• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.705-714
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• 2002

We consider a jump-diffusion model generated by a Levy process for an asset price. We present an error estimate for the option prices between the jump-diffusion model and the Black-scholes model when the former converges weakly to the latter.

• Honam Mathematical Journal
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• v.15 no.1
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• pp.129-136
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• 1993

In this paper we present of a class infinite M A (moving-average) sequences of multivariate random vectors. We use the theory of positive dependence to show that in a variety of cases the classes of M A sequences are associated. We then apply the association to establish some probability bounds and moment inequalities for multivariate processes.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.835-844
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• 2007

This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.

• School Mathematics
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• v.4 no.4
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• pp.555-563
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• 2002

The purpose of this paper is to try formulating a working definition of connection of informal and formal mathematical knowledge. Many researchers have suggested that informal mathematical knowledge should be connected with school mathematics in the process of learning and teaching it. It is because informal mathematical knowledge might play a important role as a cognitive anchor for understanding school mathematics. To implement the connection of them we need to know what the connection means. In this paper, the connection between informal and formal mathematical knowledge refers to the making of relationship between common attributions involved with the two knowledge. To make it clear, it is discussed that informal knowledge consists of two properties of procedures and conceptions as well as formal mathematical knowledge does. Then, it is possible to make a connection of them. Now it is time to make contribution of our efforts to develop appropriate models to connect informal and formal mathematical knowledge.

• Journal of the Korean Statistical Society
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• v.2 no.1
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• pp.3-7
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• 1973

Zellner, Kmenta, Dreze (1966) and later Hedges (1969) showed that consistent estimates of the parameters of Cobb-Douglas or CES production functions can be obtained by the single equation estimation methods if the models incorporate the assumption that firms maximize the mathematical expectation of profits. This note demonstrates that the results of the above-cited works can be extended to a class of VES production function models.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.157-171
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• 1999

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for system modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, an information extractor from CPN models has been developed in this work. In order to convert the extracted information to the PVS specification language, a translator also has been developed. ML that is a higher-order functional language programs the information extractor and translator. This combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip). As a result of this application, we could prove completeness and consistency of the requirement logically. Through this work, in short, an axiom or lemma based-analysis method for CPN models is newly suggested in order to complement CPN analysis methods and a guideline for the use of formal methods is proposed in order to apply them to NPP Software Verification and Validation.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.53.2-53.2
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• 2017

Stochasitc gravitational wave background (SGWB) is expected to be contributed by primordial sources (e.g. inflation signature) and astrophysical sources (e.g., incoherent superposition of a large numbers of compact binary inspirals throughout in the Universe). Theoretically, SGWB is predicted to span in a broad frequency range between less than nHz up to kHz. Many gravitational-wave (GW) detectors such as LIGO or LISA aim to detect or constrain SGWB in different frequency band that is most sensitive for each detector. In this talk, we focus on the prospectives of constraining the energy density of SGWB between 0.1-10 Hz. We introduce the characteristics of SGWB and representative models for primordial and astrophysical sources. Then, we propose a signal extraction scheme to detect SGWB using one or several omni-directional GW detectors such as SLGT(Superconducting Low-frequency Gravitational-wave Telescope). Considering SLGT sensitivity, we discuss how to observe SGWB in 0.1-10 Hz if we have SLGT network. Finally, we highlight interesting SGWB models that can be constrained in 0.1-10 Hz with SLGT.

• Journal of Science Education
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• v.34 no.1
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• pp.175-184
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• 2010

We agree with Hanna and Jahnke's assertion on the use of arguments from physics in mathematical proofs and analyze their educational example of the use of arguments from physics in the proof of the center of gravity of a triangle. Moreover, we suggest practical models for the center of gravity of a triangle for the demonstration in a classroom. Comparing with the traditional mathematical arguments, the role of concepts and models from physics in arguments from physics will be clearly pointed out. Also, the necessity for arguments from physics in the classroom will be discussed in this paper.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.5
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• pp.2674-2697
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• 2019

Identity authentication is a crucial line of defense for network security, and passwords are still the mainstream of identity authentication. So far trawling password attacking has been extensively studied, but the research related with personal information is always sporadic. Probabilistic context-free grammar (PCFG) and Markov chain-based models perform greatly well in trawling guessing. In this paper we propose a systematic targeted attacking model based on structure partition and string reorganization by migrating the above two models to targeted attacking, denoted as TG-SPSR. In structure partition phase, besides dividing passwords to basic structure similar to PCFG, we additionally define a trajectory-based keyboard pattern in the basic grammar and introduce index bits to accurately characterize the position of special characters. Moreover, we also construct a BiLSTM recurrent neural network classifier to characterize the behavior of password reuse and modification after defining nine kinds of modification rules. Extensive experimental results indicate that in online attacking, TG-SPSR outperforms traditional trawling attacking algorithms by average about 275%, and respectively outperforms its foremost counterparts, Personal-PCFG, TarGuess-I, by about 70% and 19%; In offline attacking, TG-SPSR outperforms traditional trawling attacking algorithms by average about 90%, outperforms Personal-PCFG and TarGuess-I by 85% and 30%, respectively.

• Structural Engineering and Mechanics
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• v.84 no.2
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• pp.285-293
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• 2022

Lumped damage mechanics (LDM) is a recent nonlinear theory with several applications to civil engineering structures, such as reinforced concrete and steel buildings. LDM apply key concepts of classic fracture and damage mechanics on plastic hinges. Therefore, the lumped damage models are quite successful in reproduce actual structural behaviour using concepts well-known by engineers in practice, such as ultimate moment and first cracking moment of reinforced concrete elements. So far, lumped damage models are based in the strain energy equivalence hypothesis, which is one of the fictitious states where the intact material behaviour depends on a damage variable. However, there are other possibilities, such as the energy equivalence hypothesis. Such possibilities should be explored, in order to pursue unique advantages as well as extend the LDM framework. Therewith, a lumped damage model based on the energy equivalence hypothesis is proposed in this paper. The proposed model was idealised for reinforced concrete structures, where a damage variable accounts for concrete cracking and the plastic rotation represents reinforcement yielding. The obtained results show that the proposed model is quite accurate compared to experimental responses.