• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.363-375
• /
• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.19 no.3
• /
• pp.4449-4461
• /
• 1977

Subsurface Drinage Problems arise from many causes. Flatland tends to be poorly drained, particularly where the subsoil permeability is low. There are many wet areas, however, where there is no evident connection between the area of seepage, or a high water table, and the topography of the site. High water tables may occur where the soil is either slowly or rapidly permeable, where the climate is either humid or arid, and where the land is either sloping or flat. This study is to bring light on subjects relating to increasing yield of crop and possibility of double crops a year in water logging paddy fields. Obtained results are briefly summarized as follows: 1. Effect of crop-yield in the plot A resulted 20.2 percent higher than the ordinary plot with yield of brown rice. 2. Possibility of double-crops a year is investigated. Effect of the barley production of the test plot resulted 168.2 percent higher than the other uplands near test plot with the yield of 1977 production and it is 3.8 percent higher compare with the yearly yields. 3. Decreasing depth of water level was measured 23.9mm per day and 14.3mm per day at the test plot and ordinary plot respectively and the amounts of subsurface drainage measured 30mm to 35mm per day. It is required that the relief well should be controled carefully and adequately. 4. Mean depth of ground water levl was measured 0.4∼0.5m regardless the width of corrugated pipe. It is significantly lowere than the ordinary plot(0.15∼0.20m) 5. The ground temperature of the test plot is higher 1 degree of centigarade or more than the ordinary plot and soil moisture content of the ordinary plot is higher 12.4∼27.8 percent than the plot reversely. There should be a relationship between rising of ground temperature and soil moisture.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.185-191
• /
• 2006

This paper observes that the induced homomorphisms on cohomology groups by a cyclic map are trivial. For a CW-complex X, we use the fact to obtain some conditions of X so that the n-th Gottlieb group $G_n(X)$ is trivial for an even positive integer n. As corollaries, for any positive integer m, we obtain $G_{2m}(S^{2m})\;=\;0\;and\;G_2(CP^m)\;=\;0$ which are due to D. H. Gottlieb and G. Lang respectively, where $S^{2m}$ is the 2m- dimensional sphere and $CP^m$ is the complex projective m-space. Moreover, we show that $G_4(HP^m)\;=\;0\;and\;G_8(II)\;=\;0,\;where\;HP^m$ is the quaternionic projective m-space for any positive integer m and II is the Cayley projective space.

• The Pure and Applied Mathematics
• /
• v.23 no.3
• /
• pp.319-328
• /
• 2016

In this paper, we solve the additive ρ-functional inequalities (0.1) ||f(2x-y)+f(y-x)-f(x)|| $\leq$ ||${\rho}(f(x+y)-f(x)-f(y))$||, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ||f(x+y)-f(x)-f(y)|| $\leq$ ||${\rho}(f(2x-y)-f(y-x)-f(x))$||, where ρ is a fixed complex number with |ρ| < $\frac{1}{2}$. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in β-homogeneous F-spaces.

• Journal of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.235-254
• /
• 2022

Let ℍⁿ be the Heisenberg group and Q = 2n + 2 be its homogeneous dimension. Let 𝓛 = -∆_ℍⁿ + V be the Schrödinger operator on ℍⁿ, where ∆_ℍⁿ is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class $B_{q_1}$ for q₁ ≥ Q/2. Let H^p_𝓛(ℍⁿ) be the Hardy space associated with the Schrödinger operator 𝓛 for Q/(Q+𝛿₀) < p ≤ 1, where 𝛿₀ = min{1, 2 - Q/q₁}. In this paper, we consider the Hardy type estimates for the operator T_𝛼 = V^𝛼(-∆_ℍⁿ + V )^-𝛼, and the commutator [b, T_𝛼], where 0 < 𝛼 < Q/2. We prove that T_𝛼 is bounded from H^p_𝓛(ℍⁿ) into L^p(ℍⁿ). Suppose that b ∈ BMO^𝜃_𝓛(ℍⁿ), which is larger than BMO(ℍⁿ). We show that the commutator [b, T_𝛼] is bounded from H¹_𝓛(ℍⁿ) into weak L¹(ℍⁿ).

• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.725-737
• /
• 1995

Let $X_t = (X_t^(1), X_t^(2))', t \geqslant 0$, be a real stationary 2-dimensional Gaussian process with $EX_t^(1) = EX_t^(2) = 0$ and $$ EX_0 X'_t = (_{\rho(t) r(t)}^{r(t) \rho(t)}), $$ where $r(t) \sim $\mid$t$\mid$^-\alpha, 0 < \alpha < 1/2, \rho(t) = o(r(t)) as t \to \infty, r(0) = 1, and \rho(0) = \rho (0 \leqslant \rho < 1)$. For $t > 0, u > 0, and \upsilon > 0, let L_t (u, \upsilon)$ be the time spent by $X_s, 0 \leqslant s \leqslant t$, above the level $(u, \upsilon)$.

• East Asian mathematical journal
• /
• v.19 no.1
• /
• pp.133-150
• /
• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.983-1002
• /
• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Journal of Ginseng Research
• /
• v.14 no.3
• /
• pp.432-436
• /
• 1990

Incidence of damping-off callsed by Rhizoctonia solani was 0.6-10.9% at "Yangjik" seedbed in Pocheon, Korea. The seedbeds where the lengths of etiolated stems (underground portion) of ginseng seedlings were 0.78-1.25 cm showed 0.8-3.2% of the disease, while 6.9-10.9% disease incidence was observed at the seedbeds with the longer etiolated stem (1.89-2.26 cm). The pathogen produced a typical girdle symptom on the etiolated portion of ginseng stems close to the soil surface. The deeper the seeds were sown, the more the disease occurred in pot soil inoculated with the pathogen, AG 2-1, showing 18.4, 27.4 and 32.9% of damping-off at the seeding depth of 1, 2 and 4 cm, respectively. Cuticle layers of colored stems (over ground portion) were well - developed to be 42.8, 58.0, and 55.0 um in thickness compared to the etiolated stems with 8.5, 15.0 and 8.0um for seedling, 2 year-old, and 3 year-old ginsengs, respectively, when the disease occurred. In the seedling and 2 year-old ginseng, the colored stems were more rigid than the etiolated. There was however, no difference in rigidness of the stem of the 3 year-old ginseng where the disease is not severe as in seedlings and 2 year-old ginseng plants.ng plants.

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