion and Costume Design Association
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• v.14 no.4
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• pp.191-204
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• 2012

The purpose of this study is to investigate the effect of interactivity on consumer-internet brand relationship and consumer's repurchase intention according to relationship tendency with internet brand. The survey was limited to the respondents over 20 years old living in Seoul and other metropolitan areas who had purchased fashion products in internet shopping mall. Questionnaire was collected from February 1, 2012 to February 12, 2012 and 562 useful data were analyzed using Amos 19. The results of this study were as follows: First, after respondents were divided into the strong relationship group and the weak relationship group, the path model was verified according to each group. All the paths except 'affective commitment${\rightarrow}$ repurchase intention' were accepted for the strong relationship group, while three paths were accepted for the weak relationship group. As for the weak relationship group, people-people interactivity dimension had a significantly positive effect on consumer-internet brand relationship. Also it showed stronger effect on each consumer-internet brand relationship dimension for both groups compared with contents-people interactivity. Second, respondents were divided into 'more than one year' group and 'less than one year' group according to relationship period. All the paths were accepted for 'more than one year' group, while three paths were accepted for 'less than one year' group. Both interactivity dimensions showed stronger effect on 'trust' than on 'affective commitment'.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1311-1325
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• 2021

One says that a ring homomorphism R → S is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element f ∈ S, there is a unique smallest ideal of R whose extension to S contains f, called the content of f. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically 'yes' in dimension one, but 'no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.131-144
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• 2020

Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫₁, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.321-323
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• 2001

Compressible, magnetohydrodynamic (MHD) turbulence in two dimension is studied through high-resolution, numerical simulations with the isothermal equation of state. First, hydrodynamic turbulence with Mach number $(M)_{rms}\;\~$1 is generated by enforcing a random force. Next, initial, uniform magnetic field of various strengths with Alfvenic Mach number Ma $\gg$ 1 is added. Then, the simulations are followed until MHD turbulence is fully developed. Such turbulence is expected to exist in a variety of astrophysical environments including clusters of galaxies. Although no dissipation is included explicitly in our simulations, truncation errors produce dissipation which induces numerical resistivity. It mimics a hyper-resistivity in our second-order accurate code. After saturation, the resulting flows are categorized as SF (strong field), WF (weak field), and VWF (very weak field) classes respectively, depending on the average magnetic field strength described with Alfvenic Mach number, $(Ma)_{rms}{\ge}1$, $(Ma)_{rms}{\~}1$, and $(Ma)_{rms}{\gg}1$. The characteristics of each class are discussed.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.939-948
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• 2006

The structural anisotropy and heterogeneity of rock mass, caused by discontinuities and weak zones, have a great influence on the deformation behavior of tunnel. Tunnel construction in these complex ground conditions is very difficult. No matter how excellent a geological investigation is, local uncertainties of rock mass conditions still remain. Under these uncertain circumstances, an accurate forecast of the ground conditions ahead of the advancing tunnel face is indispensable to safe and economic tunnel construction. This paper presents the effect of anisotropy and heterogeneity of the rock masses to be excavated by numerical analysis. The influences of distance from weak zone, the size or dimension, the different stiffness and the orientation of weak zones are analysedby 2-D and 3-D finite element analysis. By analysing these numerical results, the tunnel behavior due to excavation can be well understood and the prediction of rock mass condition ahead of tunnel face can be possible.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1187-1198
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• 2019

Let R be a domain with its field Q of quotients. An R-module M is said to be weak w-projective if $Ext^1_R(M,N)=0$ for all $N{\in}{\mathcal{P}}^{\dagger}_w$, where ${\mathcal{P}}^{\dagger}_w$ denotes the class of GV-torsionfree R-modules N with the property that $Ext^k_R(M,N)=0$ for all w-projective R-modules M and for all integers $k{\geq}1$. In this paper, we define a domain R to be w-Matlis if the weak w-projective dimension of the R-module Q is ${\leq}1$. To characterize w-Matlis domains, we introduce the concept of w-Matlis cotorsion modules and study some basic properties of w-Matlis modules. Using these concepts, we show that R is a w-Matlis domain if and only if $Ext^k_R(Q,D)=0$ for any ${\mathcal{P}}^{\dagger}_w$-divisible R-module D and any integer $k{\geq}1$, if and only if every ${\mathcal{P}}^{\dagger}_w$-divisible module is w-Matlis cotorsion, if and only if w.w-pdRQ/$R{\leq}1$.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.503-516
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• 2003

We show in this paper that every domain in a separable Hilbert space, say H, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Krantz [10] and subsequent improvement of Byun/Gaussier/Kim [3] in the infinite dimensions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.213-226
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• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.