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STABILITY OF HAHN DIFFERENCE EQUATIONS IN BANACH ALGEBRAS

  • Abdelkhaliq, Marwa M.;Hamza, Alaa E.
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1141-1158
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    • 2018
  • Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

THE KÄHLER DIFFERENT OF A SET OF POINTS IN ℙm × ℙn

  • Hoa, Nguyen T.;Linh, Tran N.K.;Long, Le N.;Nhan, Phan T.T.;Nhi, Nguyen T.P.
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.4
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    • pp.929-949
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    • 2022
  • Given an ACM set 𝕏 of points in a multiprojective space ℙm×ℙn over a field of characteristic zero, we are interested in studying the Kähler different and the Cayley-Bacharach property for 𝕏. In ℙ1×ℙ1, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the Kähler different. However, this result fails to hold in ℙm×ℙn for n > 1 or m > 1. In this paper we start an investigation of the Kähler different and its Hilbert function and then prove that 𝕏 is a complete intersection of type (d1, …, dm, d'1, …, d'n) if and only if it has the Cayley-Bacharach property and the Kähler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of 𝕏 under certain assumptions.

Entire Functions and Their Derivatives Share Two Finite Sets

  • Meng, Chao;Hu, Pei-Chu
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.473-481
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    • 2009
  • In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

A Case of Peripheral Neuropathy after Acupuncture (의인성(醫因性) 말초신경병증(末梢神經病症) 치험(治驗) 1례(例))

  • Lee, Kyung-Min;Seo, Jung-Chul;Lim, Seong-Chul;Jung, Tae-Young;Han, Sang-Won
    • Korean Journal of Acupuncture
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    • v.21 no.3
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    • pp.137-146
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    • 2004
  • Objective : The purpose of this study is to report the patient with peripheral neuropathy, who improved by Oriental medical treatment. Methods : The patient was managed by acupuncture, moxibustion, physical treatment and herbal medicine. We checked digital infrared thermographic imaging(D.I.T.I.), electromyography(E.M.G.), nerve conduction velocity(N.C.V.), deep tendon reflex(D.T.R.), sensory recover area and range of motion(R.O.M.) of knee & ankle. Results : After 6 week treatment, clinical sign(the movement and sense of leg) of improvement was appeared. Also E.M.G., N.C.V., D.T.R. and D.I.T.I. was recovered to nearly normal range. Conclusion : The results suggest that combination of acupunture, moxibustion and herbal medicine is good method for treatment of peripheral neuropathy. But further studies may be required to concretely prove the effectiveness of this methods for treating peripheral neuropathy.

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T Cells Development Is Different between Thymus from Normal and Intrauterine Growth Restricted Pig Fetus at Different Gestational Stage

  • Lin, Yan;Wang, Junjun;Wang, Xiaoqiu;Wu, Weizong;Lai, Changhua
    • Asian-Australasian Journal of Animal Sciences
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    • v.26 no.3
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    • pp.343-348
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    • 2013
  • This experiment was conducted to evaluate the development of T cells in intrauterine growth retarded (IUGR) piglets at different gestational stages, and tentatively explore the relationship between T cells development and the Notch signaling pathway. A total of 18 crossbred (Landrace${\times}$Large white) primiparous sows were mated at similar weights and estruses and euthanized at d 60, 90 and 110 of gestation with six replicates for each time point. One IUGR and one normal fetus were picked from each litter. The T-cell subsets, mRNA expression of Delta-like1, Delta-like4, Jagged1, and Notch2 genes in the thymus were investigated. Compared to normal piglets, $CD3^+CD4^-CD8^+$ cells in IUGR fetuses at d 90 was 0.13% lower (p<0.05). At d 110 of gestation $CD8^+$ T cells in IUGR fetuses was 0.19% lower (p<0.05). The percentage of $CD8^+$ T cells was 3.14% lower (p<0.05) of the total T cells in IUGR pigs at d 60. The abundance of Notch2 and Delta-like4 mRNA at d 110 was 20.93% higher and 0.77% (p<0.05) lower, and Delta-like1 mRNA at d 90 was 0.19% (p<0.05) higher compared to normal pigs. These results suggested that normal fetuses had a greater proportion of T-cell subsets at earlier gestation periods, and the Notch signaling pathway was likely partially responsible for these differences to some degree.

Reevaluation of the Neonatal Screening Test for Congenital Hypothyroidism (선천성 갑상선기능저하증에 대한 신생아 선별검사의 재평가)

  • Kang, So Young;Chang, Young Pyo;Yu, Jeesuk
    • Clinical and Experimental Pediatrics
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    • v.48 no.4
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    • pp.387-394
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    • 2005
  • Purpose : We performed this study to compare the TSH and free $T_4$ levels according to gestational age and birth weight, and to reevaluate the cut-off values in the neonatal screening test for congenital hypothyroidism. Methods : Total 2,133 neonates(1,749 healthy newborns and 384 sick neonates) were screened in Dankook University Hospital from May 2000 to January 2003. Neonates with abnormal TSH values (higher than $20{\mu}IU/mL$) or abnormal free $T_4$ levels(lower than 1 ng/dL) were recalled to recheck the thyroid function test. At that time, physical examinations and history-taking regarding perinatal problem, medication history, and mother's illness were undertaken. Results : Serum TSH and free $T_4$ values revealed no significant difference according to sex, delivery type, and Apgar score. The free $T_4$ levels showed statistically significant differences, with gestational age or birth weight(P<0.01). The recall rate of neonates due to abnormal screening test was 7.48 percent. Compared with original cut-off values, the recall rate of the new cut-off values setted to TSH higher than $20{\mu}IU/mL$ or free $T_4$ lower than 0.64 ng/dL decreased from 7.48 percent to 4.8 percent in the healthy group. But, it compromised sensitivity when applied to the sick group. Conclusion : In this study, neonatal free $T_4$ levels were significantly different according to birth weight, gestational age, and the presence of compromised condition. Although the recall rate by TSH > $20{\mu}IU/mL$ or free $T_4$ <1 ng/dL was relatively high, it was impossible to set up new cut-off values without compromising sensitivity. We think studies including a larger study population will be required to change the cut-off values.

Applications and Strategies on Defense Acquisition based CPS & IoT Technology (사이버물리시스템(CPS)과 사물인터넷(loT) 기술의 군사적 활용방안 및 추진전략)

  • Kye, J.E.;Park, P.J.;Kim, W.T.;Lim, C.D.
    • Electronics and Telecommunications Trends
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    • v.30 no.4
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    • pp.92-101
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    • 2015
  • 미래 전장은 정보 지식 기반의 첨단 전력체계를 확충하기 위해 향후 전력구조를 통합, 지휘통제통신(C4I) 체계와 생존성과 통합성이 향상된 전장의 네트워크중심전(NCW) 수행능력을 향상시킬 것이다. 사이버물리시스템(Cyber-Physical Systems: CPS)은 함정전투체계에 적용되고 있는 DDS를 포함하여 국방 M&S의 근간인 Live, Virture, Constructive(L-V-C) 체계의 큰 축을 형성하고 있다. 사물인터넷(Internet of Things: IoT) 기술은 센서네트워크, 통신, Radio Frequency Identification(RFID), Ubiquitous Sensor Network(USN), Machine to Machine(M2M), D2D 기술 및 상황인지, 지능서비스를 위한 정보수집/가공/융합/분석/예측기술을 포괄적으로 포함한 기술로서 미래산업을 이끌어 갈 차세대 선도 기술이며, 특히 군사적으로도 감시정찰 센서네트워크(USN), 견마형로봇, 경전투로봇과 무인기 기술 및 전술정보통신망체계(TICN) 등 첨단 통신네트워크 기술의 전력화 추세는 IoT 기술의 적용영역을 넓혀주고 있다. 감시정찰체계(Sensor)에서는 감시정찰 분야 영상정보 처리, 표적탐지 등과 관련된 IoT 기술 소요와 지휘통제통신(C4I) 체계의 상호운용성, 데이터링크, 지능형 통신체계 등 C4I 관련 IoT 기술 소요 및 타격체계(Shooter)의 내장형 SW 등 유 무인 무기체계 관련 IoT 기술의 소요가 증대될 것으로 예상된다. 본고는 CPS 및 IoT 기술의 군사적 활용방안 및 획득전략에 대한 적용기술 및 발전방향을 살펴본다.

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1,25-dihydroxyvitamin D3 affects thapsigargin-induced endoplasmic reticulum stress in 3T3-L1 adipocytes

  • Dain Wi;Chan Yoon Park
    • Nutrition Research and Practice
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    • v.18 no.1
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    • pp.1-18
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    • 2024
  • BACKGROUND/OBJECTIVES: Endoplasmic reticulum (ER) stress in adipose tissue causes an inflammatory response and leads to metabolic diseases. However, the association between vitamin D and adipose ER stress remains poorly understood. In this study, we investigated whether 1,25-dihydroxyvitamin D3 (1,25(OH)2D3) alleviates ER stress in adipocytes. MATERIALS/METHODS: 3T3-L1 cells were treated with different concentrations (i.e., 10-100 nM) of 1,25(OH)2D3 after or during differentiation (i.e., on day 0-7, 3-7, or 7). They were then incubated with thapsigargin (TG, 500 nM) for an additional 24 h to induce ER stress. Next, we measured the mRNA and protein levels of genes involved in unfold protein response (UPR) and adipogenesis using real-time polymerase chain reaction and western blotting and quantified the secreted protein levels of pro-inflammatory cytokines. Finally, the mRNA levels of UPR pathway genes were measured in adipocytes transfected with siRNA-targeting Vdr. RESULTS: Treatment with 1,25(OH)2D3 during various stages of adipocyte differentiation significantly inhibited ER stress induced by TG. In fully differentiated 3T3-L1 adipocytes, 1,25(OH)2D3 treatment suppressed mRNA levels of Ddit3, sXbp1, and Atf4 and decreased the secretion of monocyte chemoattractant protein-1, interleukin-6, and tumor necrosis factor-α. However, downregulation of the mRNA levels of Ddit3, sXbp1, and Atf4 following 1,25(OH)2D3 administration was not observed in Vdr-knockdown adipocytes. In addition, exposure of 3T3-L1 preadipocytes to 1,25(OH)2D3 inhibited transcription of Ddit3, sXbp1, Atf4, Bip, and Atf6 and reduced the p-alpha subunit of translation initiation factor 2 (eIF2α)/eIF2α and p-protein kinase RNA-like ER kinase (PERK)/PERK protein ratios. Furthermore, 1,25(OH)2D3 treatment before adipocyte differentiation reduced adipogenesis and the mRNA levels of adipogenic genes. CONCLUSIONS: Our data suggest that 1,25(OH)2D3 prevents TG-induced ER stress and inflammatory responses in mature adipocytes by downregulating UPR signaling via binding with Vdr. In addition, the inhibition of adipogenesis by vitamin D may contribute to the reduction of ER stress in adipocytes.

A study on the flume for a current meter rating (유속계 검정용수로에 관한 연구)

  • 정준석;박정응
    • Water for future
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    • v.6 no.2
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    • pp.30-37
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    • 1973
  • The coefficient of the current meter generally determined by the maker Its coefficient is subject to being changed with time. Therefore the coefficient of the current meter has to be checked up before it is ready to be used Such an inspection is termed a current meter rating The current meter equipped an electronic apparatus and all the others are to be rated in a rating flume. The price current meter which is most widely used for measuring flow velocities ranging between 0.3m/sec and 3.5m/sec has been used in this study. The length of the flume and the optimum range of the rating in the cross section are determined in the range of 20∼120cm deep, 50∼160cm wide of the flume. In this study, the 23 different kinds of the current meter rating enabled us to determine the constants a and b of the following equation. V=an+b(m/sec) where, n is number of revolution per second(n=N/T) V is velocity(v=D/T) The above constant can be determined by the least squares method and plotting, using the velocity(V=D/T) and the number of revolution per second(n=N/T) obtained from the running distance(D), time(T), the number of revolutin(N), and the running number(m). From the experiments the following conclusions are drawn: 1) The rating flume is large enough if the flume is 110∼120cm deep, and 40∼50m long. 2) The optimum depth for rating of a current meter is in the range of h=40∼50cm.

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