• 대한수학회보
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• 제41권2호
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• pp.387-391
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• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

• Bulletin of the Korean Chemical Society
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• 제30권10호
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• pp.2259-2264
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• 2009

A new high-energy organic potassium salt, 2-(dinitromethylene)-1,3-diazepentane potassium salt K(DNDZ), was synthesized by reacting of 2-(dinitromethylene)-1,3-diazepentane (DNDZ) and potassium hydroxide. The thermal behavior and non-isothermal decomposition kinetics of K(DNDZ) were studied with DSC, TG/DTG methods. The kinetic equation is $\frac{d{\alpha}}{dT}$ = $\frac{10^{13.92}}{\beta}$3(1 - $\alpha$[-ln(1 - $\alpha$)]$^{\frac{2}{3}}$ exp(-1.52 ${\times}\;10^5$ / RT). The critical temperature of thermal explosion of K(DNDZ) is $208.63\;{^{\circ}C}$. The specific heat capacity of K(DNDZ) was determined with a micro-DSC method, and the molar heat capacity is 224.63 J $mol^{-1}\;K^{-1}$ at 298.15 K. Adiabatic time-to-explosion of K(DNDZ) obtained is 157.96 s.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.445-454
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• 2006

We describe a solution to the Ornstein-Uhlenbeck equation $\frac{dI}{dt}-\frac{1}{\tau}$I(t)=cV(t) where V(t) is a constant multiple of a Gaussian white noise. Our solution is based on a discrete set of Gaussian white noise obtained by taking sample points from a sum of single frequency harmonics that have random amplitudes, random frequencies, and random phases. Hence, it is different from the solution by the standard random walk using random numbers generated by the Box-Mueller algorithm. We prove that the power of the signal has the additive property, from which we derive that the Lyapunov characteristic exponent for our solution is positive. This compares with the solution by other methods where the noise is kept to be in an error range so that its Lyapunov exponent is negative.

• East Asian mathematical journal
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• 제33권1호
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• pp.67-74
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• 2017

Let k, m and t be positive integers with $m{\geq}4$ and even. It is shown that $K_{km+1(2t)}$ has a decomposition into gregarious m-cycles. Also, it is shown that $K_{km(2t)}$ has a decomposition into gregarious m-cycles if ${\frac{(m-1)^2+3}{4m}}$ < k. In this article, we make a remark that the decompositions can be circulant in the sense that it is preserved by the cyclic permutation of the partite sets, and we will exhibit it by examples.

• 대한수학회논문집
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• 제12권1호
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• pp.69-73
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• 1997

We show that if T is an $\varepsilon$-approximate Jordan functional such that T(a) = 0 implies $T(a^2) = 0 (a \in A)$ then T is continuous and $\Vert T \Vert \leq 1 + \varepsilon$. Also we prove that every $\varepsilon$-near Jordan mapping is an $g(\varepsilon)$-approximate Jordan mapping where $g(\varepsilon) \to 0$ as $\varepsilon \to 0$ and for every $\varepsilon > 0$ there is an integer m such that if T is an $\frac {\varepsilon}{m}$-approximate Jordan mapping on a finite dimensional Banach algebra then T is an $\varepsilon$-near Jordan mapping.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.67-72
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• 2022

For a locus with two alleles (I^A and I^B), the frequencies of the alleles are represented by $$p=f(I^A)={\frac{2N_{AA}+N_{AB}}{2N},\;q=f(I^B)={\frac{2N_{BB}+N_{AB}}{2N}$$ where N_AA, N_AB and N_BB are the numbers of I^AI^A, I^AI^B and I^BI^B respectively and N is the total number of populations. The frequencies of the genotypes expected are calculated by using p², 2pq and q². Choi showed the method of whether some genotypes is in these probabalities. Also he calculate the probability generating function for offspring number of genotype under a diploid model( [1]). In this paper, let x(t, p) be the probability that I^A become fixed in the population by time t-th generation, given that its initial frequency at time t = 0 is p. We find adapted equations for x using the mean change of frequence of alleles and fitness of genotype. Also we apply this adapted equations to several diploid model and it also will apply to actual examples.

• Investigative Magnetic Resonance Imaging
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• 제23권3호
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• pp.202-209
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• 2019

Purpose: To investigate the temperature-based differences of cortical bone ultrashort echo time MRI (UTE-MRI) biomarkers between body and room temperatures. Investigations of ex vivo UTE-MRI techniques were performed mostly at room temperature however, it is noted that the MRI properties of cortical bone may differ in vivo due to the higher temperature which exists as a condition in the live body. Materials and Methods: Cortical bone specimens from fourteen donors ($63{\pm}21$ years old, 6 females and 8 males) were scanned on a 3T clinical scanner at body and room temperatures to perform T1, $T2^*$, inversion recovery UTE (IR-UTE) $T2^*$ measurements, and two-pool magnetization transfer (MT) modeling. Results: Single-component $T2^*$, $IR-T2^*$, short and long component $T2^*s$ from bi-component analysis, and T1 showed significantly higher values while the noted macromolecular fraction (MMF) from MT modeling showed significantly lower values at body temperature, as compared with room temperature. However, it is noted that the short component fraction (Frac1) showed higher values at body temperature. Conclusion: This study highlights the need for careful consideration of the temperature effects on MRI measurements, before extending a conclusion from ex vivo studies on cortical bone specimens to clinical in vivo studies. It is noted that the increased relaxation times at higher temperature was most likely due to an increased molecular motion. The T1 increase for the studied human bone specimens was noted as being significantly higher than the previously reported values for bovine cortical bone. The prevailing discipline notes that the increased relaxation times of the bound water likely resulted in a lower signal loss during data acquisition, which led to the incidence of a higher Frac1 at body temperature.

• 대한수학회논문집
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• 제35권1호
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• pp.301-319
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• 2020

In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ₀ where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.

• 한국수산과학회지
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• 제8권4호
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• pp.197-201
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• 1975

다랭이 주낚의 양승방식에는 방향의 양승(On-tracing retrieve)방식과 역방향의 양승(Back-tracing retrieve) 방식의 두가지 방식이 있다. 순방향의 양승은 최초에 투승된 주낙끝에서부터 양승하기 시작하여 투승한 순과 같은 순으로 양승하는 것이고 역방향의 양승은 최후에 투승된 주낚끝에서부터 양승하기 시작하며 투승한 순과 반대순으로 양승하는 것이다. 주낚의 조업소요시간을 변갱하지 않고 양승방식만 변갱한다면 주낚의 평균침지시간은 변하지 않고 다만 침지시간의 분포구간만 변한다. 투승작업시간을 $\tau_1$, 투승작업이 끝나고 양승작업을 시작하기까지의 대기시간을 $\tau_2$, 양승작업시간을 $\tau_3$하면 주낚의 침지시간분포범위는 양승방식에 따라 다음과 같이 서로 다르다. $\tau_2$부터 $\tau_1+\tau_2+\tau_3$까지의 범위 역방향으로 양승할 때 $\tau_1+\tau_2$부터 $\tau_2+\tau_3$까지의 범위 임의시의 낚시 어획성능은 $F_0\varrho-^{-zt}$ ($F_0$는 초기어획성능, z는 감소계수, t는 투승후 경과시간)으로 나타낼 수 있고 침지시간 t인 낚시 Hro의 어획미수는 $H_{F_0}\frac{1-\varrho^{-zt}}{z}$로 나타낼 수 있으므로 주낙조업에서 낚시수 $H_G$개 이고 침지시간이 $\tau_\alpha$와 $\tau_\beta$ 범위내에서 분포하면 어획미수는 $C_G$는 다음과 같이 나타낼 수 있다. $$C_G=\frac{H_G}{\tau_\beta-\tau_\alpha}{\cdot}\frac{F_0}{Z}\int^{\tau_\beta}_{\tau_\alpha}(1-\varrho^{-zt})dt$$ $\tau_\alpha,\;\tau_\beta$의 값은 순방향의 양승에 있어서는 $\tau_\alpha=\tau_1+\tau_2,\;\tau_\beta=\tau_2+\tau_3$, 역방향은 양승에 있어서는 $\tau_\alpha=\tau_2,\;\tau_\beta=\tau_1+\tau_2+\tau_3$. 따라서 다랭이 주낚의 어획미수는 그 양승방식에 따라 차가 있고 순방향의 양승으로 더 많은 어획미수를 얻을 수 있다.

• 대한수학회보
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• 제54권4호
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• pp.1195-1219
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• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.