• Korean Journal of Mathematics
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• v.17 no.4
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.389-399
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• 2021

In recent years, word embedding has been a popular field of natural language processing research and a skip-gram has become one successful word embedding method. It assigns a word embedding vector to each word using contexts, which provides an effective way to analyze text data. However, due to the limitation of vector space model, primary word embedding methods assume that every word only have a single meaning. As one faces multi-sense words, that is, words with more than one meaning, in reality, Neelakantan (2014) proposed a multi-sense skip-gram (MSSG) to find embedding vectors corresponding to the each senses of a multi-sense word using a clustering method. In this paper, we propose a modified method of the MSSG to improve statistical accuracy. Moreover, we propose a data-adaptive choice of the number of clusters, that is, the number of meanings for a multi-sense word. Some numerical evidence is given by conducting real data-based simulations.

• Journal of Magnetics
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• v.1 no.2
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• pp.75-81
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• 1996

Study on the HDDr Characteristics of Nd16Fe76-xB8Zrx (x=0-2.0) Alloys and the Magnetic Properties of the HDDR Materials Nd16Fe76-xB8Zrx (where x=0-2.0) have been studied to see the effect of Zr addition on HDDR characteristics. A particular emphasis was place upon the anisotropy of the HDDR material. Anisotropy of the HDDR powder material has been evaluated by comparing the remanence values of the aligned sample measured along the aligning direction and the direction perpendicular to it. The HDDR characteristics of the alloys were investigated by means of DAT and TPA. Magnetic chracterisation of the HDDR processed materials was performed using a VSM and a TMA. The magnetic domain structure of the HDDR materials was examined by means of polarised microscope using a solid HDDR processed material. It has veen found that small addition (0.1 at %) of Zr to Nd-Fe-B-type alloy retards thedisproportionatio kinetics of the hydrogenated material. Desorption characteristic of the disproportionated materials has been found not to be affected significantly by the Zr addition. The Zr addition has been found to facilitate size of the powder. As the particle size decreases, the intrinsic coercivity decreases radically, and this is explained in terms of structural damage and/or oxidation caused during mechanical milling. It has also been found that the degree of alignment representing the anisotropic character of the HDDR powder is enhanced with decreasing particle size. Alloys with compositions based on

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.139-145
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• 1996

We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.43-53
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• 1988

The main result of this paper is a characterization of almost projective modules over art in algebras by means of irreducible maps and almost split sequences. A module X is an almost projective module if and only if it has a presentation $0{\longrightarrow}L{\longrightarrow^{\alpha}}P{\longrightarrow}X{\longrightarrow}0$ with projective module P and irreducible maps ${\alpha}$. Let X be an injective almost projective non simple module and $0{\rightarrow}Dtr(x){\rightarrow}E{\rightarrow}X{\rightarrow}0$ be an almost split sequence. If $E=E_1{\oplus}E_2$ is a direct decomposition of indecomposable modules then ${\ell}(X)=3$.

• 전기의세계
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• v.26 no.2
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• pp.66-71
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• 1977

A mathematical model, which can be used for the study of an influenza epidemic, was derived. The model of influenza takes into full consideration the incubation period and inapparent infection. That was analysed by means of digital computer under the conditions of changing the infection rate, .betha., from 4 to 5, for three types of communities (First type: the initial distribution of population, x$_{1}$(0)=89% susceptibles, x$_{2}$(0)=3% incubatives, x$_{3}$(0)=0.5% carriers, x$_{4}$(0)=7.5% immunes; Second type: x$_{1}$(0)=79%, x$_{2}$(0)=3%, x$_{3}$(0)=0.5%, x$_{4}$(0)=17.5%; Third type: x$_{1}$(0)=69%, x$_{2}$(0)=3%, x$_{3}$(0)=0.5%, x$_{4}$(0)=27.5%, considering the rate of population increase, in Seoul. In conclusion, the outcomes of this study are summarized as follow. 1) The new model is quite reasonable in representing many phenomena connected with influenza spread. 2) The more influenza does prevail, the smaller the valve of attack rate becomes, while the contagious period becomes slightly longer. 3) The average infection rate, .betha., of influenza is approximately 5 per week time and X$_{4}$(0) is about 27.5 percent of the total population in Seoul spring 1961. 4) The number of carriers of influenza in Seoul spring 1961 becomes maximum within approximately 2.4 weeks after the attack of diseases. 5) About 68 percent of all cases in the contagious period is infected with influenza from 5 to 15 days after the attack of diseases. The auther believes that the method to study the influenza models in this paper will be helpful to study the characteristics of other epidemics. It will also contribute to public healthe management and the preventive policy decision against epidemics.

• Journal of KIISE
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• v.41 no.9
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• pp.617-624
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• 2014

Malicious traffic, such as DDoS attack and botnet communications, refers to traffic that is generated for the purpose of disturbing internet networks or harming certain networks, servers, or hosts. As malicious traffic has been constantly evolving in terms of both quality and quantity, there have been many researches fighting against it. In this paper, we propose an effective malicious traffic detection method that exploits the X-means clustering algorithm. We also suggest how to analyze statistical characteristics of malicious traffic and to define metrics that are used when clustering. Finally, we verify effectiveness of our method by experiments with two released traffic data.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 2009

With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.619-631
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• 2006

When X and Y have independent Poisson distributions, we develop a Bayesian one-sided testing procedures for the ratio of two Poisson means. We propose the objective Bayesian one-sided testing procedures for the ratio of two Poisson means based on the fractional Bayes factor and the intrinsic Bayes factor. Some real examples are provided.