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A TIME-INDEPENDENT CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • Honam Mathematical Journal
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    • v.35 no.2
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    • pp.179-200
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    • 2013
  • Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.

CONDITIONAL INTEGRAL TRANSFORMS OF FUNCTIONALS ON A FUNCTION SPACE OF TWO VARIABLES

  • Bong Jin, Kim
    • Korean Journal of Mathematics
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    • v.30 no.4
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    • pp.593-601
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    • 2022
  • Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τm,n = {(si, tj)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s0 < s1 < . . . < sm = S and 0 = t0 < t1 < . . . < tn = T, define a random vector Xτ : C(Q) → ℝmn by Xτ (x) = (x(s1, t1), . . . , x(sm, tn)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function Xτ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

Effects of Taraxacum mongolicum Extract on Blood Glucose Levels and Lipid Profiles in Streptozotocin-Induced Diabetic Rats

  • Hye Kyoung Han;Eun Young Choi
    • The Korean Journal of Food And Nutrition
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    • v.36 no.1
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    • pp.50-57
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    • 2023
  • This study was designed to evaluate antihyperglycemic and antihyperlipidemic effects of ethanol extracts of Taraxacum mongolicum(T.m.) on streptozotocin (STZ)-induced diabetic rats. Sprague-Dawley rats were randomly assigned to five groups: normal (NC), STZ-control (DC), and three experimental groups. Diabetes was induced in Sprague-Dawley rats with a single intravenous injection [45 mg/kg body weight (b.w.)] of STZ. An ethanol extract of T.m. was orally given to diabetic rats for 14 days. Three experimental groups were additionally treated with T.m. extract at doses of 1 g/kg b.w./day for T.m.-1, 2 g/kg b.w./day for T.m.-2, and 3 g/kg b.w./day for T.m.-3. Oral administration of T.m.-2 significantly increased their body weights. T.m.-1 and T.m.-2 significantly decreased aspartate aminotransferase (AST) levels than DC. T.m.-1 and T.m.-2 group significantly decreased blood glucose levels. Total cholesterol, triglycerides, and free fatty acids were significantly decreased whereas high-density lipoprotein cholesterol was significantly increased in groups treated with T.m. extract than those in the DC group. These results support the fact that administration of T.m. extract can reduce hyperglycemia and hyperlipidemia risk in diabetic rats.

A Study on Changes of Serum $fT_3\;and\;rT_3$ Concentration in Nonthyroidal Critical Illness (비갑상선 중증 질환에서 혈청 $fT_3$$rT_3$의 변화에 관한 연구)

  • Lee, Jong-Wha;Kim, Ju-Ock;Yu, Cheol-Jae;Moon, Youn-Sung;Shin, Young-Tae;Ro, Heung-Kyu
    • The Korean Journal of Nuclear Medicine
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    • v.19 no.1
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    • pp.103-111
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    • 1985
  • Recently changes in thyroid physiology during acute and chronic medical illness were demonstrated. The serum $fT_3,\;rT_3,\;T_4,\;T_3,\;fT_4$, and TSH concentration were measured by radioimmunoassay method in 49 patients with critical illness and 10 normal subjects to assess the change of thyroid function in critical illness. The results were as follows; 1) The mean serum $fT_3$ concentration was $6.68{\pm}1.05pmol/ml$ in normal subjects while in patients with critical illness the serum $fT_3$ concentration was significantly lowered to $1.55{\pm}1.15pmol/ml$(p<0.001). 2) The mean serum $rT_3$ concentration was $0.22{\pm}0.44ng/ml$ in normal subjects and $0.42{\pm}0.37ng/ml$ in patient with critical illness. There was increment in critically ill patients as compared to normal subjects but no statistically significant difference(p>0.05). 3) The mean serum $T_3$ concentration was $1.24{\pm}0.25ng/ml$ in normal subjects and $0.56{\pm}0.56ng/ml$ in patients with criticial illness and there was significant difference in each other(p<0.005). 4) The mean serum $T_4,\;fT_4$, and TSH concentrations were $7.80{\pm}1.02{\mu}g/dl,\;1.26{\pm}0.39ng/dl,\;1.87{\pm}0.45{\mu}U/ml$ in normal subjects respectively and $6.02{\pm}3.06{\mu}g/dl,\;1.46{\pm}0.80ng/dl,\;1.74{\pm}0.79{\mu}U/ml$ in patients with critical illness and there was no significant difference between critically ill patients and normal subjects. 5) The ratio of mean serum concentration of $fT_3$ and $rT_3(fT_3/rT_3)$, $30.42{\pm}5.58$ in normal subjects was significantly higher(p<0.005) than the coresponding patients with critical illness. 6) The mean serum $fT_3$ concentration in expired cases(n=12) during admission was significant difference between expired and survived cases(p<0.005). The mean serum $rT_3$ centration was $0.67{\pm}0.58ng/ml$ in expired cases and $0.34{\pm}0.22ng/ml$ in survived cases with significant difference(p<0.005). Half of the cases who showed less than $3{\mu}g/dl$ of serum $T_4$ level were expired.

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INTERVAL OSCILLATION CRITERIA FOR A SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

  • Zhang, Cun-Hua
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1165-1176
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    • 2009
  • This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

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APPROXIMATE IDENTITY OF CONVOLUTION BANACH ALGEBRAS

  • Han, Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.4
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    • pp.497-504
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    • 2020
  • A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.

Effects of Reed (Phragmites communis) on Growth Performance, Carcass Characteristics, and Meat Quality in Hanwoo Steers (갈대 급여가 한우 거세우의 발육, 도체 및 육질특성에 미치는 영향)

  • Lee, Sang Min;Chang, Sun Sik;Chung, Ki Yong;Kim, Hyeong Cheol;Choi, Sun Ho;Jeong, Ha Yeon;Yang, Boh Suk;Lee, Sung Sill;Cho, Young Moo
    • Journal of Life Science
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    • v.22 no.10
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    • pp.1392-1398
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    • 2012
  • This study investigated the effects of diet of different forages on growth performance and carcass characteristics of Hanwoo steers. Twenty-one Hanwoo steers were randomly allocated to three groups (fed hay, reed, and reed with rice straw) of seven steers each. Initial and final body weights of control, T1, and T2 groups were 125.5, 128.3, 128.3 kg and 697.4, 614.6, 706.7 kg, respectively. Average daily gain tended to increase in controls (0.70 kg/d) and the T2 group (0.71 kg/d) but not as much in the T1 group (0.60 kg/d); however, there was no significant difference. DMI was not significantly different among the treatment groups, but T1 was relatively lower than the other groups. For the yield traits, carcass weight was not significantly different between controls and the T2 group but was greater in the T2 group compared to the T1 group (p<0.05). Back fat thickness and rib eye area were higher in controls and T2 compared to T1; yield grade (A:B:C, %) was greater in T1 (43:57:0) compared to the other groups (control 0:71:29; T2 29:42:29). For the quality traits, fat color and texture were not significantly different among groups. However, meat color and maturity were significantly greater in T1 compared to T2 (p<0.05). Marbling score and appearance rate of over 1st meat quality grade were greater in the control and T2 groups compared to the T1 group. Based on the results, growth performance, feed utilization, and carcass traits appeared to improve when roughage containing rice straw plus reed was offered. Therefore, reed is worth considering as a roughage source for fattening Hanwoo steers.

The Effects of Preoperative Sprayed 10% Lidocaine on the Hemodynamic Response during Suspension Microlaryngeal Surgery (술 전 분무한 10% lidocaine이 현미경 하의 후두 미세 수술 시 혈역학적 반응에 미치는 영향)

  • Lee, Deok-Hee;Do, Hyun-Seok
    • Journal of Yeungnam Medical Science
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    • v.24 no.2
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    • pp.162-169
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    • 2007
  • Purpose : It is well known that suspension microlaryngeal surgery produces marked increases in arterial blood pressure and heart rate. In this study, we evaluated the effects of 10% lidocaine preoperatively sprayed for attenuation of the perioperative hemodynamic response during suspension microlaryngeal surgery. Materials and Methods : Fifty American Society of Anesthesiologists (ASA) class 1 patients scheduled for excision of a vocal polyp by suspension laryngoscopy were randomly divided into two groups (n=25 for each group). They were intubated without 10% lidocaine spray (control group) or given 1.5 mg/kg of 10% lidocaine sprayed onto the pharyngolaryngeal and intratracheal sites 90 sec prior to intubation (10% lidocaine group). Anesthesia was maintained using desflurane in $O_2/N_2O$ 50%. The arterial blood pressure and heart rate were measured at preinduction (T0), 1 min (T1), 3 min (T2), 5 min (T3) after tracheal intubation, and 1 min (T4), 3 min (T5), 5 min (T6) and 10 min (T7) after the suspension laryngoscopy. Results : In the 10% lidocaine group, the arterial blood pressure and heart rate at 1 (T1), 3 (T2) min after tracheal intubation and 1 (T4), and 3 (T5) min after suspension laryngoscopy were lower than the same measurements in the control group. Conclusion : 10% lidocaine sprayed onto the pharyngolaryngeal and intratracheal sites before intubation was an effective method for attenuation of the perioperative hemodynamic response during suspension microlaryngeal surgery.

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Effects of Total Mixed Fermentations with Spent Mushroom (Flammuliua velutipes) and Wet Brewer's Grain on Growth Performance, Feed Intake and Nutrient Digestibility in Korean Black Goats (버섯폐배지와 맥주박 첨가 섬유질발효사료 급여가 흑염소의 생산성, 사료섭취량 및 영양소 소화율에 미치는 영향)

  • Hwangbo, Soon
    • Journal of The Korean Society of Grassland and Forage Science
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    • v.34 no.1
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    • pp.45-51
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    • 2014
  • This study was conducted to investigate the feeding effects of total mixed fermentations (TMF) with spent mushroom (Flammuliua velutipes) and wet brewer's grain on estimating the productivity and nutrient utilization of Korean black goats. Four experimental groups were set up with each of the 5 animals for a 30-day feeding trial on growth performance. 12 black goats with regard to nutrient digestibility were allocated to 4 groups of 3 animals each by a latin-square design control group (offered concentrate and rice straw) and 3 treatment groups (TMF with 15% spent mushroom and 25% wet brewer's grain (T1), 10, 30% (T2) and 5, 35% (T3)). The average daily gain (ADG) of the control and T1 treatment groups was higher than that of the T3 treatment group (p<0.05). Dry matter (DM) and organic matter (OM) intake (kg/head) for T1 and T2 treatment groups were significantly higher than those of the control group (p<0.05). The digestibility of DM and OM for the control group (62.39~63.39%) and the T1 treatment group (65.02~65.25%) were significantly higher than those of the T3 treatment group (56.39, 59.01%) (p<0.05). Further, nitrogen retention was significantly higher in the T1 treatment group (p<0.05). Thus, these results conveyed that productivity and nutrient utilization were similar between TMF with spent mushroom and wet brewer's grain and commercial feeds. However, this study also suggested that feed must contain 25~30% spent mushroom due to the fact that the productivity of Korean black goats was decreased by increasing the content of spent mushroom.

Reliability of Stereotactic Coordinates of 1.5-Tesla and 3-Tesla MRI in Radiosurgery and Functional Neurosurgery

  • Kim, Hae Yu;Lee, Sun-Il;Jin, Seong Jin;Jin, Sung-Chul;Kim, Jung Soo;Jeon, Kyoung Dong
    • Journal of Korean Neurosurgical Society
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    • v.55 no.3
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    • pp.136-141
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    • 2014
  • Objective : The aims of this study are to identify interpersonal differences in defining coordinates and to figure out the degree of distortion of the MRI and compare the accuracy between CT, 1.5-tesla (T) and 3.0T MRI. Methods : We compared coordinates in the CT images defined by 2 neurosurgeons. We also calculated the errors of 1.5T MRI and those of 3.0T. We compared the errors of the 1.5T with those of the 3.0T. In addition, we compared the errors in each sequence and in each axis. Results : The mean difference in the CT images between the two neurosurgeons was $0.48{\pm}0.22mm$. The mean errors of the 1.5T were $1.55{\pm}0.48mm$ (T1), $0.75{\pm}0.38$ (T2), and $1.07{\pm}0.57$ (FLAIR) and those of the 3.0T were $2.35{\pm}0.53$ (T1), $2.18{\pm}0.76$ (T2), and $2.16{\pm}0.77$ (FLAIR). The smallest mean errors out of all the axes were in the x axis : 0.28-0.34 (1.5T) and 0.31-0.52 (3.0T). The smallest errors out of all the MRI sequences were in the T2 : 0.29-0.58 (1.5T) and 0.31-1.85 (3.0T). Conclusion : There was no interpersonal difference in running the Gamma $Plan^{(R)}$ to define coordinates. The errors of the 3.0T were greater than those of the 1.5T, and these errors were not of an acceptable level. The x coordinate error was the smallest and the z coordinate error was the greatest regardless of the MRI sequence. The T2 sequence was the most accurate sequence.