• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.725-743
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• 2022

In this paper, the concepts of ω-linked homomorphisms, the ω_𝜙-operation, and DW_𝜙 rings are introduced. Also the relationships between ω_𝜙-ideals and ω-ideals over a ω-linked homomorphism 𝜙 : R → T are discussed. More precisely, it is shown that every ω_𝜙-ideal of T is a ω-ideal of T. Besides, it is shown that if T is not a DW_𝜙 ring, then T must have an infinite number of maximal ω_𝜙-ideals. Finally we give an application of Cohen's Theorem over ω-factor rings, namely it is shown that an integral domain R is an SM-domain with ω-dim(R) ≤ 1, if and only if for any nonzero ω-ideal I of R, (R/I)_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, (R/(a))_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, R satisfies the descending chain condition on ω-ideals of R containing a.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.173-181
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• 1995

Our objective is to investigate approximate controllability of a class of partial integrodifferential systems. This work continuous the investigations of [8]. As a model for this class one may take the equation $\frac{\partialy(t,\;\xi)}{\partialt}\;=\;\frac{\partial}{\partial\xi}(a(t,\;\xi\frac{\partialy(t,\;\xi)}{\partial\xi})\;+\;F(t,\;y(t\;-\;r,\;\xi),\;{{\int_0}^t}\;k(t,\;s,\;y(s\;-\;r,\;\xi))ds)\;+\;b(\xi)u(t),\;0\;\leq\;\xi\;\leq\;1,\;\leq\;t\;\leq\;T$ with initial-boundary conditions y(t,\;0)\;=\;y(t,\;1)\;=\;0,\;0\;\leq\;t\;\leq\;T,\;y(t,\;\xi)\;=\;\phi(t,\;\xi),\;0\;\leq\;1,\;-r\;\leq\;t\;\leq\;0$.(omitted)

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.521-530
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• 2000

We find the values of numerical invariants col(R) and row (R) for R=k[te, te+1, t(e-1)e-1] where k is a field and e$\geq$4. We also show that col(R) = crs (R) and row (R) = drs(R), but they are strictly less than the reduction number of R plus 1.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.9 no.1
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• pp.1-18
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• 1973

For regulating the depth of midwater trawl nets towed at the optimum constant speed, the changes in the shape of warps caused by adding a weight on an arbitrary point of the warp of catenary shape is studied. The shape of a warp may be approximated by a catenary. The resultant inferences under this assumption were experimented. Accordingly feasibilities for the application of the result of this study to the midwater trawl nets were also discussed. A series of experiments for basic midwater trawl gear models in water tank and a couple of experiments of a commercial scale gears at sea which involve the properly designed depth control devices having a variable attitude horizontal wing were carried out. The results are summarized as follows: 1. According to the dimension analysis the depth y of a midwater trawl net is introduced by $$y=kLf(\frac{W_r}{R_r},\;\frac{W_o}{R_o},\;\frac{W_n}{R_n})$$) where k is a constant, L the warp length, f the function, and $W_r,\;W_o$ and $W_n$ the apparent weights of warp, otter board and the net, respectively, 2. When a boat is towing a body of apparent weight $W_n$ and its drag $D_n$ by means of a warp whose length L and apparent weight $W_r$ per unit length, the depth y of the body is given by the following equation, provided that the shape of a warp is a catenary and drag of the warp is neglected in comparison with the drag of the body: $$y=\frac{1}{W_r}\{\sqrt{{D_n^2}+{(W_n+W_rL)^2}}-\sqrt{{D_n^2+W_n}^2\}$$ 3. The changes ${\Delta}y$ of the depth of the midwater trawl net caused by changing the warp length or adding a weight ${\Delta}W_n$_n to the net, are given by the following equations: $${\Delta}y{\approx}\frac{W_n+W_{r}L}{\sqrt{D_n^2+(W_n+W_{r}L)^2}}{\Delta}L$$ $${\Delta}y{\approx}\frac{1}{W_r}\{\frac{W_n+W_rL}{\sqrt{D_n^2+(W_n+W_{r}L)^2}}-{\frac{W_n}{\sqrt{D_n^2+W_n^2}}\}{\Delta}W_n$$ 4. A change ${\Delta}y$ of the depth of the midwater trawl net by adding a weight $W_s$ to an arbitrary point of the warp takes an equation of the form $${\Delta}y=\frac{1}{W_r}\{(T_{ur}'-T_{ur})-T_u'-T_u)\}$$ Where $$T_{ur}^l=\sqrt{T_u^2+(W_s+W_{r}L)^2+2T_u(W_s+W_{r}L)sin{\theta}_u$$ $$T_{ur}=\sqrt{T_u^2+(W_{r}L)^2+2T_uW_{r}L\;sin{\theta}_u$$ $$T_{u}^l=\sqrt{T_u^2+W_s^2+2T_uW_{s}\;sin{\theta}_u$$ and $T_u$ represents the tension at the point on the warp, ${\theta}_u$ the angle between the direction of $T_u$ and horizontal axis, $T_u^2$ the tension at that point when a weights $W_s$ adds to the point where $T_u$ is acted on. 5. If otter boards were constructed lighter and adequate weights were added at their bottom to stabilize them, even they were the same shapes as those of bottom trawls, they were definitely applicable to the midwater trawl gears as the result of the experiments. 6. As the results of water tank tests the relationship between net height of H cm velocity of v m/sec, and that between hydrodynamic resistance of R kg and the velocity of a model net as shown in figure 6 are respectively given by $$H=8+\frac{10}{0.4+v}$$ $$R=3+9v^2$$ 7. It was found that the cross-wing type depth control devices were more stable in operation than that of the H-wing type as the results of the experiments at sea. 8. The hydrodynamic resistance of the net gear in midwater trawling is so large, and regarded as nearly the drag, that sweeping depth of the gear was very stable in spite of types of the depth control devices. 9. An area of the horizontal wing of the H-wing type depth control device was $1.2{\times}2.4m^2$. A midwater trawl net of 2 ton hydrodynamic resistance was connected to the devices and towed with the velocity of 2.3 kts. Under these conditions the depth change of about 20m of the trawl net was obtained by controlling an angle or attack of $30^{\circ}$.

• Journal of Veterinary Clinics
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• v.16 no.2
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• pp.332-338
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• 1999

This study was carried out to investigate weight gain and prevention of diarrhea in suckling calves which were injected with recombinant bovine somatopropin (rBST). A total of 101 breeding cows were assigned to the six groups according to the administered dosage and injected time, respectively. Groups T-1, T-3, T-4 and T-6 were injected starting 1 week before calving and groups T-2 and T-5 were injected on the calving day. The six groups were injected five times at two week intervals. Groups T-1 and T-2 were injected with 250mg composite rBST, Group T-3 was injected with 375 mg composite rBST. Groups T-4 and T-5 were injected with 500mg composite rBST, And group T-6 was injected with 500mg rBST-S. The control group was not injected with BST. The groups injected with 500 mg BrST had a lower rate of morbidity from diarrhea than the control group or the groups injected with 250 mg rBST (T-1 and T-2). Weight gain was higher in group T-4 than in the control group or groups T-1 and T-2. In Korean Native Cattle, the total weight gain was greater in group T-4 than in the control group (p<0.05). In crossbred cows, total weight gain was the highest in group T-4, and the total weight gain rate was greater than in group T-4 and the control group (p<0.05). The results of the hematological values showed that injections of rBST did not affect the level of the RBC, TP and BUN in the breeding cows at 9 weeks after postpartum or the neonatal calves. The results of this study indicate that injecting breeding cows with 500 mg rBST before calving would be effective in the preventing of diarrhea and in increasing weight gain of calves from birth to weaning.

• Journal of the Korean Ceramic Society
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• v.18 no.2
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• pp.119-125
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• 1981

The thermostable resistor was made by using P.T.C.R-N.T.C.R. ceramics. In this study $BaTiO_3$ type P.T.C.R. ceramics and $SnO_2-Sb_2O_3$ type N.T.C.R. ceramics were cocrystallized in one body and electrical resistance was stable under the temperature variation between $25^{\circ}C$-40$0^{\circ}C$. The ceramics showed the most stable electrical resistance for the mal variation when the composition was 0.6P.T.C.R. $BaTiO_3$,$ 0.4SnO_2$ and 0.01 $Sb_2O_3$.

• Korean Journal of Microbiology
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• v.48 no.3
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• pp.180-186
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• 2012

Pseudomonas aeruginosa, a Gram-negative bacterium, is an ubiquitous and opportunistic human pathogen, which expresses many virulence factors through quorum sensing (QS) regulation. QscR, one of the QS signal receptors of P. aeruginosa, has unique features that make it possible to distinguish QscR from other QS receptors. In the present study, we focused on amino acid residues responsible for such a broad signal specificity of QscR. Thus we constructed mutant QscRs: $QscR_{T72I}$, $QscR_{R132M}$, and $QscR_{T140I}$ by substituting $72^{nd}$ threonine, $132^{nd}$ arginine, and $140^{th}$ threonine residues with isoleucine, methionine, and isoleucine, respectively by site-directed mutagenesis. When we examined the activity of these mutant QscRs, $QscR_{R132M}$ failed to respond to N-3-oxododecanoyl homoserine lactone (3OC12-HSL), but $QscR_{T72I}$ and $QscR_{T140I}$ remained the ability to respond to 3OC12-HSL despite much reduction of the sensitivity. When we treated a variety of acyl-HSLs with different structure, $QscR_{T72I}$ and $QscR_{T140I}$ showed better responsiveness to N-decanoyl HSL (C10-HSL) or N-dodecanoyl HSL (C12-HSL) that has no oxo-moiety at $3^{rd}$ carbon of acyl group than to 3OC12-HSL, and $QscR_{R132M}$ showed no responsiveness to any acyl-HSLs tested here. In addition, $QscR_{T72I}$ and $QscR_{T140I}$ were inhibited by 5f, a QscR inhibitor as similarly as wild type QscR was. These results suggest that while the $130^{th}$ arginine is crucial in both activity and acyl-HSL binding of QscR, the $72^{nd}$ and $140^{th}$ threonines are important in the activity, but they are little responsible for the discrimination of acyl-HSLs or competitive inhibitor.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.455-466
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• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.