• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.53-66
• /
• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.

• Journal of Computing Science and Engineering
• /
• v.9 no.2
• /
• pp.73-82
• /
• 2015

Understanding how the topic evolves is an important and challenging task. A topic usually consists of multiple related events, and the accurate identification of event evolution relationship plays an important role in topic evolution analysis. Existing research has used the traditional vector space model to represent the event, which cannot be used to accurately compute the semantic similarity between events. This has led to poor performance in identifying event evolution relationship. This paper suggests constructing a semantic aspect-based vector space model to represent the event: First, use hierarchical Dirichlet process to mine the semantic aspects. Then, construct a semantic aspect-based vector space model according to these aspects. Finally, represent each event as a point and measure the semantic relatedness between events in the space. According to our evaluation experiments, the performance of our proposed technique is promising and significantly outperforms the baseline methods.

• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• pp.193-202
• /
• 2005

We define a general space $H_{{\omega},p}$ of the Hardy space and improve that Aleman's results to the space $H_{{\omega},p}$. It follows that the multiplication operator on this space is cellular indecomposable and that each invariant subspace contains nontrivial bounded functions.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.217-227
• /
• 2020

Let ψ be an analytic function on 𝔻, the unit disc in the complex plane, and φ be an analytic self-map of 𝔻. Let 𝓑 be a Banach space of functions analytic on 𝔻. The weighted composition operator W_φ,ψ on 𝓑 is defined as W_φ,ψf = ψf ◦ φ, and the composition operator C_φ defined by C_φf = f ◦ φ for f ∈ 𝓑. Consider α > -1 and 1 ≤ p < ∞. In this paper, we prove that if φ ∈ H^∞(𝔻), then C_φ has closed range on any weighted Dirichlet space 𝒟_α if and only if φ(𝔻) satisfies the reverse Carleson condition. Also, we investigate the closed rangeness of weighted composition operators on the weighted Bergman space A^p_α.

• Journal of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.79-87
• /
• 1975

• Kyungpook Mathematical Journal
• /
• v.21 no.2
• /
• pp.251-262
• /
• 1981

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.4
• /
• pp.1129-1140
• /
• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1891-1908
• /
• 2018

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions of the Dirichlet problem of the one-dimension Minkowski-curvature equation $$\{\(\frac{u^{\prime}}{\sqrt{1-u^{{\prime}2}}}\)^{\prime}+{\lambda}a(x)f(u)=0,\;x{\in}(0,1),\\u(0)=u(1)=0$$, where ${\lambda}$ is a positive parameter, $f{\in}C[0,{\infty})$, $a{\in}C[0,1]$. The proofs of main results are based upon the bifurcation techniques.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.219-231
• /
• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Korean Journal of Mathematics
• /
• v.4 no.2
• /
• pp.179-193
• /
• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.