• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.983-992
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• 1996

Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.479-488
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• 2024

Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is C¹-smooth on [0, ∞), vanishes at zero, and is positive on (0, ∞). A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.5
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• pp.1-9
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• 1998

The analysis concerns collapse behavior of framed vehicle models with the change of design parameters at the initial stage of conceptual design. Collapse analysis of a vehicle model with framed structures has been carried out using finite element limit analysis. The analysis makes sequential changes of design parameters from an initial model with frames of uniform section so as to stage then weak parts. As a result of those design changes, the collapse load of a model has been increased and the deflection toward a passenger room has been reduced. The results demonstrate the versatility of finite element limit analysis as a tool that confirms the safety of vehicle models.

• Journal of KIISE:Information Networking
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• v.35 no.4
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• pp.282-291
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• 2008

This paper focuses on message complexity performance analysis of MANET AAPs in reference to link errors generated by the mobile wireless nodes. To obtain the message complexity performance of AAPs in reference to the link error probability ($P_e$), an enhancement was made by proposing the retransmission limit (S) to be computed for error recovery (based on the link error probability), and then for each of the AAPs the control procedures for the retransmission limit have been properly included. The O-notation has been applied in analyzing the upper bound of the number of messages generated by a MANET group of N nodes. Based on a link error probability range of $P_e=0$ to 0.8, the AAPs investigated in this paper are Strong DAD, Weak DAD with proactive routing protocol (WDP), Weak DAD with on-demand routing protocol (WDO), and MANETconf. Based on the simulation results and analysis of the message complexity, for nominal situations, the message complexity of WDP was lowest, closely followed by WDO. The message complexity of MANETconf is higher than that of WDO, and Strong DAD results to be most complex among the four AAPs.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.121-128
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.35-43
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• 2003

We study the weak convergence to Fractional Brownian motion and some examples with applications to traffic modeling. Finally, we get loss probability for queue-length distribution related to self-similar process.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1185-1201
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• 2022

Feller introduced an unfair-fair-game in his famous book [3]. In this game, at each trial, player will win 2^k yuan with probability p_k = 1/2^kk(k + 1), k ∈ ℕ, and zero yuan with probability p₀ = 1 - Σ^∞_k=1 p_k. Because the expected gain is 1, player must pay one yuan as the entrance fee for each trial. Although this game seemed "fair", Feller [2] proved that when the total trial number n is large enough, player will loss n yuan with its probability approximate 1. So it's an "unfair" game. In this paper, we study in depth its convergence in probability, almost sure convergence and convergence in distribution. Furthermore, we try to take 2^k = m to reduce the values of random variables and their corresponding probabilities at the same time, thus a new probability model is introduced, which is called as the related model of Feller's unfair-fair-game. We find out that this new model follows a long-tailed distribution. We obtain its weak law of large numbers, strong law of large numbers and central limit theorem. These results show that their probability limit behaviours of these two models are quite different.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.225-238
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• 2006

Generalized order statistics (gos) introduced by Kamps [8] as a unified approach to several models of order random variables (rv's), e.g., (ordinary) order statistics (oos), records, sequential order statistics (sos). In a wide subclass of gos, included oos and sos, the possible limit distribution functions (df's) of the maximum gos are obtained in Nasri-Roudsari [10]. In this paper, for this subclass, as the df of the suitably normalized extreme gos converges on an interval [c, d] to one of possible limit df's of the extreme gos, the continuation of this (weak) convergence on the whole real line to this limit df is proved.

• Journal of Communications and Networks
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• v.11 no.1
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• pp.84-93
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• 2009

This paper focuses on message complexity performance analysis of mobile ad hoc network (MANET) address autoconfiguration protocols (AAPs) in reference to link errors generated by mobile wireless nodes. An enhancement was made using a proposed retransmission limit, S, to be computed for error recovery (based on the link error probability), to measure message complexity of AAPs in reference to the link error probability, $P_e$. The control procedures for the retransmission limit have been included for each of the AAPs. Retransmission limit control is critical for efficient energy consumption of MANET nodes operating on limited portable energy. O-notation has been applied to analyze the upper bound of the number of messages generated by a MANET group of nodes. The AAPs investigated in this paper are strong duplicate address detection (DAD), weak DAD with proactive routing protocol (WDP), weak DAD with on-demand routing protocol (WDO), and MANETConf. Each AAP reacts different to link errors, as each AAP has different operational procedures. The required number of broadcasting, unicasting, relaying, and received messages of the nodes participating in a single-node joining procedure is investigated to asymptotically calculate the message complexity of each AAP. Computer simulation was conducted and the results have been analyzed to verify the theoretical message complexity bounds derived. The message complexity of WDP was lowest, closely followed byWDO, based on the simulation results and analysis of the message complexity under nominal situations. The message complexity of MANETConf was higher than WDO, and strong DAD resulted to be most complex among the four AAPs.