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HIGHER DERIVATIVE VERSIONS ON THEOREMS OF S. BERNSTEIN

  • Singh, Thangjam Birkramjit;Devi, Khangembam Babina;Reingachan, N.;Soraisam, Robinson;Chanam, Barchand
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.2
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    • pp.323-329
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    • 2022
  • Let $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ be a polynomial of degree n and $p^{\prime}(z)$ its derivative. If $\max\limits_{{\mid}z{\mid}=r}{\mid}p(z){\mid}$ is denoted by M(p, r). If p(z) has all its zeros on |z| = k, k ≤ 1, then it was shown by Govil [3] that $$M(p^{\prime},\;1){\leq}\frac{n}{k^n+k^{n-1}}M(p,\;1)$$. In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

VANISHING PROPERTIES OF p-HARMONIC ℓ-FORMS ON RIEMANNIAN MANIFOLDS

  • Nguyen, Thac Dung;Pham, Trong Tien
    • Journal of the Korean Mathematical Society
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    • v.55 no.5
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    • pp.1103-1129
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    • 2018
  • In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

New large-update primal interior point algorithms based on kernel functions for LCPs

  • Kim, Min-Kyung;Cho, Gyeong-Mi
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.4
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    • pp.69-88
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    • 2007
  • In this paper we propose new large-update primal-dual interior point algorithms for $P_{\neq}({\kappa})$ linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on a specific class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{t^{-q}-1}{q}}$, q>0, $p{\in}[0,\;1]$, which are the generalized form of the ones in [3] and [12]. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*({\kappa})$LCPs. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*({\kappa})$ LCPs have the best known complexity $O((1+2{\kappa}){\sqrt{2n}}(log2n)log{\frac{n}{\varepsilon}})$ when p=1 and $q=\frac{1}{2}(log2n)-1$.

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Fabrication and Characterization of Lateral p-i-n photodiodes and design of stub mounted optically controlled phase shifter (수평형 p-i-n 광다이오드의 제작, 특성 측정 및 광제어 스터브 장착 위상기의 설계)

  • 한승엽;정상구
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.32A no.1
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    • pp.89-96
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    • 1995
  • Lateral p-i-n photodiodes have been fabricated, electrically tested, and incorporated into microwave control circuits such as an optically excited microwave atttenuator and reflection type phase shifter. Circuit design procedures for the loaded-line phase shifter with the optically controlled p-i-n photodiode are presented. The equal loss loading mode presented for the first time for the phase shifter circuits with lossy load allows an equal insertion loss of the phase shifter in both of its phase states. It is found that the insertion loss of the equal loss loading mode phase shifter constructed with the fabricated p-i-n photodiode load are about 3dB for 11.25$^{\circ}$ bit and 1dB for 5.625$^{\circ}$ bit for the frequency range of 2GHz to 11GHz.

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A VLSI Array Processor Architecture for High-Speed Processing of Full Search Block Matching Algorithm (완전탐색 블럭정합 알고리즘의 고속 처리를 위한 VLSI 어레이 프로세서의 구조)

  • 이수진;우종호
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.27 no.4A
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    • pp.364-370
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    • 2002
  • In this paper, we propose a VLSI array architecture for high speed processing of FBMA. First of all, the sequential FBMA is transformed into a single assignment code by using the index space expansion, and then the dependance graph is obtained from it. The two dimensional VLSI array is derived by projecting the dependance graph along the optimal direction. Since the candidate blocks in the search range are overlapped with columns as well as rows, the processing elements of the VLSI array are designed to reuse the overlapped data. As the results, the number of data inputs is reduced so that the processing performance is improved. The proposed VLSI array has (N$^2$+1)${\times}$(2p+1) processing elements and (N+2p) input ports where N is the block size and p is the maximum search range. The computation time of the rat reference block is (N$^2$+2(p+1)N+6p), and the block pipeline period is (3N+4p-1).

The influence of the implant-abutment complex on marginal bone and peri-implant conditions: A retrospective study

  • Tokgoz, Selen Ergin;Bilhan, Hakan
    • The Journal of Advanced Prosthodontics
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    • v.13 no.1
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    • pp.46-54
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    • 2021
  • Purpose. The design of the implant-abutment complex is thought to be responsible for marginal bone loss (MBL) and might affect the condition of the peri-implant tissues. This the present study aimed to evaluate the influence of the implant-abutment complex on MBL and the peri-implant tissues in partially edentulous patients treated with dental implants and determine the most advantageous design. Materials and Methods. A total of ninety-one endosseous implants with different designs of implant-abutment complex [tissue level-TL (n = 30), platform switch-PS (n = 18), and platform match-PM (n = 43)] were reviewed for MBL, Probing Pocket Depth (PPD) and Bleeding on Probing (BoP). MBL was calculated for first year of the insertion and the following years. Results. The median MBL for the PM implants (2.66 ± 1.67 mm; n = 43) in the first year was significantly higher than those for the other types (P=.033). The lowest rate of MBL (0.61 ± 0.44 mm; n = 18) was observed with PS implants (P=.000). The position of the crown-abutment border showed a statistically significant influence (P=.019) and a negative correlation (r=-0.395) on MBL. BoP was found significantly higher in PM implants (P=.006). The lowest BoP scores were detected in PS implants, but the difference was not significant (P=.523). The relation between PPD and connection type revealed no statistically significant influence (P>.05). Conclusion. Within the limitations of the present study, it may be concluded that PS implants seem to show better peri-implant soft tissue conditions and cause less MBL.

Comparison of Cognitive Controls in Patients with Bipolar I Disorder and Their Unaffected First-Degree Relatives (양극성 I형 장애 환자와 발병하지 않은 일차 친족에서 인지조절의 비교)

  • Yun, Hyerim;Woo, Seonjin;Lee, Sang-Won;Jin, Bo-Hyun;Woo, Jungmin;Won, Seunghee
    • Korean Journal of Biological Psychiatry
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    • v.25 no.1
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    • pp.9-15
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    • 2018
  • Objectives This study intended to identify the deficits of cognitive control among patients with bipolar I disorder and their first-degree relatives, and identify the possibility of cognitive control as an endophenotype of bipolar disorder. Methods The study included three groups: euthymic states patients with bipolar I disorder (n = 55), unaffected first-degree relatives of probands with bipolar I disorder (n = 30), and a healthy control group (n = 51), that was matched on age, sex, and years of education. The AX version of the continuous performance test (CPT) was used to examine cognitive control. Error rate, correct response times of each subsets (AX, BX, AY, BY), and d' as an indication of accuracy sensitivity index were calculated. Psychopathology, intelligence, and psychomotor speed were also assessed. Results Patients with bipolar I disorder showed significantly worse error rates in the AX (p = 0.01) and BX (p = 0.02) subsets and d' (p = 0.05) than the others. They also showed more delayed correct response times than the healthy control group and first-degree relatives in all subsets (p < 0.01). But first-degree relatives showed neither high error rates nor delayed correct response times than healthy control group. Conclusions These findings suggest that cognitive control is impaired in bipolar I disorder but less likely to be an endophynotype of bipolar I disorder.

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Runoff Characteristics of Non-point Pollutants Source in Suwon City (수원시 비점오염물질의 유출 특성)

  • Chi, Hong-Jin;Lee, Sang-Eun;Lee, Jae-Dong
    • Journal of Environmental Science International
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    • v.22 no.4
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    • pp.493-505
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    • 2013
  • This study was to investigate the runoff characteristics of non-point pollutants source at the urban area in Suwon city. The highest T-N and T-P concentration of rainfall runoff observed in agricultural area. In residential area, the highest $BOD_5$ and SS concentration of rainfall runoff was investigated. During rainfall events, the peak concentrations of SS and $BOD_5$ were observed after 1~2 hours of rainfall in urban area. Whereas, the peak concentrations occurred within 1~2 hours after rainfall and then the highest concentrations of SS and $BOD_5$ sharply decreased, showing strong first flush effect in urban area. The EMC results indicated that the highest value of T-N and T-P in agricultural area was observed. While residential area was shown the lowest EMC value as T-N and T-P. Non-point pollutant loads on the land use types in urban area were investigated in the order of residential>industrial>agricultural>highway. $BOD_5$ and SS loads on urban watershed were investigated in the order of Suwon>Hwangguji>Seoho>Wonchunri. Whereas, T-N and T-P loads on urban watershed were investigated in the order of Hwangguji>Suwon>Wonchunri>Seho.

The Effects of n-6/n-3 and P/S Ratio of Dietary Lipid on Lipid Metabolism of Rats at Different Age (n-6/n-3 비율과 P/S 비율을 변화시킨 식이지방이 나이가 다른 흰쥐의 체내 지방대사에 미치는 영향)

  • 김숙희
    • Journal of Nutrition and Health
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    • v.27 no.7
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    • pp.687-698
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    • 1994
  • The effects of age and dietary fatty acid composition on lipid metabolism were investigated in Sprague-Dawley strain male rats. These animals weighing 88.6$\pm$2.2g were fed 10% dietary fat(W/W, 20% of total energy) with 0.5, 1, 2 P/S ratio and in each P/S ratio there were three different levels of n-6/n-3 fatty acid ratio ; 2, 4, 8. The experimental period was 1 month, 6 months and 12 months. The results of this study were as follows. The body weight of rats increased rapidly for the first two months, then increased slowly until 7 to 8 months. After 10 months of dietary regimen their weight decreased. The weight of liver, kidney and epidydimal fat pad increased along with the body weight and then decreased in the 12 months. Plasma total lipid increased with age and it decreased significantly when P/S ratio of dietary fatty acid was high. In creased with age and it decreased significantly when P/S ratio of dietary fatty acid was high. In creasing n-3 fatty acid intake in each P/S ratio resulted in lower plasma total lipid although was not statistically significant. The amount of plasma total cholesterol increased at 6 months, but decreased at 12 months. In case of 1, 12 months, increasing P/S ratio significantly plasma total cholesterol and LDL-cholesterol were decreased and hepatic cholesterol was increased, VLDL-HDL-cholesterol did not changed. The n-6/n-3 ratio did not affect any of theses. The amount of plasma triglyceride and VLDL-triglyceride increased at 6 month then decreased. When the rats consumed higher amount of n-3 fatty acid in each P/S ratio, their plasma triglyceride and hepatic triglyceride increased at 1, 12months.

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