• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.1-22
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• 2023

Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑^f_n=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·10⁵.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.507-516
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• 2011

Comparative studies on generalized binomial models (Moon, 2003; Ng, 1989; Paul, 1985; Kupper and Haseman, 1978; Griffiths, 1973) are restrictive in that the models compared are rather limited and MSE of the estimates is the only measure considered for the model adequacy. This paper is aimed to report simulation results which provide possible guidelines for selecting a proper model. We examine Pearson type of goodness-of-fit statistic to its degrees of freedom and AIC for the overall model quality. MSE and Bias of the individual estimates are also considered as the component fit measures. Performance of some models varies widely for a certain range of the parameter space while most of the models are quite competent. Our evaluation shows that the Extended Beta-Binomial model (Prentice, 1986) turns out to be particularly favorable in the point that it provides consistently excellent fit almost all over the values of the intra-class correlation coefficient and the probability of success.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.12
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• pp.1631-1637
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• 2019

In this paper, we propose a low-complexity robust maximum likelihood (ML) receiver for generalized spatial modulation. The proposed receiver performs the transmit antenna partition to lower the computational loads. After we divide the transmit antenna combinations into two parts, one of which is "the likely TAC part," and the other of which is "the unlikely TAC part", based on the minimum mean square error (MMSE) filtering output. We first perform the maximum likelihood detection only in the likely TAC part. Then we evaluate the reliability of the solution found in the first search, and based its reliability we decide whether we continue the search in the unlikely TAC part. This partitioned search strategy maintains the performance of the conventional robust maximum likelihood receiver and simultaneously lowers computational loads. Through simulation, we found that our newly-proposed receiver achieves considerable gains over the conventional robust ML detector in terms of the computational loads while providing almost the same performance.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.03a
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• pp.434-443
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• 2009

Slope stability analysis is an essential part of rock slope design. For highly fractured rock, the limit equilibrium method (LEM) based slope stability analysis with a circular failure surface is often carried out assuming the rock mass behaves more or less as a continuum. This paper examines first, the applicability of the finite-element method (FEM) based shear strength reduction (SSR) technique for highly fractured rock slope, and second the use of Mohr-Coulomb (MC) failure criterion in conjunction with generalized Hoek-Brown (HB) failure criterion. The numerical results on a number of cases are compared in terms of the factor of safety (FS). The results indicated that the FEM-based SSR technique yields almost the same FSs from LEM, and that the MC and HB failure criteria yield almost identical FSs when the strength parameters for MC failure criterion are obtained based on the modified HB failure criterion if and only if value of the Hoek-Brown constant $m_i$ is smaller than 10 and slope angle is smaller than 1:1, otherwise MC failure criteria over-estimate the factor of safety.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.885-892
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• 2012

Energy transfer dynamics of excited vibrational energy of OH stretching bonds in liquid water is theoretically studied. With time-dependent vibrational Hamiltonian obtained from a mixed quantum/classical calculation, we construct a master equation describing the energy transfer dynamics. Survival probability predicted by the master equation is compared with numerically exact one and we found that incoherent picture of energy transfer is reasonably valid for long-time population dynamics. Within the incoherent picture, we assess the validity of independent pair approximation (IPA) often introduced in the theoretical models utilized in the analysis of experimental data. Our results support that the IPA is almost perfectly valid as applied for the vibrational energy transfer in liquid water. However, proper incorporation of radial and orientational correlations between two OH bonds is found to be critical for a theory to be quantitatively valid. Consequently, it is suggested that the Forster model should be generalized by including the effects of the pair correlations in order to be applied for vibrational energy transfer in liquid water.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.4
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• pp.97-109
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• 2000

This work proposes a neural network approach to solve vehicle routing problems which have diverse application areas such as vehicle routing and robot programming. In solving these problems, classical mathematical approaches have many difficulties. In particular, it is almost impossible to implement a real-time vehicle routing with multiple vehicles. Recently, many researchers proposed methods to overcome the limitation by adopting heuristic algorithms, genetic algorithms, neural network techniques and others. The most basic model for path planning is the Travelling Salesman Problem(TSP) for a minimum distance path. We extend this for a problem with dynamic upcoming of new positions with multiple vehicles. In this paper, we propose an algorithm based on SOM(Self-Organization Map) to obtain a sub-optimal solution for a real-time vehicle routing problem. We develope a model of a generalized multiple TSP and suggest and efficient solving procedure.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.792-795
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• 2004

Despite is product that ship, vehicles, development equipment and Metal Bearing for plant equipment that is mass-produced by present domestic companies Cast White Metal Lining Bearing that is Bimetal Bearing standing 2 generation is accomplishing master and servant and this is foreseen to be used widely on industry whole in hereafter but Cast White Metal Bearing need minuteness processing, while price competitive power is depending on income from superior another thing area than itself manufacture already in advanced nation to lowdown that the technique is generalized widely, when take into account technology change aspect of industrial technology developing country, Go added value creation by deepening of price competition is judged to be difficult hereafter. Because domestic production and supply are wholly lacking almost in Metal Bearing Cladding that take advantage of these technology, Data-base about connection technology is weak with technique and Know-How for product. This research unites Back Steel and Aluminium Alloy different kind metal and make the Clad river studying technology about union of Gogangseong Dacheung metal bearing hereupon.

• Journal of Information Processing Systems
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• v.13 no.2
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• pp.340-347
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• 2017

A watermark is a signal added to the original signal in order to preserve the copyright of the owner of the digital content. The basic challenge for designing a watermarking system is a dilemma between transparency and robustness. If we want a higher rate of transparency, there has to be a compromise in terms of its robustness and vice versa. Also, until now, watermarking is generalized, resulting in the need for a specialized algorithm to work for a specialized image processing application domain. Our proposed technique takes into consideration the image characteristics for watermark insertion and it optimizes transparency and robustness. It achieved a 99.98% retrieval efficiency for an image blurring attack and counterfeits other attacks. Our proposed technique counterfeits almost all of the image processing attacks.

• Structural Engineering and Mechanics
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• v.49 no.4
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• pp.499-508
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• 2014

We apply the Finite Fracture Mechanics criterion to address the problem of a V-notched structure subjected to mode II loading, i.e., we provide a way to determine the direction and the load at which a crack propagates from the notch tip and express the critical conditions in terms of the generalized stress intensity factor. Weight functions for V-notch emanated cracks available in the literature allow us to implement the fracture criterion proposed in an almost completely analytical manner: the determination of the critical load and the direction of crack growth is reduced to a stationary point problem. A comparison with experimental data presented in the Literature concludes the paper.