• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1159-1173
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• 2009

This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents $q_1,\;q_2\;{\in}\;(0,+{\infty})$) with $q_1\;{<}\;q_2$. In other words, when q belongs to different intervals (0, $q_1),\;(q_1,\;q_2),\;(q_2,+{\infty}$), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0, $q_2$]. However, when q ${\in}\;(q_2,+{\infty}$), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval ($q_1,+{\infty}$), while for q ${\in}\;(0,\;q_1$), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = $q_1$ is concerned, the other parameter ${\lambda}$ will play an important role. In other words, when $\lambda$ belongs to different interval (0, ${\lambda}_1$) or (${\lambda}_1$,+${\infty}$), where ${\lambda}_1$ is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.429-441
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• 2020

Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓_α^p, M(𝓓_p-1^p, 𝓓_q-1^q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓_p-2+s^p, 𝓓_q-2+s^q) = {0}. However, X ∩ 𝓓_p-1^p ⊆ X ∩ 𝓓_q-1^q and X ∩ 𝓓_p-2+s^p ⊆ X ∩ 𝓓_q-2+s^p whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 _p-2+s^p, X∩𝓓_q-2+s^q) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓_p-2+s^p, X ∩ 𝓓_q-2+s^q) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗^∞.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.731-736
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• 2017

It is well-known that there exists a constant-weight $[s{\theta}_{k-1},k,sq^{k-1}]_q$ code for any positive integer s, which is an s-fold simplex code, where ${\theta}_j=(q^{j+1}-1)/(q-1)$. This gives an upper bound $n_q(k,sq^{k-1}+d){\leq}s{\theta}_{k-1}+n_q(k,d)$ for any positive integer d, where $n_q(k,d)$ is the minimum length n for which an $[n,k,d]_q$ code exists. We construct a two-weight $[s{\theta}_{k-1}+1,k,sq^{k-1}]_q$ code for $1{\leq}s{\leq}k-3$, which gives a better upper bound $n_q(k,sq^{k-1}+d){\leq}s{\theta}_{k-1}+1+n_q(k-1,d)$ for $1{\leq}d{\leq}q^s$. As another application, we prove that $n_q(5,d)={\sum_{i=0}^{4}}{\lceil}d/q^i{\rceil}$ for $q^4+1{\leq}d{\leq}q^4+q$ for any prime power q.

• Korean Journal of Optics and Photonics
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• v.24 no.2
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• pp.58-63
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• 2013

A theoretical analysis of the impact of rise time of a Q-switch on the output pulse performance is carried out in an Ytterbium-doped actively Q-switched fiber laser. The finite difference time domain (FDTD) method is used to numerically simulate the Q-switched fiber laser. It is shown that stable Gaussian-like pulse shape can be generated when the Q-switch rise time is increased and pulse repetition rate is enlarged.

• Journal of IKEEE
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• v.24 no.4
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• pp.991-997
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• 2020

Reinforcement learning has been applied mainly in sequential decision-making problems. Especially in recent years, reinforcement learning combined with neural networks has brought successful results in previously unsolved fields. However, reinforcement learning using deep neural networks has the disadvantage that it is too complex for immediate use in the field. In this paper, we implemented path planning algorithm for mobile robots using Q-learning, one of the easy-to-learn reinforcement learning algorithms. We used real-time Q-learning to update the Q-table in real-time since the Q-learning method of generating Q-tables in advance has obvious limitations. By adjusting the exploration strategy, we were able to obtain the learning speed required for real-time Q-learning. Finally, we compared the performance of real-time Q-learning and DQN.

• Journal of Korea Foresty Energy
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• v.19 no.2
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• pp.61-68
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• 2000

This study was carried ou to compare sprouting and sprout growth after the stumps of four Quercus species(Q. mongolica, Q. variabilis, Q. acutissima and Q. dentata) were cut at 20cm from the soil surface in 1996 and 2000 at Mt. Taehwa, Kwangju-Gun, Kyounggi-Do, Korea. The results obtained were as follows: ⑴ Q. mongolica showed most vigorous sprouting, followed by Q. variabilis, Q. dentata, and Q. acutissima. ⑵ The sprouting ability was more vigorous when cut in winter to earl spring than that in summer. ⑶ The initial diameter growth of the sprouts for 2 year after cutting was the highest in Q. acutissima, followed by Q. dentata, Q. mongolica and Q.variabilis, but the growth for 5years after cutting was Q. variabilis > Q. mongolica > Q. dentata > Q. acutissima. ⑷ The height growth of sprouts for 2 years after cutting was the highest in Q. acutissima and followed by Q. mongolica, Q. dentata and Q. variabilis, but the growth for 5 years after cutting was Q. variabilis > Q. mongolica > Q. dentata > Q. acutissima. ⑸ Tending is needed for the stands of Q. variabilis and Q. acutissima to be regenerated successully by sprouting. ⑹ The sprouting ability of Quercus species decreased with incerasing stump diameter, while its diameter growth seemed to increase.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.473-482
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• 2010

In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the generalized basic hypergeometric functions of one and more variables are deduced as the applications of the main result.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.963-975
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• 2003

The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.