• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.319-357
• /
• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.6
• /
• pp.837-841
• /
• 2008

In this paper, we consider interval probability as a unifying concept for uncertainty and Choquet integrals with resect to a capacity functional. By using interval probability, we will define an interval-valued capacity functional and Choquet integral with respect to an interval-valued capacity functional. Furthermore, we investigate Choquet weak convergence of interval-valued capacity functionals of random sets.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.1
• /
• pp.13-33
• /
• 2021

The aim of this paper is to establish common fixed point theorems under generalized (ψ - ϕ)-weak contractions in the setting of complete S-metric spaces and we support our result by some examples. Also an application of our results, we obtain some fixed point theorems of integral type. Our results extend Theorem 2.1 and 2.2 of Doric [5], Theorem 2.1 of Dutta and Choudhury [6], and many other several results from the existing literature.

• Journal of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.821-841
• /
• 2022

In this paper, we introduce and study regular rings relative to the hereditary torsion theory w (a special case of a well-centered torsion theory over a commutative ring), called w-regular rings. We focus mainly on the w-regularity for w-coherent rings and w-Noetherian rings. In particular, it is shown that the w-coherent w-regular domains are exactly the Prüfer v-multiplication domains and that an integral domain is w-Noetherian and w-regular if and only if it is a Krull domain. We also prove the w-analogue of the global version of the Serre-Auslander-Buchsbaum Theorem. Among other things, we show that every w-Noetherian w-regular ring is the direct sum of a finite number of Krull domains. Finally, we obtain that the global weak w-projective dimension of a w-Noetherian ring is 0, 1, or ∞.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.4
• /
• pp.499-503
• /
• 2009

Y. R$\acute{e}$ball$\acute{e}$ [11] discussed the representation of necessity measure through the Choquet integral criterian. He also consider a decision maker who ranks necessity measures related with Choquet integral representation. In this paper, we consider a decision maker have an "ambiguity"(say, interval-valued) necessity measure according to their Choquet's expected utility. Furthermore, we prove two theorems which are weak Choquet integral representation of preferences with a monotone set function for interval-valued necessity measures and strong Choquet integral representation of preferences with an interval-valued utility function for necessity measures.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1241-1257
• /
• 2014

We consider a class of hypoelliptic operators of the following type $$L=\sum_{i,j=1}^{p_0}a_{ij}{\partial}^2_{x_ix_j}+\sum_{i,j=1}^{N}b_{ij}x_i{\partial}_{x_j}-{\partial}_t$$, where ($a_{ij}$), ($b_{ij}$) are constant matrices and ($a_{ij}$) is symmetric positive definite on $\mathbb{R}^{p_0}$ ($p_0{\leqslant}N$). By establishing global Morrey estimates of singular integral on the homogenous space and the relation between Morrey space and weak Morrey space, we obtain the global weak Morrey estimates of the operator L on the whole space $\mathbb{R}^{N+1}$.

• Computational Structural Engineering
• /
• v.7 no.2
• /
• pp.111-120
• /
• 1994

Cracks in rubber bonded to a rigid material such as steel are analyzed with the aid of a mixed finite element technique. Firstly the weak form is derived for finite element analysis of an incompressible material, and the Mooney-Rivlin form is assumed for the constitutive modeling of rubber. The numerical results from finite element analysis is examined to confirm the accuracy and convergence of solution by way of comparison to other numerical results. The interpretation of the J-integral for large elastic deformation as the energy release rate is confirmed, and the J-integral is calculated for varing crack length. The crack growth stability is discussed using the result of finite element analysis.

• Bulletin of the Korean Chemical Society
• /
• v.28 no.4
• /
• pp.607-612
• /
• 2007

Relationship between charge transfer mechanism and quantum coherence has been investigated using a realtime quantum dynamics approach. In the on-the-fly filtered propagator functional path integral simulation, by separating paths that belong to different mechanisms and by integrating contributions of correspondingly sorted paths, it was possible to accurately obtain quantitative contribution of different transport mechanisms. For a 5'-GAGGG-3' DNA sequence, we analyze charge transfer processes quantitatively such that the governing mechanism alters from coherent to incoherent charge transfer with respect to the friction strength arising from dissipative environments. Although the short DNA sequence requires substantially strong dissipation for completely incoherent hopping transfer mechanism, even a weak system-environment interaction markedly destroys the coherence within the quantum mechanical system and the charge transfer dynamics becomes incoherent to some degree. Based on the forward-backward path deviation analysis, the coherence variation depending on the environment is investigated numerically.

• Journal of Communications and Networks
• /
• v.6 no.2
• /
• pp.133-146
• /
• 2004

Recently, many active queue management (AQM) algorithms have been proposed to address the performance degradation. of end-to-end congestion control under tail-drop (TD) queue management at Internet routers. However, these AQM algorithms show performance improvement only for limited network environments, and are insensitive to dynamically changing network situations. In this paper, we propose an adaptive queue management algorithm, called PID-controller, that uses proportional-integral-derivative (PID) feedback control to remedy these weak-Dalles of existing AQM proposals. The PID-controller is able to detect and control congestion adaptively and proactively to dynamically changing network environments using incipient as well as current congestion indications. A simulation study over a wide range of IP traffic conditions shows that PID-controller outperforms other AQM algorithms such as Random Early Detection (RED) [3] and Proportional-Integral (PI) controller [9] in terms of queue length dynamics, packet loss rates, and link utilization.

• The Pure and Applied Mathematics
• /
• v.28 no.4
• /
• pp.355-376
• /
• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.